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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Accumulated Amortization</link:label>
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    <link:label id="lab_us-gaap_InvestmentPolicyTextBlock_019bffd7-5158-77cd-93ed-75203900f7a0_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:label id="lab_us-gaap_InvestmentPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentPolicyTextBlock"/>
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    <link:label id="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt and Equity Securities, FV-NI [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock_019bffd7-5158-7ae1-8fc9-3ae16551ae57_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Debt Securities, Available-for-Sale</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealizedInvestmentGainsLosses_019bffd7-5158-721d-835b-0bc59c7a22e8_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RealizedInvestmentGainsLosses" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net realized (gains) losses on investments</link:label>
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    <link:label id="lab_us-gaap_RealizedInvestmentGainsLosses_label_en-US" xlink:label="lab_us-gaap_RealizedInvestmentGainsLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Realized Investment Gains (Losses)</link:label>
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    <link:label id="lab_us-gaap_ChangeDuringPeriodFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_ChangeDuringPeriodFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changes Measurement [Member]</link:label>
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    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined</link:label>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_label_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined [Flag]</link:label>
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    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearThree_019bffd7-515a-72f8-a90b-c8f09e780740_terseLabel_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearThree_label_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense, Year Three</link:label>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearThree_documentation_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense, Year Three</link:label>
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    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis_019bffd7-5159-7fc5-b9cd-a0642e9ea8f0_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets [Axis]</link:label>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis_label_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets [Axis]</link:label>
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    <link:label id="lab_logan_MortgageAndCorporateLoansSegmentMember_019bffd7-5158-7e77-9079-baa9dc9b4c34_terseLabel_en-US" xlink:label="lab_logan_MortgageAndCorporateLoansSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total mortgage and corporate loans</link:label>
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    <link:label id="lab_logan_MortgageAndCorporateLoansSegmentMember_documentation_en-US" xlink:label="lab_logan_MortgageAndCorporateLoansSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage And Corporate Loans Segment</link:label>
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    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_019bffd7-5157-7eff-a228-25d3ef28b7c1_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
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    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_019bffd7-5158-7dfe-abf0-e8a40cd6d7f0_verboseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Recently adopted accounting pronouncements and Recently issued accounting pronouncements</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs_019bffd7-5159-738d-ac6e-4242b8fd6381_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Charge-offs</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs" xlink:to="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_019bffd7-5159-7c1a-8bc6-e7d857c5901a_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, by Balance Sheet Grouping</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByBalanceSheetGroupingTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesMember_019bffd7-5158-767a-ae38-b44163aa2c96_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt securities</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesMember" xlink:to="lab_us-gaap_DebtSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_OtherGovernmentAndAgencyMember_019bffd7-5158-7bee-98ed-c8206f72e199_terseLabel_en-US" xlink:label="lab_logan_OtherGovernmentAndAgencyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other government and agency</link:label>
    <link:label id="lab_logan_OtherGovernmentAndAgencyMember_label_en-US" xlink:label="lab_logan_OtherGovernmentAndAgencyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Government And Agency [Member]</link:label>
    <link:label id="lab_logan_OtherGovernmentAndAgencyMember_documentation_en-US" xlink:label="lab_logan_OtherGovernmentAndAgencyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Government And Agency</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_OtherGovernmentAndAgencyMember" xlink:href="logan-20251231.xsd#logan_OtherGovernmentAndAgencyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_OtherGovernmentAndAgencyMember" xlink:to="lab_logan_OtherGovernmentAndAgencyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillLineItems_019bffd7-5159-7402-b602-eaf68560e763_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Line Items]</link:label>
    <link:label id="lab_us-gaap_GoodwillLineItems_label_en-US" xlink:label="lab_us-gaap_GoodwillLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillLineItems" xlink:to="lab_us-gaap_GoodwillLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InvestmentRiskDomain_019bffd7-5158-7179-b99f-ee946e66d56b_terseLabel_en-US" xlink:label="lab_logan_InvestmentRiskDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Risk [Domain]</link:label>
    <link:label id="lab_logan_InvestmentRiskDomain_label_en-US" xlink:label="lab_logan_InvestmentRiskDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Risk [Domain]</link:label>
    <link:label id="lab_logan_InvestmentRiskDomain_documentation_en-US" xlink:label="lab_logan_InvestmentRiskDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Risk [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InvestmentRiskDomain" xlink:href="logan-20251231.xsd#logan_InvestmentRiskDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InvestmentRiskDomain" xlink:to="lab_logan_InvestmentRiskDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_019bffd7-5158-7083-b498-31d5833c6b42_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:to="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToCompAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAxis" xlink:to="lab_ecd_AdjToCompAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_019bffd7-515b-7448-a04a-e1e16ffc4d1c_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related parties</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_label_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NamedExecutiveOfficersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:to="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_GeneralAdministrativeAndOtherExpensesAdjusted_019bffd7-515b-7d72-87bb-056ac3369253_negatedTerseLabel_en-US" xlink:label="lab_logan_GeneralAdministrativeAndOtherExpensesAdjusted" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">General, administrative and other</link:label>
    <link:label id="lab_logan_GeneralAdministrativeAndOtherExpensesAdjusted_label_en-US" xlink:label="lab_logan_GeneralAdministrativeAndOtherExpensesAdjusted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General, Administrative And Other Expenses, Adjusted</link:label>
    <link:label id="lab_logan_GeneralAdministrativeAndOtherExpensesAdjusted_documentation_en-US" xlink:label="lab_logan_GeneralAdministrativeAndOtherExpensesAdjusted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">General, Administrative And Other Expenses, Adjusted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_GeneralAdministrativeAndOtherExpensesAdjusted" xlink:href="logan-20251231.xsd#logan_GeneralAdministrativeAndOtherExpensesAdjusted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_GeneralAdministrativeAndOtherExpensesAdjusted" xlink:to="lab_logan_GeneralAdministrativeAndOtherExpensesAdjusted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_019bffd7-5159-765e-a640-7554b2e6b82a_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue from service contracts</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain_019bffd7-5158-7f57-ba08-caa2d322abf5_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable Portfolio Segment [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable Portfolio Segment [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablePortfolioSegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:to="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_019bffd7-515a-7885-b887-fee69d08a4ec_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable" xlink:to="lab_us-gaap_ScheduleOfStockByClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1_019bffd7-5159-7ec9-87cc-7457e1c45e53_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Option, Changes in Fair Value, Gain (Loss)</link:label>
    <link:label id="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1_label_en-US" xlink:label="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Option, Changes in Fair Value, Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOptionChangesInFairValueGainLoss1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOptionChangesInFairValueGainLoss1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueOptionChangesInFairValueGainLoss1" xlink:to="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_TermLoanMember_019bffd7-5159-784c-8f4b-7a97cd378038_terseLabel_en-US" xlink:label="lab_logan_TermLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term Loan</link:label>
    <link:label id="lab_logan_TermLoanMember_label_en-US" xlink:label="lab_logan_TermLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Term Loan [Member]</link:label>
    <link:label id="lab_logan_TermLoanMember_documentation_en-US" xlink:label="lab_logan_TermLoanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Term Loan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_TermLoanMember" xlink:href="logan-20251231.xsd#logan_TermLoanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_TermLoanMember" xlink:to="lab_logan_TermLoanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTable_019bffd7-5159-7caa-a1cb-f0b212c683a4_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Indefinite-Lived [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Indefinite-Lived [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTable" xlink:to="lab_us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceRollForward_019bffd7-515a-77dd-b4c2-0219bed27c53_terseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceRollForward_label_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderAccountBalanceRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderAccountBalanceRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyholderAccountBalanceRollForward" xlink:to="lab_us-gaap_PolicyholderAccountBalanceRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumInterestIncome_019bffd7-515a-7f53-81fc-6ee0d64318db_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumInterestIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest accrual</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumInterestIncome_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumInterestIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Net Premium, Interest Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumInterestIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumInterestIncome"/>
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    <link:label id="lab_logan_RepaymentsOfBorrowingsOfAssetManagementBusiness_019bffd7-5158-7974-a52a-5693b5c620c2_negatedTerseLabel_en-US" xlink:label="lab_logan_RepaymentsOfBorrowingsOfAssetManagementBusiness" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repayments of borrowings of asset management business</link:label>
    <link:label id="lab_logan_RepaymentsOfBorrowingsOfAssetManagementBusiness_label_en-US" xlink:label="lab_logan_RepaymentsOfBorrowingsOfAssetManagementBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments Of Borrowings Of Asset Management Business</link:label>
    <link:label id="lab_logan_RepaymentsOfBorrowingsOfAssetManagementBusiness_documentation_en-US" xlink:label="lab_logan_RepaymentsOfBorrowingsOfAssetManagementBusiness" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Repayments Of Borrowings Of Asset Management Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_RepaymentsOfBorrowingsOfAssetManagementBusiness" xlink:href="logan-20251231.xsd#logan_RepaymentsOfBorrowingsOfAssetManagementBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_RepaymentsOfBorrowingsOfAssetManagementBusiness" xlink:to="lab_logan_RepaymentsOfBorrowingsOfAssetManagementBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefit_019bffd7-515a-7293-a117-6ff00ce39350_totalLabel_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current tax</link:label>
    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationPriorYearIncomeTaxes_019c8fbc-a778-7035-9415-b2bac2260f0e_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationPriorYearIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred True Up</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationPriorYearIncomeTaxes_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationPriorYearIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Prior Year Income Taxes, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationPriorYearIncomeTaxes" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationPriorYearIncomeTaxes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationPriorYearIncomeTaxes" xlink:to="lab_us-gaap_IncomeTaxReconciliationPriorYearIncomeTaxes" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_019bffd7-515b-73d8-b701-75e6fffa42cf_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">% of total</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskPercentage1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskPercentage1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskPercentage1" xlink:to="lab_us-gaap_ConcentrationRiskPercentage1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_019bffd7-5158-7310-8ee3-e9fc2a38c8c8_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherOperatingAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitExpectedNetPremiumIncreaseDecreaseOfActualVarianceFromExpectedExperience_019bffd7-515a-7fad-9eae-5b889daa9455_terseLabel_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitExpectedNetPremiumIncreaseDecreaseOfActualVarianceFromExpectedExperience" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of actual variances from expected experience</link:label>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitExpectedNetPremiumIncreaseDecreaseOfActualVarianceFromExpectedExperience_label_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitExpectedNetPremiumIncreaseDecreaseOfActualVarianceFromExpectedExperience" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Net Premium, Increase (Decrease) of Actual Variance from Expected Experience</link:label>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitExpectedNetPremiumIncreaseDecreaseOfActualVarianceFromExpectedExperience_documentation_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitExpectedNetPremiumIncreaseDecreaseOfActualVarianceFromExpectedExperience" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Net Premium, Increase (Decrease) of Actual Variance from Expected Experience</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_LiabilityForFuturePolicyBenefitExpectedNetPremiumIncreaseDecreaseOfActualVarianceFromExpectedExperience" xlink:href="logan-20251231.xsd#logan_LiabilityForFuturePolicyBenefitExpectedNetPremiumIncreaseDecreaseOfActualVarianceFromExpectedExperience"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_LiabilityForFuturePolicyBenefitExpectedNetPremiumIncreaseDecreaseOfActualVarianceFromExpectedExperience" xlink:to="lab_logan_LiabilityForFuturePolicyBenefitExpectedNetPremiumIncreaseDecreaseOfActualVarianceFromExpectedExperience" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_019bffd7-5158-7c2b-805c-7bd622d34b77_verboseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_019bffd7-5158-7ca0-a861-ee8637e97fdb_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity based compensation</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_IncentiveFeeIncomeMember_019bffd7-5157-7781-a2b1-903def6a8148_terseLabel_en-US" xlink:label="lab_logan_IncentiveFeeIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Incentive fees</link:label>
    <link:label id="lab_logan_IncentiveFeeIncomeMember_label_en-US" xlink:label="lab_logan_IncentiveFeeIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incentive Fee Income [Member]</link:label>
    <link:label id="lab_logan_IncentiveFeeIncomeMember_documentation_en-US" xlink:label="lab_logan_IncentiveFeeIncomeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Incentive Fee Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_IncentiveFeeIncomeMember" xlink:href="logan-20251231.xsd#logan_IncentiveFeeIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_IncentiveFeeIncomeMember" xlink:to="lab_logan_IncentiveFeeIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidTaxes_019bffd7-515a-79da-8d6a-9c9002ea68ea_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidTaxes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid income taxes</link:label>
    <link:label id="lab_us-gaap_PrepaidTaxes_label_en-US" xlink:label="lab_us-gaap_PrepaidTaxes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Taxes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidTaxes" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrepaidTaxes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidTaxes" xlink:to="lab_us-gaap_PrepaidTaxes" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesReceivableNet_019bffd7-5158-7640-a6b3-10372b8a5870_totalLabel_en-US" xlink:label="lab_us-gaap_NotesReceivableNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Financing receivable, net</link:label>
    <link:label id="lab_us-gaap_NotesReceivableNet_label_en-US" xlink:label="lab_us-gaap_NotesReceivableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesReceivableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NotesReceivableNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesReceivableNet" xlink:to="lab_us-gaap_NotesReceivableNet" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DeferredTaxAssetsDeferredAcquisitionCosts_019bffd7-515a-74f2-83dd-ff693a26b700_terseLabel_en-US" xlink:label="lab_logan_DeferredTaxAssetsDeferredAcquisitionCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred acquisition costs</link:label>
    <link:label id="lab_logan_DeferredTaxAssetsDeferredAcquisitionCosts_label_en-US" xlink:label="lab_logan_DeferredTaxAssetsDeferredAcquisitionCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Deferred Acquisition Costs</link:label>
    <link:label id="lab_logan_DeferredTaxAssetsDeferredAcquisitionCosts_documentation_en-US" xlink:label="lab_logan_DeferredTaxAssetsDeferredAcquisitionCosts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Deferred Acquisition Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DeferredTaxAssetsDeferredAcquisitionCosts" xlink:href="logan-20251231.xsd#logan_DeferredTaxAssetsDeferredAcquisitionCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DeferredTaxAssetsDeferredAcquisitionCosts" xlink:to="lab_logan_DeferredTaxAssetsDeferredAcquisitionCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract_019c7c0a-500e-7e36-869e-302234bf4c50_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Percent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_019bffd7-515b-7ace-a172-20ec8af73235_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractualRightsMember_019bffd7-5159-7602-85a3-86c1333950b3_terseLabel_en-US" xlink:label="lab_us-gaap_ContractualRightsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment management contracts</link:label>
    <link:label id="lab_us-gaap_ContractualRightsMember_label_en-US" xlink:label="lab_us-gaap_ContractualRightsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractual Rights [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractualRightsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractualRightsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractualRightsMember" xlink:to="lab_us-gaap_ContractualRightsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_019bffd7-5157-73ba-877d-bc2155ac143c_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019bffd7-5157-7b27-a8dd-4b548759c14e_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019bffd7-5157-77ed-8c99-671abd38c3fc_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_NY_019c7c1d-d183-70c5-9c5f-48164c721018_terseLabel_en-US" xlink:label="lab_stpr_NY" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NY State</link:label>
    <link:label id="lab_stpr_NY_label_en-US" xlink:label="lab_stpr_NY" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">NEW YORK</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_NY" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_NY"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_NY" xlink:to="lab_stpr_NY" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_019bffd7-5157-7291-9498-3786a9b45bd2_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract_019bffd7-5159-789e-b406-56cf1e221e38_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial assets</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments, Financial Assets, Balance Sheet Groupings [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:to="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StateAndLocalJurisdictionMember_019c8250-6ff9-7567-9697-b13af70f7ce0_terseLabel_en-US" xlink:label="lab_us-gaap_StateAndLocalJurisdictionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State and Local Jurisdiction [Member]</link:label>
    <link:label id="lab_us-gaap_StateAndLocalJurisdictionMember_label_en-US" xlink:label="lab_us-gaap_StateAndLocalJurisdictionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">State and Local Jurisdiction [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StateAndLocalJurisdictionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StateAndLocalJurisdictionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StateAndLocalJurisdictionMember" xlink:to="lab_us-gaap_StateAndLocalJurisdictionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableOtherCurrentAndNoncurrent_019bffd7-5157-7eb6-8404-82a96558eed8_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableOtherCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due to related parties</link:label>
    <link:label id="lab_us-gaap_AccountsPayableOtherCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableOtherCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable, Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableOtherCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableOtherCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableOtherCurrentAndNoncurrent" xlink:to="lab_us-gaap_AccountsPayableOtherCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_019bffd7-5158-73cc-adec-37142e897ef8_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_019bffd7-5158-7b9c-a132-b53c4ab1631b_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MaximumMember" xlink:to="lab_srt_MaximumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AociLiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeTax_019bffd7-515a-7d1e-962e-75c216a5ef32_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AociLiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Effect of changes in discount rate assumptions</link:label>
    <link:label id="lab_us-gaap_AociLiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeTax_label_en-US" xlink:label="lab_us-gaap_AociLiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI, Liability for Future Policy Benefit, Expected Future Policy Benefit, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AociLiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AociLiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AociLiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeTax" xlink:to="lab_us-gaap_AociLiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_019bffd7-5159-7701-9040-f66db8f08fae_totalLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition_019bffd7-5158-7c0c-8601-2478ee5e7348_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Loss Position</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract_019bffd7-515a-7460-92f7-2fc332349132_terseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Policyholder Benefits and Claims Incurred, Net [Abstract]</link:label>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract_label_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Benefits and Claims Incurred, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract" xlink:to="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost_019bffd7-5158-7a1e-a161-22fbf6a63013_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_019bffd7-5159-76e6-8831-172a2ea40a9c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019bffd7-515a-7ff1-8676-86588e21e0e0_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
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    <link:label id="lab_us-gaap_ConcentrationRiskDisclosureTextBlock_019bffd7-515b-7732-b4e0-0372db4f12f6_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration of Risks</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:to="lab_us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
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    <link:label id="lab_us-gaap_DebtLongtermAndShorttermCombinedAmount_019bffd7-5157-77bc-84af-308ac60023f4_terseLabel_en-US" xlink:label="lab_us-gaap_DebtLongtermAndShorttermCombinedAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt obligations</link:label>
    <link:label id="lab_us-gaap_DebtLongtermAndShorttermCombinedAmount_label_en-US" xlink:label="lab_us-gaap_DebtLongtermAndShorttermCombinedAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Long-Term and Short-Term, Combined Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtLongtermAndShorttermCombinedAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtLongtermAndShorttermCombinedAmount"/>
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    <link:label id="lab_us-gaap_DirectPremiumsEarned_019bffd7-515a-7a6c-ad83-17cfb6384580_terseLabel_en-US" xlink:label="lab_us-gaap_DirectPremiumsEarned" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Direct premiums</link:label>
    <link:label id="lab_us-gaap_DirectPremiumsEarned_label_en-US" xlink:label="lab_us-gaap_DirectPremiumsEarned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct Premiums Earned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DirectPremiumsEarned" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DirectPremiumsEarned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DirectPremiumsEarned" xlink:to="lab_us-gaap_DirectPremiumsEarned" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PayableInvestmentPurchase_019bffd7-515a-70e3-af55-01464d4509a5_terseLabel_en-US" xlink:label="lab_us-gaap_PayableInvestmentPurchase" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payable for investments purchased</link:label>
    <link:label id="lab_us-gaap_PayableInvestmentPurchase_label_en-US" xlink:label="lab_us-gaap_PayableInvestmentPurchase" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payable, Investment, Purchase</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PayableInvestmentPurchase" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PayableInvestmentPurchase"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PayableInvestmentPurchase" xlink:to="lab_us-gaap_PayableInvestmentPurchase" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019bffd7-5157-728c-bcf5-a90fd0f8ce03_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income (loss) before taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019bffd7-515a-710d-8c3a-85661415872b_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income (loss) before taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019c47f6-61da-75fd-89ab-12a1091dd1a2_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fee and Spread related earnings</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_019c2cc2-970d-7fe0-9d6a-6c1e38ae01c0_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTable_019bffd7-5159-76af-9789-e0c546cfbb66_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitAfterReinsurance_019bffd7-515a-7b26-bdc7-a5005ebc2902_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitAfterReinsurance" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total future policy benefits</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitAfterReinsurance_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitAfterReinsurance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, after Reinsurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitAfterReinsurance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitAfterReinsurance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitAfterReinsurance" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitAfterReinsurance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
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    <link:label id="lab_us-gaap_OperatingSegmentsMember_019bffd7-515b-77ee-be90-68e41d914d52_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Segments</link:label>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_label_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Segments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingSegmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingSegmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingSegmentsMember" xlink:to="lab_us-gaap_OperatingSegmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock_019c7c16-8fb1-73d9-a5c7-1c5df6d8e7fb_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Income Taxes Paid</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Cash Flow, Supplemental Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock"/>
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    <link:label id="lab_logan_IncreaseDecreaseFundsHeldUnderReinsuranceAgreementsLiability_019bffd7-5158-7c33-8555-16c0d7c31dc1_terseLabel_en-US" xlink:label="lab_logan_IncreaseDecreaseFundsHeldUnderReinsuranceAgreementsLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Funds held under reinsurance contracts</link:label>
    <link:label id="lab_logan_IncreaseDecreaseFundsHeldUnderReinsuranceAgreementsLiability_label_en-US" xlink:label="lab_logan_IncreaseDecreaseFundsHeldUnderReinsuranceAgreementsLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) Funds Held Under Reinsurance Agreements, Liability</link:label>
    <link:label id="lab_logan_IncreaseDecreaseFundsHeldUnderReinsuranceAgreementsLiability_documentation_en-US" xlink:label="lab_logan_IncreaseDecreaseFundsHeldUnderReinsuranceAgreementsLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (Decrease) Funds Held Under Reinsurance Agreements, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_IncreaseDecreaseFundsHeldUnderReinsuranceAgreementsLiability" xlink:href="logan-20251231.xsd#logan_IncreaseDecreaseFundsHeldUnderReinsuranceAgreementsLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_IncreaseDecreaseFundsHeldUnderReinsuranceAgreementsLiability" xlink:to="lab_logan_IncreaseDecreaseFundsHeldUnderReinsuranceAgreementsLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_MortgageLoansMember_019bffd7-5158-7aa1-8b6a-2ee669868d93_terseLabel_en-US" xlink:label="lab_logan_MortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage loans</link:label>
    <link:label id="lab_logan_MortgageLoansMember_label_en-US" xlink:label="lab_logan_MortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans [Member]</link:label>
    <link:label id="lab_logan_MortgageLoansMember_documentation_en-US" xlink:label="lab_logan_MortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_MortgageLoansMember" xlink:href="logan-20251231.xsd#logan_MortgageLoansMember"/>
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    <link:label id="lab_us-gaap_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossOci_019bffd7-5159-7c24-80ee-5ffd4754a596_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossOci" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in unrealized gains (losses) included in OCI on Level 3 assets and liabilities still held</link:label>
    <link:label id="lab_us-gaap_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossOci_label_en-US" xlink:label="lab_us-gaap_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossOci" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Asset, Recurring Basis, Still Held, Unrealized Gain (Loss), OCI</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossOci" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossOci"/>
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    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
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    <link:label id="lab_us-gaap_InterestExpenseOperating_019bffd7-5157-7682-862d-09a2b49128ce_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseOperating_019bffd7-515b-72c9-8d63-a1c4a14efc09_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseOperating_label_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseOperating" xlink:to="lab_us-gaap_InterestExpenseOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic_019bffd7-515a-7848-b54f-ad4f5179a1d4_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">United States</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Domestic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic"/>
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    <link:label id="lab_stpr_TX_019c7c1d-d183-7c8f-ad22-3cd3306dd4bc_terseLabel_en-US" xlink:label="lab_stpr_TX" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Texas</link:label>
    <link:label id="lab_stpr_TX_label_en-US" xlink:label="lab_stpr_TX" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">TEXAS</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_TX" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_TX"/>
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    <link:label id="lab_logan_DebentureUnitsMember_019bffd7-5159-7959-9b77-474868acf0ad_terseLabel_en-US" xlink:label="lab_logan_DebentureUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debenture Units</link:label>
    <link:label id="lab_logan_DebentureUnitsMember_label_en-US" xlink:label="lab_logan_DebentureUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debenture Units [Member]</link:label>
    <link:label id="lab_logan_DebentureUnitsMember_documentation_en-US" xlink:label="lab_logan_DebentureUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debenture Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DebentureUnitsMember" xlink:href="logan-20251231.xsd#logan_DebentureUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DebentureUnitsMember" xlink:to="lab_logan_DebentureUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_019c46d4-89c1-7a8d-b381-e4b4d63da1f5_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitPeriodIncreaseDecrease_019bffd7-515a-739f-ac08-e6f8ca366ab3_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitPeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase in liability for future policy benefits</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitPeriodIncreaseDecrease_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitPeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Future Policy Benefit, Period Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitPeriodIncreaseDecrease" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitPeriodIncreaseDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitPeriodIncreaseDecrease" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitPeriodIncreaseDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTextBlock_019bffd7-5159-7191-8514-4094666c7168_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Net Gains on Financial Instruments For Which Fair Value Option Was Elected</link:label>
    <link:label id="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Option, Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOptionQuantitativeDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOptionQuantitativeDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueOptionQuantitativeDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputRevenueMultipleMember_019bffd7-5159-7d1c-a0b4-fd7413fd5803_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputRevenueMultipleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Enterprise Value, Multiple</link:label>
    <link:label id="lab_us-gaap_MeasurementInputRevenueMultipleMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputRevenueMultipleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Revenue Multiple [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputRevenueMultipleMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputRevenueMultipleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputRevenueMultipleMember" xlink:to="lab_us-gaap_MeasurementInputRevenueMultipleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_019bffd7-5158-7e05-bb32-7b6f4259a689_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedTranslationAdjustmentMember_019bffd7-515a-7738-b8de-3afeb06bc75e_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cumulative translation adjustment</link:label>
    <link:label id="lab_us-gaap_AccumulatedTranslationAdjustmentMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Foreign Currency Adjustment Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedTranslationAdjustmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:to="lab_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingRelationshipDomain_019bffd7-5159-72ac-bffe-86e9ea194dc0_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingRelationshipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Domain]</link:label>
    <link:label id="lab_us-gaap_HedgingRelationshipDomain_label_en-US" xlink:label="lab_us-gaap_HedgingRelationshipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingRelationshipDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HedgingRelationshipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingRelationshipDomain" xlink:to="lab_us-gaap_HedgingRelationshipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDividendsPayableTextBlock_019bffd7-515a-727a-935e-264cb5a617bd_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Declared on Common Shares</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDividendsPayableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Dividends Payable [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDividendsPayableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDeferredPolicyAcquisitionCosts_019bffd7-5158-766e-8b7b-f172b490eef7_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDeferredPolicyAcquisitionCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in deferred acquisition costs</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDeferredPolicyAcquisitionCosts_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDeferredPolicyAcquisitionCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Deferred Policy Acquisition Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInDeferredPolicyAcquisitionCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInDeferredPolicyAcquisitionCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInDeferredPolicyAcquisitionCosts" xlink:to="lab_us-gaap_IncreaseDecreaseInDeferredPolicyAcquisitionCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_019bffd7-5158-706d-8c9b-bd5c84b8c001_terseLabel_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_label_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_EquityMethodInvesteeNameDomain" xlink:to="lab_srt_EquityMethodInvesteeNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_AbilityAcquisitionSellerNoteMember_019bffd7-5159-784a-8235-3d8fc5001c94_terseLabel_en-US" xlink:label="lab_logan_AbilityAcquisitionSellerNoteMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Seller note &#8212; Ability Acquisition</link:label>
    <link:label id="lab_logan_AbilityAcquisitionSellerNoteMember_label_en-US" xlink:label="lab_logan_AbilityAcquisitionSellerNoteMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ability Acquisition Seller Note [Member]</link:label>
    <link:label id="lab_logan_AbilityAcquisitionSellerNoteMember_documentation_en-US" xlink:label="lab_logan_AbilityAcquisitionSellerNoteMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Ability Acquisition Seller Note</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_AbilityAcquisitionSellerNoteMember" xlink:href="logan-20251231.xsd#logan_AbilityAcquisitionSellerNoteMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_AbilityAcquisitionSellerNoteMember" xlink:to="lab_logan_AbilityAcquisitionSellerNoteMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_019c2cbe-ce19-7e27-9ffc-63b6cf99826a_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationsPolicy_019bffd7-5158-754a-a1af-19c22fd68957_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business combinations</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationsPolicy_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationsPolicy" xlink:to="lab_us-gaap_BusinessCombinationsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ServicingFeesExpenses_019bffd7-5159-7bdf-a9ba-36a1b7845546_terseLabel_en-US" xlink:label="lab_logan_ServicingFeesExpenses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing fees</link:label>
    <link:label id="lab_logan_ServicingFeesExpenses_label_en-US" xlink:label="lab_logan_ServicingFeesExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Fees (Expenses)</link:label>
    <link:label id="lab_logan_ServicingFeesExpenses_documentation_en-US" xlink:label="lab_logan_ServicingFeesExpenses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Servicing Fees (Expenses)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ServicingFeesExpenses" xlink:href="logan-20251231.xsd#logan_ServicingFeesExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ServicingFeesExpenses" xlink:to="lab_logan_ServicingFeesExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance_019c7c0b-a191-78d4-bd4d-0804663499a5_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax assets not recognized (valuation allowance)</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross_019bffd7-515a-7673-a9c6-8685932b83a9_terseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Policyholder Benefits and Claims Incurred, Direct</link:label>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross_label_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Benefits and Claims Incurred, Direct</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderBenefitsAndClaimsIncurredGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross" xlink:to="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_019bffd7-5157-7e3e-ac88-5640357a1987_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity based compensation (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Shares, Share-Based Payment Arrangement, after Forfeiture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities_019bffd7-5157-7fae-bb8c-7eaf5823bc16_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other liabilities</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities_019bffd7-515a-723b-8a93-5b76d02bc01e_totalLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other liabilities</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities_label_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Liabilities and Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedLiabilitiesAndOtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:to="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_019c2cbb-a0da-7a2d-a771-e436e57f41b1_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortTermDebtTypeDomain_019bffd7-5158-7048-a757-78ab6a13ebad_terseLabel_en-US" xlink:label="lab_us-gaap_ShortTermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ShortTermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_ShortTermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortTermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermDebtTypeDomain" xlink:to="lab_us-gaap_ShortTermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_YearsToCashFlowsMember_019bffd7-5159-7488-8644-bff07af98e99_terseLabel_en-US" xlink:label="lab_logan_YearsToCashFlowsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Years To Cash Flows</link:label>
    <link:label id="lab_logan_YearsToCashFlowsMember_label_en-US" xlink:label="lab_logan_YearsToCashFlowsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Years To Cash Flows [Member]</link:label>
    <link:label id="lab_logan_YearsToCashFlowsMember_documentation_en-US" xlink:label="lab_logan_YearsToCashFlowsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Years To Cash Flows</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_YearsToCashFlowsMember" xlink:href="logan-20251231.xsd#logan_YearsToCashFlowsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_YearsToCashFlowsMember" xlink:to="lab_logan_YearsToCashFlowsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_U.S.StateTerritoriesAndMunicipalitiesMember_019bffd7-5158-74b9-9b4b-63c7e0557979_terseLabel_en-US" xlink:label="lab_logan_U.S.StateTerritoriesAndMunicipalitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. state, territories and municipalities</link:label>
    <link:label id="lab_logan_U.S.StateTerritoriesAndMunicipalitiesMember_label_en-US" xlink:label="lab_logan_U.S.StateTerritoriesAndMunicipalitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">U.S. State, Territories, And Municipalities [Member]</link:label>
    <link:label id="lab_logan_U.S.StateTerritoriesAndMunicipalitiesMember_documentation_en-US" xlink:label="lab_logan_U.S.StateTerritoriesAndMunicipalitiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">U.S. State, Territories, And Municipalities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_U.S.StateTerritoriesAndMunicipalitiesMember" xlink:href="logan-20251231.xsd#logan_U.S.StateTerritoriesAndMunicipalitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_U.S.StateTerritoriesAndMunicipalitiesMember" xlink:to="lab_logan_U.S.StateTerritoriesAndMunicipalitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsNet_019bffd7-515a-78cb-95ea-70ed5fea985f_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total deferred tax assets, net of valuation allowance</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsNet_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Net of Valuation Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsNet" xlink:to="lab_us-gaap_DeferredTaxAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_SaleOfStockNumberOfSharesExpiredValue_019c7c2c-4e9c-77c1-a059-d23206af8f91_terseLabel_en-US" xlink:label="lab_logan_SaleOfStockNumberOfSharesExpiredValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of stock, number of shares expired , value</link:label>
    <link:label id="lab_logan_SaleOfStockNumberOfSharesExpiredValue_label_en-US" xlink:label="lab_logan_SaleOfStockNumberOfSharesExpiredValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Number of Shares Expired, Value</link:label>
    <link:label id="lab_logan_SaleOfStockNumberOfSharesExpiredValue_documentation_en-US" xlink:label="lab_logan_SaleOfStockNumberOfSharesExpiredValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sale of Stock, Number of Shares Expired, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_SaleOfStockNumberOfSharesExpiredValue" xlink:href="logan-20251231.xsd#logan_SaleOfStockNumberOfSharesExpiredValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_SaleOfStockNumberOfSharesExpiredValue" xlink:to="lab_logan_SaleOfStockNumberOfSharesExpiredValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_019bffd7-5158-71b0-8c5a-fc77d64c4405_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">RSU's</link:label>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_019bffd7-515a-7c66-88f6-40252fcc54ca_verboseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">RSUs</link:label>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock Units (RSUs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedStockUnitsRSUMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:to="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_GainLossOnAcquisitionOfBusiness_019bffd7-5158-7175-9177-709e4693085b_terseLabel_en-US" xlink:label="lab_logan_GainLossOnAcquisitionOfBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain on acquisition of business</link:label>
    <link:label id="lab_logan_GainLossOnAcquisitionOfBusiness_label_en-US" xlink:label="lab_logan_GainLossOnAcquisitionOfBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (loss) On Acquisition of Business</link:label>
    <link:label id="lab_logan_GainLossOnAcquisitionOfBusiness_documentation_en-US" xlink:label="lab_logan_GainLossOnAcquisitionOfBusiness" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain (loss) On Acquisition of Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_GainLossOnAcquisitionOfBusiness" xlink:href="logan-20251231.xsd#logan_GainLossOnAcquisitionOfBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_GainLossOnAcquisitionOfBusiness" xlink:to="lab_logan_GainLossOnAcquisitionOfBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditLossFinancialInstrumentPolicyTextBlock_019bffd7-5158-75a7-a726-293b06c38a26_terseLabel_en-US" xlink:label="lab_us-gaap_CreditLossFinancialInstrumentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit losses</link:label>
    <link:label id="lab_us-gaap_CreditLossFinancialInstrumentPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_CreditLossFinancialInstrumentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Loss, Financial Instrument [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditLossFinancialInstrumentPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditLossFinancialInstrumentPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditLossFinancialInstrumentPolicyTextBlock" xlink:to="lab_us-gaap_CreditLossFinancialInstrumentPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_019c3737-aa7f-7b87-b317-70f0c94b7eb6_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Purchase price consideration</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_019bffd7-5158-79e6-bf2e-140775a07b27_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Purchase price consideration</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationConsiderationTransferred1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:to="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ProceedsFromTheIssuanceOfDebentureShares_019c7bd5-8dbb-72d2-9998-cb97dc37f6a6_terseLabel_en-US" xlink:label="lab_logan_ProceedsFromTheIssuanceOfDebentureShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from the issuance of debenture shares</link:label>
    <link:label id="lab_logan_ProceedsFromTheIssuanceOfDebentureShares_label_en-US" xlink:label="lab_logan_ProceedsFromTheIssuanceOfDebentureShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From The Issuance of Debenture Shares</link:label>
    <link:label id="lab_logan_ProceedsFromTheIssuanceOfDebentureShares_documentation_en-US" xlink:label="lab_logan_ProceedsFromTheIssuanceOfDebentureShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From The Issuance of Debenture Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ProceedsFromTheIssuanceOfDebentureShares" xlink:href="logan-20251231.xsd#logan_ProceedsFromTheIssuanceOfDebentureShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ProceedsFromTheIssuanceOfDebentureShares" xlink:to="lab_logan_ProceedsFromTheIssuanceOfDebentureShares" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_019bffd7-5157-7c86-adcb-0f43449c077c_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_NewYorkCityMember_019c7c1d-d183-7df3-a0f1-e2201ca03a86_terseLabel_en-US" xlink:label="lab_logan_NewYorkCityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NY City</link:label>
    <link:label id="lab_logan_NewYorkCityMember_label_en-US" xlink:label="lab_logan_NewYorkCityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New York City [Member]</link:label>
    <link:label id="lab_logan_NewYorkCityMember_documentation_en-US" xlink:label="lab_logan_NewYorkCityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">New York City</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_NewYorkCityMember" xlink:href="logan-20251231.xsd#logan_NewYorkCityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_NewYorkCityMember" xlink:to="lab_logan_NewYorkCityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_019bffd7-5159-7753-ae3e-d863526c8bab_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract_019bffd7-5158-7405-a8c4-49ecf18245df_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">(Increase) decrease in operating assets:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Operating Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOperatingAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OciLiabilityForFuturePolicyBenefitGainLossAfterReclassificationAdjustmentBeforeTaxParent_019bffd7-5157-752b-91ad-704aed139299_terseLabel_en-US" xlink:label="lab_us-gaap_OciLiabilityForFuturePolicyBenefitGainLossAfterReclassificationAdjustmentBeforeTaxParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remeasurement gains (losses) on future policy benefits related to discount rate</link:label>
    <link:label id="lab_us-gaap_OciLiabilityForFuturePolicyBenefitGainLossAfterReclassificationAdjustmentBeforeTaxParent_label_en-US" xlink:label="lab_us-gaap_OciLiabilityForFuturePolicyBenefitGainLossAfterReclassificationAdjustmentBeforeTaxParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OCI, Liability for Future Policy Benefit, Gain (Loss), after Reclassification Adjustment, before Tax, Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OciLiabilityForFuturePolicyBenefitGainLossAfterReclassificationAdjustmentBeforeTaxParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OciLiabilityForFuturePolicyBenefitGainLossAfterReclassificationAdjustmentBeforeTaxParent"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_019bffd7-515a-784f-be8e-0b0392596fc6_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Options outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
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    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_019bffd7-5159-7c18-a75f-59b1b6aaad63_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Transaction costs (net of amortization)</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_label_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFinanceCostsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFinanceCostsNet" xlink:to="lab_us-gaap_DeferredFinanceCostsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_019cf68e-d422-7a36-b4e7-96834639474d_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative, Gain (Loss) on Derivative, Net</link:label>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_label_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Gain (Loss) on Derivative, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeGainLossOnDerivativeNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:to="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_019bffd7-5159-7596-b932-fe6d8554bf6c_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets &#8212; indefinite life</link:label>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets (Excluding Goodwill)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:to="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomeAmount_019bffd7-515a-7666-9dd0-43a49eaeafd1_terseLabel_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomeAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign accrual property income impact</link:label>
    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomeAmount_label_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomeAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Foreign Accrual Property Income, Amount</link:label>
    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomeAmount_documentation_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomeAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Foreign Accrual Property Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomeAmount" xlink:href="logan-20251231.xsd#logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomeAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomeAmount" xlink:to="lab_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomeAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToContingentlyIssuableShares_019bffd7-515b-766e-ac3a-bd11b39cea59_terseLabel_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToContingentlyIssuableShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares potentially issuable (in shares)</link:label>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToContingentlyIssuableShares_label_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToContingentlyIssuableShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incremental Common Shares Attributable to Dilutive Effect of Contingently Issuable Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncrementalCommonSharesAttributableToContingentlyIssuableShares" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncrementalCommonSharesAttributableToContingentlyIssuableShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncrementalCommonSharesAttributableToContingentlyIssuableShares" xlink:to="lab_us-gaap_IncrementalCommonSharesAttributableToContingentlyIssuableShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019bffd7-5157-737c-b091-7ce0394ceb6a_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019bffd7-5157-7dc1-afeb-16c9351e880f_periodStartLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019bffd7-5157-72de-a45e-eca37583e3e9_periodEndLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InsuranceAbstract_label_en-US" xlink:label="lab_us-gaap_InsuranceAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InsuranceAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InsuranceAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InsuranceAbstract" xlink:to="lab_us-gaap_InsuranceAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable_019bffd7-5159-7a37-ae8e-2286c342f34b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable_label_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:to="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsFairValueDisclosure_019bffd7-5159-7225-bcec-d4c196ef7e1f_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other invested assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_OtherAssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsFairValueDisclosure" xlink:to="lab_us-gaap_OtherAssetsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceLiabilitiesAbstract_019bffd7-515a-7438-ae85-6111467a479f_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Funds held under reinsurance contracts</link:label>
    <link:label id="lab_us-gaap_ReinsuranceLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_ReinsuranceLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceLiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceLiabilitiesAbstract" xlink:to="lab_us-gaap_ReinsuranceLiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTableTextBlock_019bffd7-5159-7236-a818-958650761810_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisaggregationOfRevenueTableTextBlock"/>
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    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitUndiscountedBeforeReinsurance_019bffd7-515a-76d0-9cf0-dae5f1f935b3_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitUndiscountedBeforeReinsurance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Benefit payments, Undiscounted</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitUndiscountedBeforeReinsurance_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitUndiscountedBeforeReinsurance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Future Policy Benefit, Undiscounted, before Reinsurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitUndiscountedBeforeReinsurance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitUndiscountedBeforeReinsurance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitUndiscountedBeforeReinsurance" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitUndiscountedBeforeReinsurance" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_CreditLossMember_019bffd7-5158-7959-a650-700705a55dc6_terseLabel_en-US" xlink:label="lab_logan_CreditLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Loss</link:label>
    <link:label id="lab_logan_CreditLossMember_label_en-US" xlink:label="lab_logan_CreditLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Loss [Member]</link:label>
    <link:label id="lab_logan_CreditLossMember_documentation_en-US" xlink:label="lab_logan_CreditLossMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_CreditLossMember" xlink:href="logan-20251231.xsd#logan_CreditLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_CreditLossMember" xlink:to="lab_logan_CreditLossMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossUnrealized_019bffd7-5158-71db-ac21-2547bc7cfd3d_negatedLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossUnrealized" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Net change in unrealized (gains) losses on foreign currency</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossUnrealized_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossUnrealized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss), Foreign Currency Transaction, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyTransactionGainLossUnrealized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ForeignCurrencyTransactionGainLossUnrealized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignCurrencyTransactionGainLossUnrealized" xlink:to="lab_us-gaap_ForeignCurrencyTransactionGainLossUnrealized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract_019bffd7-515a-75ff-9fe4-79f5ce5f0fba_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current tax</link:label>
    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Income Tax Expense (Benefit), Continuing Operations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:to="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_MultiFamilyMortgageLoansMember_019bffd7-5158-78c6-be6c-c9246f60ea45_terseLabel_en-US" xlink:label="lab_logan_MultiFamilyMortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multi-family mortgage loans</link:label>
    <link:label id="lab_logan_MultiFamilyMortgageLoansMember_label_en-US" xlink:label="lab_logan_MultiFamilyMortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Multi-family Mortgage Loans [Member]</link:label>
    <link:label id="lab_logan_MultiFamilyMortgageLoansMember_documentation_en-US" xlink:label="lab_logan_MultiFamilyMortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Multi-family Mortgage Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_MultiFamilyMortgageLoansMember" xlink:href="logan-20251231.xsd#logan_MultiFamilyMortgageLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_MultiFamilyMortgageLoansMember" xlink:to="lab_logan_MultiFamilyMortgageLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_019bffd7-515a-7dad-89df-a8ad0dcaa39b_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Options issued (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Shares Issued in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_RunwayGrowthCapitalLLCMember_019bffd7-515a-7f86-ac80-6cffcc4ae098_terseLabel_en-US" xlink:label="lab_logan_RunwayGrowthCapitalLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Runway Growth Capital LLC</link:label>
    <link:label id="lab_logan_RunwayGrowthCapitalLLCMember_label_en-US" xlink:label="lab_logan_RunwayGrowthCapitalLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Runway Growth Capital LLC [Member]</link:label>
    <link:label id="lab_logan_RunwayGrowthCapitalLLCMember_documentation_en-US" xlink:label="lab_logan_RunwayGrowthCapitalLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Runway Growth Capital LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_RunwayGrowthCapitalLLCMember" xlink:href="logan-20251231.xsd#logan_RunwayGrowthCapitalLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_RunwayGrowthCapitalLLCMember" xlink:to="lab_logan_RunwayGrowthCapitalLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_label_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:to="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesAbstract_019bffd7-515a-7445-b64e-4e67ac886f14_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesAbstract_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverables, Including Reinsurance Premium Paid [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverablesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverablesAbstract" xlink:to="lab_us-gaap_ReinsuranceRecoverablesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_019bffd7-5159-73c3-98c9-07c504adbc0d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Finite-Lived Intangible Assets, Future Amortization Expense</link:label>
    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Finite-Lived Intangible Assets, Future Amortization Expense [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:to="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent_019bffd7-515a-72d4-a8fc-882235635d14_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable and accrued liabilities</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable and Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:to="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_SaleOfStockPercentageOfSharesOutstanding_019c7c26-a7bf-7b34-a377-07b03a8ad087_terseLabel_en-US" xlink:label="lab_logan_SaleOfStockPercentageOfSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of stock, percentage of shares outstanding</link:label>
    <link:label id="lab_logan_SaleOfStockPercentageOfSharesOutstanding_label_en-US" xlink:label="lab_logan_SaleOfStockPercentageOfSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Percentage of Shares Outstanding</link:label>
    <link:label id="lab_logan_SaleOfStockPercentageOfSharesOutstanding_documentation_en-US" xlink:label="lab_logan_SaleOfStockPercentageOfSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sale of Stock, Percentage of Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_SaleOfStockPercentageOfSharesOutstanding" xlink:href="logan-20251231.xsd#logan_SaleOfStockPercentageOfSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_SaleOfStockPercentageOfSharesOutstanding" xlink:to="lab_logan_SaleOfStockPercentageOfSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_019bffd7-5159-77c7-9caa-54d863b2868c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective interest rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Effective Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateEffectivePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_019c2cb9-a0cb-7c11-b4e9-db3ed90e409d_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDeterminationDate_terseLabel_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:label id="lab_ecd_RestatementDeterminationDate_label_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDeterminationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDeterminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDeterminationDate" xlink:to="lab_ecd_RestatementDeterminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019bffd7-5157-7806-8894-e85a36cb9a25_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Income tax (expense) benefit &#8212; Asset Management</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019bffd7-515a-7fd3-96b3-0011f400665b_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income tax expense (benefit)</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_019bffd7-5159-7015-a33a-205cee5c555a_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssets_019bffd7-5157-765b-86d7-1b8e495dbe8e_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssets_019bffd7-515a-709c-931e-b864ea84abc2_totalLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssets_label_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssets" xlink:to="lab_us-gaap_OtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestCreditedToPolicyholdersAccountBalances_019bffd7-515a-7c0e-8084-d8059e235265_terseLabel_en-US" xlink:label="lab_us-gaap_InterestCreditedToPolicyholdersAccountBalances" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest credited</link:label>
    <link:label id="lab_us-gaap_InterestCreditedToPolicyholdersAccountBalances_label_en-US" xlink:label="lab_us-gaap_InterestCreditedToPolicyholdersAccountBalances" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance, Interest Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestCreditedToPolicyholdersAccountBalances" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestCreditedToPolicyholdersAccountBalances"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestCreditedToPolicyholdersAccountBalances" xlink:to="lab_us-gaap_InterestCreditedToPolicyholdersAccountBalances" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseOfActualVarianceFromExpectedExperience_019bffd7-515a-782d-adaf-ea68f658e8a7_terseLabel_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseOfActualVarianceFromExpectedExperience" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of actual variances from expected experience</link:label>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseOfActualVarianceFromExpectedExperience_label_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseOfActualVarianceFromExpectedExperience" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Future Policy Benefit, Increase (Decrease) of Actual Variance from Expected Experience</link:label>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseOfActualVarianceFromExpectedExperience_documentation_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseOfActualVarianceFromExpectedExperience" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Future Policy Benefit, Increase (Decrease) of Actual Variance from Expected Experience</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseOfActualVarianceFromExpectedExperience" xlink:href="logan-20251231.xsd#logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseOfActualVarianceFromExpectedExperience"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019bffd7-5159-7cd3-bd3c-4ab89bac8c49_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning Balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019bffd7-5159-7fe1-a587-edde7940c682_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending Balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019bffd7-5159-780a-9dab-26450927dedc_totalLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Level 3 Assets fair value</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationLineItems_019c7b21-3fa1-726e-96ed-742f0129a27f_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:label id="lab_dei_DocumentInformationLineItems_label_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationLineItems" xlink:to="lab_dei_DocumentInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_PaymentsToAcquireInvestmentsOperatingActivities_019bffd7-5158-7932-b34b-960721811df0_terseLabel_en-US" xlink:label="lab_logan_PaymentsToAcquireInvestmentsOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchases of investments by consolidated VIEs</link:label>
    <link:label id="lab_logan_PaymentsToAcquireInvestmentsOperatingActivities_label_en-US" xlink:label="lab_logan_PaymentsToAcquireInvestmentsOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments To Acquire Investments, Operating Activities</link:label>
    <link:label id="lab_logan_PaymentsToAcquireInvestmentsOperatingActivities_documentation_en-US" xlink:label="lab_logan_PaymentsToAcquireInvestmentsOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments To Acquire Investments, Operating Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_PaymentsToAcquireInvestmentsOperatingActivities" xlink:href="logan-20251231.xsd#logan_PaymentsToAcquireInvestmentsOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_PaymentsToAcquireInvestmentsOperatingActivities" xlink:to="lab_logan_PaymentsToAcquireInvestmentsOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsSvcCstMember" xlink:to="lab_ecd_PnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DesignatedAsHedgingInstrumentMember_019bffd7-5159-7a6f-898a-e2818e2639c1_terseLabel_en-US" xlink:label="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives designated as hedges</link:label>
    <link:label id="lab_us-gaap_DesignatedAsHedgingInstrumentMember_label_en-US" xlink:label="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Designated as Hedging Instrument [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DesignatedAsHedgingInstrumentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:to="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets_019bffd7-5157-7780-8f8c-652bc023eb6d_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share issuance for investment purchase</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Purchase of Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InsuranceSolutionsExpensesAbstract_019bffd7-5157-7178-8b93-efac2c207e12_terseLabel_en-US" xlink:label="lab_logan_InsuranceSolutionsExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance Solutions</link:label>
    <link:label id="lab_logan_InsuranceSolutionsExpensesAbstract_label_en-US" xlink:label="lab_logan_InsuranceSolutionsExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance Solutions, Expenses [Abstract]</link:label>
    <link:label id="lab_logan_InsuranceSolutionsExpensesAbstract_documentation_en-US" xlink:label="lab_logan_InsuranceSolutionsExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Insurance Solutions, Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InsuranceSolutionsExpensesAbstract" xlink:href="logan-20251231.xsd#logan_InsuranceSolutionsExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InsuranceSolutionsExpensesAbstract" xlink:to="lab_logan_InsuranceSolutionsExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_NetInvestmentIncomeLossWithheldFunds_019bffd7-5157-7863-bec1-ae86c9d549a1_terseLabel_en-US" xlink:label="lab_logan_NetInvestmentIncomeLossWithheldFunds" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net revenues of consolidated variable interest entities</link:label>
    <link:label id="lab_logan_NetInvestmentIncomeLossWithheldFunds_label_en-US" xlink:label="lab_logan_NetInvestmentIncomeLossWithheldFunds" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Investment Income (Loss), Withheld Funds</link:label>
    <link:label id="lab_logan_NetInvestmentIncomeLossWithheldFunds_documentation_en-US" xlink:label="lab_logan_NetInvestmentIncomeLossWithheldFunds" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Investment Income (Loss), Withheld Funds</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_NetInvestmentIncomeLossWithheldFunds" xlink:href="logan-20251231.xsd#logan_NetInvestmentIncomeLossWithheldFunds"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_NetInvestmentIncomeLossWithheldFunds" xlink:to="lab_logan_NetInvestmentIncomeLossWithheldFunds" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_019bffd7-5159-7948-9d12-26a0e0abd2d8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis_019bffd7-5159-7a5b-92ab-cf662376ec4b_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis"/>
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    <link:label id="lab_us-gaap_ProductLiabilityContingencyTable_019bffd7-515b-703d-9141-2690bd27f08d_terseLabel_en-US" xlink:label="lab_us-gaap_ProductLiabilityContingencyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product Liability Contingency [Table]</link:label>
    <link:label id="lab_us-gaap_ProductLiabilityContingencyTable_label_en-US" xlink:label="lab_us-gaap_ProductLiabilityContingencyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product Liability Contingency [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProductLiabilityContingencyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProductLiabilityContingencyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProductLiabilityContingencyTable" xlink:to="lab_us-gaap_ProductLiabilityContingencyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitAfterReinsuranceAbstract_019bffd7-515a-79f4-afe9-6338b907eab2_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitAfterReinsuranceAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future policy benefits</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitAfterReinsuranceAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitAfterReinsuranceAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, after Reinsurance [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitAfterReinsuranceAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitAfterReinsuranceAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitAfterReinsuranceAbstract" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitAfterReinsuranceAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InvestmentRiskAxis_019bffd7-5158-728c-aea3-cf5e3f94f5a2_terseLabel_en-US" xlink:label="lab_logan_InvestmentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Risk [Axis]</link:label>
    <link:label id="lab_logan_InvestmentRiskAxis_label_en-US" xlink:label="lab_logan_InvestmentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Risk [Axis]</link:label>
    <link:label id="lab_logan_InvestmentRiskAxis_documentation_en-US" xlink:label="lab_logan_InvestmentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Risk</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InvestmentRiskAxis" xlink:href="logan-20251231.xsd#logan_InvestmentRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InvestmentRiskAxis" xlink:to="lab_logan_InvestmentRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_AdvisoryAndTransactionFeesMember_019c371a-95b5-7eca-955e-9d5549ebb55e_terseLabel_en-US" xlink:label="lab_logan_AdvisoryAndTransactionFeesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Advisory and transaction fees, net</link:label>
    <link:label id="lab_logan_AdvisoryAndTransactionFeesMember_label_en-US" xlink:label="lab_logan_AdvisoryAndTransactionFeesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Advisory And Transaction Fees [Member]</link:label>
    <link:label id="lab_logan_AdvisoryAndTransactionFeesMember_documentation_en-US" xlink:label="lab_logan_AdvisoryAndTransactionFeesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Advisory And Transaction Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_AdvisoryAndTransactionFeesMember" xlink:href="logan-20251231.xsd#logan_AdvisoryAndTransactionFeesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_AdvisoryAndTransactionFeesMember" xlink:to="lab_logan_AdvisoryAndTransactionFeesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostsTextBlock1_019bffd7-515a-775f-bf31-16deed691312_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostsTextBlock1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred acquisition costs</link:label>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostsTextBlock1_label_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostsTextBlock1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredPolicyAcquisitionCostsTextBlock1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredPolicyAcquisitionCostsTextBlock1"/>
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    <link:label id="lab_us-gaap_OtherNonoperatingIncome_019bffd7-515b-7416-850a-4100f56574d2_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncome" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncome_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherNonoperatingIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncome" xlink:to="lab_us-gaap_OtherNonoperatingIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPaidFederalAfterRefundReceived_019c7c1d-d183-77a8-887a-3e54283b8622_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidFederalAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">US Federal</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPaidFederalAfterRefundReceived_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidFederalAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, Federal, after Refund Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPaidFederalAfterRefundReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidFederalAfterRefundReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPaidFederalAfterRefundReceived" xlink:to="lab_us-gaap_IncomeTaxPaidFederalAfterRefundReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllTradingArrangementsMember"/>
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    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote [Text Block]</link:label>
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    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
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    <link:label id="lab_logan_IncreaseDecreaseLiabilityForFuturePolicyBenefitAfterReinsurance_019bffd7-5158-7665-a8ed-79411b3dff93_terseLabel_en-US" xlink:label="lab_logan_IncreaseDecreaseLiabilityForFuturePolicyBenefitAfterReinsurance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future policy benefits</link:label>
    <link:label id="lab_logan_IncreaseDecreaseLiabilityForFuturePolicyBenefitAfterReinsurance_label_en-US" xlink:label="lab_logan_IncreaseDecreaseLiabilityForFuturePolicyBenefitAfterReinsurance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase Decrease Liability For Future Policy Benefit, After Reinsurance</link:label>
    <link:label id="lab_logan_IncreaseDecreaseLiabilityForFuturePolicyBenefitAfterReinsurance_documentation_en-US" xlink:label="lab_logan_IncreaseDecreaseLiabilityForFuturePolicyBenefitAfterReinsurance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase Decrease Liability For Future Policy Benefit, After Reinsurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_IncreaseDecreaseLiabilityForFuturePolicyBenefitAfterReinsurance" xlink:href="logan-20251231.xsd#logan_IncreaseDecreaseLiabilityForFuturePolicyBenefitAfterReinsurance"/>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationOtherAdjustments_019bffd7-5157-7c37-8512-3d013762d497_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationOtherAdjustments_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Other Adjustments, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationOtherAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationOtherAdjustments"/>
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    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesAbstract_019bffd7-515a-7ad9-9dee-c7e3982abe03_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Gross [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesAbstract" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants_019bffd7-515b-7f10-9777-787a317c2b4d_terseLabel_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assumed exercise of warrants (in shares)</link:label>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants_label_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incremental Common Shares Attributable to Dilutive Effect of Call Options and Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019bffd7-515a-7cb7-ad66-90c7de327999_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Unvested, beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019bffd7-515a-7b16-a4ae-d9e8261a3674_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Unvested, ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019bffd7-515b-7fe0-bcf8-727b45b7aedf_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
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    <link:label id="lab_us-gaap_ReinsurancePayable_019bffd7-515b-7059-9f47-a41e4f26dfd9_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsurancePayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Funds withheld payable</link:label>
    <link:label id="lab_us-gaap_ReinsurancePayable_label_en-US" xlink:label="lab_us-gaap_ReinsurancePayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsurancePayable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsurancePayable"/>
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    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeCashFlowAndReinsurance_019bffd7-515a-7f90-8992-51a2a7241371_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeCashFlowAndReinsurance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Beginning balance at locked-in discount rate</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeCashFlowAndReinsurance_019bffd7-515a-7b86-8c32-eedd5837e349_periodEndLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeCashFlowAndReinsurance" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance at locked-in discount rate</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeCashFlowAndReinsurance_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeCashFlowAndReinsurance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Net Premium, Original Discount Rate, before Cash Flow and Reinsurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeCashFlowAndReinsurance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeCashFlowAndReinsurance"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_019bffd7-5158-7f5d-87ab-122bc1d480b4_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash used in operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentTerm_019bffd7-515b-7d5e-aef4-d769f571491f_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument,term</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTerm"/>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTable_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationTable"/>
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    <link:label id="lab_us-gaap_FairValueConcentrationOfRiskInvestments_019bffd7-515b-7e7d-8626-667f147dddf5_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueConcentrationOfRiskInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value</link:label>
    <link:label id="lab_us-gaap_FairValueConcentrationOfRiskInvestments_label_en-US" xlink:label="lab_us-gaap_FairValueConcentrationOfRiskInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Concentration of Risk, Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueConcentrationOfRiskInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueConcentrationOfRiskInvestments"/>
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    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_019bffd7-515a-7011-8055-304a87eec5f6_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, per share (in dollars per shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Par or Stated Value Per Share</link:label>
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    <link:label id="lab_us-gaap_SubsequentEventMember_019bffd7-515b-7832-b9cd-727d2c9ae179_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event</link:label>
    <link:label id="lab_us-gaap_SubsequentEventMember_label_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventMember" xlink:to="lab_us-gaap_SubsequentEventMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_logan_PavoniaLifeInsuranceCompanyOfMichiganSurplusNotesMember_label_en-US" xlink:label="lab_logan_PavoniaLifeInsuranceCompanyOfMichiganSurplusNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pavonia Life Insurance Company of Michigan Surplus Notes [Member]</link:label>
    <link:label id="lab_logan_PavoniaLifeInsuranceCompanyOfMichiganSurplusNotesMember_documentation_en-US" xlink:label="lab_logan_PavoniaLifeInsuranceCompanyOfMichiganSurplusNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Pavonia Life Insurance Company of Michigan Surplus Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_PavoniaLifeInsuranceCompanyOfMichiganSurplusNotesMember" xlink:href="logan-20251231.xsd#logan_PavoniaLifeInsuranceCompanyOfMichiganSurplusNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_PavoniaLifeInsuranceCompanyOfMichiganSurplusNotesMember" xlink:to="lab_logan_PavoniaLifeInsuranceCompanyOfMichiganSurplusNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery_019bffd7-5159-7116-a418-3fec4c5e4bf2_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recoveries</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss, Recovery</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery" xlink:to="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoTotalCompAmt_label_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_019bffd7-5159-75e5-b932-1d6a1470db73_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_OtherAssetsAndAccruedExpensesAndOtherLiabilitiesTextBlock_019bffd7-515a-76c1-b464-7ab938bc2544_terseLabel_en-US" xlink:label="lab_logan_OtherAssetsAndAccruedExpensesAndOtherLiabilitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets and Accrued expenses and other liabilities</link:label>
    <link:label id="lab_logan_OtherAssetsAndAccruedExpensesAndOtherLiabilitiesTextBlock_label_en-US" xlink:label="lab_logan_OtherAssetsAndAccruedExpensesAndOtherLiabilitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets And Accrued Expenses And Other Liabilities [Text Block]</link:label>
    <link:label id="lab_logan_OtherAssetsAndAccruedExpensesAndOtherLiabilitiesTextBlock_documentation_en-US" xlink:label="lab_logan_OtherAssetsAndAccruedExpensesAndOtherLiabilitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Assets And Accrued Expenses And Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_OtherAssetsAndAccruedExpensesAndOtherLiabilitiesTextBlock" xlink:href="logan-20251231.xsd#logan_OtherAssetsAndAccruedExpensesAndOtherLiabilitiesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_OtherAssetsAndAccruedExpensesAndOtherLiabilitiesTextBlock" xlink:to="lab_logan_OtherAssetsAndAccruedExpensesAndOtherLiabilitiesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ValuationTechniqueIndependentProbabilitiesMember_019bffd7-5159-75dd-bf27-8b25ba96fad2_terseLabel_en-US" xlink:label="lab_logan_ValuationTechniqueIndependentProbabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Independent probabilities</link:label>
    <link:label id="lab_logan_ValuationTechniqueIndependentProbabilitiesMember_label_en-US" xlink:label="lab_logan_ValuationTechniqueIndependentProbabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Independent Probabilities [Member]</link:label>
    <link:label id="lab_logan_ValuationTechniqueIndependentProbabilitiesMember_documentation_en-US" xlink:label="lab_logan_ValuationTechniqueIndependentProbabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Valuation Technique, Independent Probabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ValuationTechniqueIndependentProbabilitiesMember" xlink:href="logan-20251231.xsd#logan_ValuationTechniqueIndependentProbabilitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ValuationTechniqueIndependentProbabilitiesMember" xlink:to="lab_logan_ValuationTechniqueIndependentProbabilitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityExTransitionPeriod_019bffd7-5157-786d-8248-ebe46cae216b_terseLabel_en-US" xlink:label="lab_dei_EntityExTransitionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Ex Transition Period</link:label>
    <link:label id="lab_dei_EntityExTransitionPeriod_label_en-US" xlink:label="lab_dei_EntityExTransitionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Ex Transition Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityExTransitionPeriod" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityExTransitionPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityExTransitionPeriod" xlink:to="lab_dei_EntityExTransitionPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_019bffd7-5157-788f-9c5a-ba7ff7c3b26d_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_GeneralAdministrativeAndOtherExpenses_019bffd7-5157-74a6-8a95-f16cec14d449_terseLabel_en-US" xlink:label="lab_logan_GeneralAdministrativeAndOtherExpenses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General, administrative and other</link:label>
    <link:label id="lab_logan_GeneralAdministrativeAndOtherExpenses_label_en-US" xlink:label="lab_logan_GeneralAdministrativeAndOtherExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General, Administrative And Other Expenses</link:label>
    <link:label id="lab_logan_GeneralAdministrativeAndOtherExpenses_documentation_en-US" xlink:label="lab_logan_GeneralAdministrativeAndOtherExpenses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">General, Administrative And Other Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_GeneralAdministrativeAndOtherExpenses" xlink:href="logan-20251231.xsd#logan_GeneralAdministrativeAndOtherExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_GeneralAdministrativeAndOtherExpenses" xlink:to="lab_logan_GeneralAdministrativeAndOtherExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ManagementFeeTerm_019bffd7-5158-7b52-bf64-6679407964a8_terseLabel_en-US" xlink:label="lab_logan_ManagementFeeTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Management fee, term</link:label>
    <link:label id="lab_logan_ManagementFeeTerm_label_en-US" xlink:label="lab_logan_ManagementFeeTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management Fee, Term</link:label>
    <link:label id="lab_logan_ManagementFeeTerm_documentation_en-US" xlink:label="lab_logan_ManagementFeeTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Management Fee, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ManagementFeeTerm" xlink:href="logan-20251231.xsd#logan_ManagementFeeTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ManagementFeeTerm" xlink:to="lab_logan_ManagementFeeTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceNetAmountAtRisk_019bffd7-515a-7bb0-8bee-9285d0d8ed40_terseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceNetAmountAtRisk" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net amount at risk, in the event of death</link:label>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceNetAmountAtRisk_label_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceNetAmountAtRisk" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance, Net Amount at Risk</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderAccountBalanceNetAmountAtRisk" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderAccountBalanceNetAmountAtRisk"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyholderAccountBalanceNetAmountAtRisk" xlink:to="lab_us-gaap_PolicyholderAccountBalanceNetAmountAtRisk" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_019bffd7-515b-7b98-b2e6-a23a9c272799_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reportable segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsNetOfValuationAllowanceAbstract_019bffd7-515a-7d56-833b-7f03018edcc3_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsNetOfValuationAllowanceAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsNetOfValuationAllowanceAbstract_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsNetOfValuationAllowanceAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Net of Valuation Allowance [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsNetOfValuationAllowanceAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsNetOfValuationAllowanceAbstract"/>
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    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet_019bffd7-515a-7d0c-a093-4671ee839a15_totalLabel_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Policyholder Benefits and Claims Incurred, Net, Total</link:label>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet_label_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Benefits and Claims Incurred, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderBenefitsAndClaimsIncurredNet"/>
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    <link:label id="lab_us-gaap_VariableInterestEntityDisclosureTextBlock_019bffd7-5159-79ce-bf31-3d2b6264e54f_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entities</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableInterestEntityDisclosureTextBlock"/>
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    <link:label id="lab_logan_DepositsOnInvestmentTypePoliciesAndContracts_019bffd7-5158-79ef-8b63-c6f6f9401899_terseLabel_en-US" xlink:label="lab_logan_DepositsOnInvestmentTypePoliciesAndContracts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deposits on investment-type policies and contracts</link:label>
    <link:label id="lab_logan_DepositsOnInvestmentTypePoliciesAndContracts_label_en-US" xlink:label="lab_logan_DepositsOnInvestmentTypePoliciesAndContracts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deposits On Investment-type Policies And Contracts</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DepositsOnInvestmentTypePoliciesAndContracts" xlink:to="lab_logan_DepositsOnInvestmentTypePoliciesAndContracts" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_019c2cba-5a2f-7def-9b5b-95164532d223_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_019bffd7-5159-7eeb-88db-4b97ad80cc6d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablesPeriodPastDueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:to="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_019bffd7-515b-7a2d-8967-1387ad79fb50_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:to="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectsOfReinsuranceLineItems_019bffd7-515a-7cce-836b-edf6a2b1b53e_terseLabel_en-US" xlink:label="lab_us-gaap_EffectsOfReinsuranceLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effects of Reinsurance [Line Items]</link:label>
    <link:label id="lab_us-gaap_EffectsOfReinsuranceLineItems_label_en-US" xlink:label="lab_us-gaap_EffectsOfReinsuranceLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effects of Reinsurance [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectsOfReinsuranceLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectsOfReinsuranceLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectsOfReinsuranceLineItems" xlink:to="lab_us-gaap_EffectsOfReinsuranceLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignCurrencyCashFlowHedgeGainLossToBeReclassifiedDuringNext12Months_019bffd7-5159-7474-9273-e9072f21922c_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyCashFlowHedgeGainLossToBeReclassifiedDuringNext12Months" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain (loss) to be reclassified during next 12 months</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyCashFlowHedgeGainLossToBeReclassifiedDuringNext12Months_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyCashFlowHedgeGainLossToBeReclassifiedDuringNext12Months" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Currency Cash Flow Hedge Gain (Loss) to be Reclassified During Next 12 Months</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyCashFlowHedgeGainLossToBeReclassifiedDuringNext12Months" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ForeignCurrencyCashFlowHedgeGainLossToBeReclassifiedDuringNext12Months"/>
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    <link:label id="lab_logan_WithdrawalsOnInvestmentTypePoliciesAndContracts_019bffd7-5158-7c39-9271-b1471540163a_negatedTerseLabel_en-US" xlink:label="lab_logan_WithdrawalsOnInvestmentTypePoliciesAndContracts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Withdrawals on investment-type policies and contracts</link:label>
    <link:label id="lab_logan_WithdrawalsOnInvestmentTypePoliciesAndContracts_label_en-US" xlink:label="lab_logan_WithdrawalsOnInvestmentTypePoliciesAndContracts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Withdrawals On Investment-type Policies And Contracts</link:label>
    <link:label id="lab_logan_WithdrawalsOnInvestmentTypePoliciesAndContracts_documentation_en-US" xlink:label="lab_logan_WithdrawalsOnInvestmentTypePoliciesAndContracts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Withdrawals On Investment-type Policies And Contracts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_WithdrawalsOnInvestmentTypePoliciesAndContracts" xlink:href="logan-20251231.xsd#logan_WithdrawalsOnInvestmentTypePoliciesAndContracts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_WithdrawalsOnInvestmentTypePoliciesAndContracts" xlink:to="lab_logan_WithdrawalsOnInvestmentTypePoliciesAndContracts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract_019bffd7-5157-737c-9194-55b16c58a6ef_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss), before tax:</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), before Tax, Portion Attributable to Parent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract"/>
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    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_IndividualAxis"/>
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    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_019bffd7-515a-7a56-b5f9-01543255d884_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Domain]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxAuthorityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxAuthorityDomain" xlink:to="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFour_019bffd7-515a-7897-be9c-6cfa36807203_terseLabel_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFour_label_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense, Year Four</link:label>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFour_documentation_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFour" xlink:href="logan-20251231.xsd#logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFour" xlink:to="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DirectorsAndOfficersMember_019bffd7-515b-7bb0-802e-905174aedc1e_terseLabel_en-US" xlink:label="lab_logan_DirectorsAndOfficersMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Directors and Officers</link:label>
    <link:label id="lab_logan_DirectorsAndOfficersMember_label_en-US" xlink:label="lab_logan_DirectorsAndOfficersMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Directors and Officers [Member]</link:label>
    <link:label id="lab_logan_DirectorsAndOfficersMember_documentation_en-US" xlink:label="lab_logan_DirectorsAndOfficersMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Directors and Officers</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DirectorsAndOfficersMember" xlink:href="logan-20251231.xsd#logan_DirectorsAndOfficersMember"/>
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    <link:label id="lab_us-gaap_PaymentsOfDividendsCommonStock_019bffd7-5158-7e8a-8f3d-5d0beda1865c_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Shareholder dividends</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDividendsCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Ordinary Dividends, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDividendsCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDividendsCommonStock"/>
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    <link:label id="lab_dei_DocumentAnnualReport_019c2cb4-9695-71e2-aee7-fe49817ab0fc_terseLabel_en-US" xlink:label="lab_dei_DocumentAnnualReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Annual Report</link:label>
    <link:label id="lab_dei_DocumentAnnualReport_label_en-US" xlink:label="lab_dei_DocumentAnnualReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Annual Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentAnnualReport" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentAnnualReport"/>
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    <link:label id="lab_logan_PolicyholderAccountBalanceSurrenderAndWithdrawalBenefitsAndProductCharges_019bffd7-515a-7c5e-9a54-008e13899a42_terseLabel_en-US" xlink:label="lab_logan_PolicyholderAccountBalanceSurrenderAndWithdrawalBenefitsAndProductCharges" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Surrender and withdrawal, benefits and product charges</link:label>
    <link:label id="lab_logan_PolicyholderAccountBalanceSurrenderAndWithdrawalBenefitsAndProductCharges_label_en-US" xlink:label="lab_logan_PolicyholderAccountBalanceSurrenderAndWithdrawalBenefitsAndProductCharges" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance, Surrender And Withdrawal, Benefits And Product Charges</link:label>
    <link:label id="lab_logan_PolicyholderAccountBalanceSurrenderAndWithdrawalBenefitsAndProductCharges_documentation_en-US" xlink:label="lab_logan_PolicyholderAccountBalanceSurrenderAndWithdrawalBenefitsAndProductCharges" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance, Surrender And Withdrawal, Benefits And Product Charges</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_PolicyholderAccountBalanceSurrenderAndWithdrawalBenefitsAndProductCharges" xlink:href="logan-20251231.xsd#logan_PolicyholderAccountBalanceSurrenderAndWithdrawalBenefitsAndProductCharges"/>
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    <link:label id="lab_us-gaap_PolicyholderAccountBalanceIssuance_019bffd7-515a-7603-bbe2-3db7b3fb3a76_terseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deposits</link:label>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceIssuance_019bffd7-515a-7aa8-a4ce-0cfd2d58e0ac_verboseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceIssuance" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Policies assumed</link:label>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceIssuance_label_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceIssuance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance, Issuance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderAccountBalanceIssuance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderAccountBalanceIssuance"/>
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    <link:label id="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount_019bffd7-5159-7b52-a343-394138c3fee3_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum exposure to loss</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount"/>
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    <link:label id="lab_us-gaap_CededCreditRiskTable_019bffd7-515b-75b5-8e63-cd96edae641c_terseLabel_en-US" xlink:label="lab_us-gaap_CededCreditRiskTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ceded Credit Risk [Table]</link:label>
    <link:label id="lab_us-gaap_CededCreditRiskTable_label_en-US" xlink:label="lab_us-gaap_CededCreditRiskTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ceded Credit Risk [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CededCreditRiskTable"/>
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    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYear_019bffd7-5159-7235-87e5-60dcd5fc49fc_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year four</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Year Four, Originated, Three Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_019c7b30-9b74-7b9c-a7ac-e18d3eff011b_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InterestAndOtherCreditFacilityExpenses_019bffd7-5157-7652-82f5-bb4e16303b41_terseLabel_en-US" xlink:label="lab_logan_InterestAndOtherCreditFacilityExpenses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest and other credit facility expenses</link:label>
    <link:label id="lab_logan_InterestAndOtherCreditFacilityExpenses_019cadd0-a07a-712c-8951-54134234136e_negatedLabel_en-US" xlink:label="lab_logan_InterestAndOtherCreditFacilityExpenses" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Interest and other credit facility expenses</link:label>
    <link:label id="lab_logan_InterestAndOtherCreditFacilityExpenses_label_en-US" xlink:label="lab_logan_InterestAndOtherCreditFacilityExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest And Other Credit Facility Expenses</link:label>
    <link:label id="lab_logan_InterestAndOtherCreditFacilityExpenses_documentation_en-US" xlink:label="lab_logan_InterestAndOtherCreditFacilityExpenses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest And Other Credit Facility Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InterestAndOtherCreditFacilityExpenses" xlink:href="logan-20251231.xsd#logan_InterestAndOtherCreditFacilityExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InterestAndOtherCreditFacilityExpenses" xlink:to="lab_logan_InterestAndOtherCreditFacilityExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ProceedsFromSaleOfInvestmentsOperatingActivities_019c4bd0-b8e8-7546-a646-cb2ae88eec3c_negatedLabel_en-US" xlink:label="lab_logan_ProceedsFromSaleOfInvestmentsOperatingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of investments by consolidated VIEs</link:label>
    <link:label id="lab_logan_ProceedsFromSaleOfInvestmentsOperatingActivities_label_en-US" xlink:label="lab_logan_ProceedsFromSaleOfInvestmentsOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Sale Of Investments, Operating Activities</link:label>
    <link:label id="lab_logan_ProceedsFromSaleOfInvestmentsOperatingActivities_documentation_en-US" xlink:label="lab_logan_ProceedsFromSaleOfInvestmentsOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Sale Of Investments, Operating Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ProceedsFromSaleOfInvestmentsOperatingActivities" xlink:href="logan-20251231.xsd#logan_ProceedsFromSaleOfInvestmentsOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ProceedsFromSaleOfInvestmentsOperatingActivities" xlink:to="lab_logan_ProceedsFromSaleOfInvestmentsOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionEquityInterestIssuedOrIssuableTextBlock_019bffd7-5158-7a1d-a8c0-d27f2e25eff6_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionEquityInterestIssuedOrIssuableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Purchase Price</link:label>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionEquityInterestIssuedOrIssuableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionEquityInterestIssuedOrIssuableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Equity Interest [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionEquityInterestIssuedOrIssuableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionEquityInterestIssuedOrIssuableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionEquityInterestIssuedOrIssuableTextBlock" xlink:to="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionEquityInterestIssuedOrIssuableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DebtRepaymentOnMaturityDateAdjustmentAmount_019bffd7-5159-7b96-9970-6385b858a07b_terseLabel_en-US" xlink:label="lab_logan_DebtRepaymentOnMaturityDateAdjustmentAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt repayment on maturity date, adjustment amount</link:label>
    <link:label id="lab_logan_DebtRepaymentOnMaturityDateAdjustmentAmount_label_en-US" xlink:label="lab_logan_DebtRepaymentOnMaturityDateAdjustmentAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Repayment On Maturity Date, Adjustment Amount</link:label>
    <link:label id="lab_logan_DebtRepaymentOnMaturityDateAdjustmentAmount_documentation_en-US" xlink:label="lab_logan_DebtRepaymentOnMaturityDateAdjustmentAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Repayment On Maturity Date, Adjustment Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DebtRepaymentOnMaturityDateAdjustmentAmount" xlink:href="logan-20251231.xsd#logan_DebtRepaymentOnMaturityDateAdjustmentAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DebtRepaymentOnMaturityDateAdjustmentAmount" xlink:to="lab_logan_DebtRepaymentOnMaturityDateAdjustmentAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_BusinessCombinationOtherAdjustmentsRelatedToExpenses_019bffd7-5158-7816-8a33-647c1e79c49e_terseLabel_en-US" xlink:label="lab_logan_BusinessCombinationOtherAdjustmentsRelatedToExpenses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other deal adjustments for expenses incurred</link:label>
    <link:label id="lab_logan_BusinessCombinationOtherAdjustmentsRelatedToExpenses_label_en-US" xlink:label="lab_logan_BusinessCombinationOtherAdjustmentsRelatedToExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Other Adjustments Related To Expenses</link:label>
    <link:label id="lab_logan_BusinessCombinationOtherAdjustmentsRelatedToExpenses_documentation_en-US" xlink:label="lab_logan_BusinessCombinationOtherAdjustmentsRelatedToExpenses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Other Adjustments Related To Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_BusinessCombinationOtherAdjustmentsRelatedToExpenses" xlink:href="logan-20251231.xsd#logan_BusinessCombinationOtherAdjustmentsRelatedToExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_BusinessCombinationOtherAdjustmentsRelatedToExpenses" xlink:to="lab_logan_BusinessCombinationOtherAdjustmentsRelatedToExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DebentureUnitPaidInKindPercentage_019bffd7-5159-7372-a153-37700764d35e_terseLabel_en-US" xlink:label="lab_logan_DebentureUnitPaidInKindPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debenture, paid-in-kind, percentage</link:label>
    <link:label id="lab_logan_DebentureUnitPaidInKindPercentage_label_en-US" xlink:label="lab_logan_DebentureUnitPaidInKindPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debenture Unit, Paid-In-Kind, Percentage</link:label>
    <link:label id="lab_logan_DebentureUnitPaidInKindPercentage_documentation_en-US" xlink:label="lab_logan_DebentureUnitPaidInKindPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debenture Unit, Paid-In-Kind, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DebentureUnitPaidInKindPercentage" xlink:href="logan-20251231.xsd#logan_DebentureUnitPaidInKindPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DebentureUnitPaidInKindPercentage" xlink:to="lab_logan_DebentureUnitPaidInKindPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTable_019bffd7-5159-786d-9e81-586a05ce6af3_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table]</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTable_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisaggregationOfRevenueTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueTable" xlink:to="lab_us-gaap_DisaggregationOfRevenueTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_019bffd7-515a-7b7e-a2fa-1acf4de035ed_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tax benefit of loss carryforward</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwards"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:to="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableOriginatedInCurrentFiscalYear_019bffd7-5159-71e7-bef8-be0271190798_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableOriginatedInCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year one</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableOriginatedInCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableOriginatedInCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Year One, Originated, Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableOriginatedInCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableOriginatedInCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableOriginatedInCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableOriginatedInCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InternalCreditAssessmentLevelTwoMember_019bffd7-5158-7bf8-a917-83e0b0fa7c7a_terseLabel_en-US" xlink:label="lab_logan_InternalCreditAssessmentLevelTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 2</link:label>
    <link:label id="lab_logan_InternalCreditAssessmentLevelTwoMember_label_en-US" xlink:label="lab_logan_InternalCreditAssessmentLevelTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment Level Two [Member]</link:label>
    <link:label id="lab_logan_InternalCreditAssessmentLevelTwoMember_documentation_en-US" xlink:label="lab_logan_InternalCreditAssessmentLevelTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment Level Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InternalCreditAssessmentLevelTwoMember" xlink:href="logan-20251231.xsd#logan_InternalCreditAssessmentLevelTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InternalCreditAssessmentLevelTwoMember" xlink:to="lab_logan_InternalCreditAssessmentLevelTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipDomain_019bffd7-515b-788f-b74e-60be0e7fafeb_terseLabel_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:label id="lab_srt_OwnershipDomain_label_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipDomain" xlink:to="lab_srt_OwnershipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FrontStreetReMember_019bffd7-515a-73d7-81d0-b96ecd2c389e_terseLabel_en-US" xlink:label="lab_logan_FrontStreetReMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Front Street Re</link:label>
    <link:label id="lab_logan_FrontStreetReMember_019c4c0b-ad60-7fb1-adde-4ce9f563d898_verboseLabel_en-US" xlink:label="lab_logan_FrontStreetReMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Front Street Re</link:label>
    <link:label id="lab_logan_FrontStreetReMember_label_en-US" xlink:label="lab_logan_FrontStreetReMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Front Street Re [Member]</link:label>
    <link:label id="lab_logan_FrontStreetReMember_documentation_en-US" xlink:label="lab_logan_FrontStreetReMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Front Street Re</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FrontStreetReMember" xlink:href="logan-20251231.xsd#logan_FrontStreetReMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FrontStreetReMember" xlink:to="lab_logan_FrontStreetReMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsMiscellaneous_019bffd7-515a-717b-ab65-58bc1b734862_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsMiscellaneous" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_OtherAssetsMiscellaneous_label_en-US" xlink:label="lab_us-gaap_OtherAssetsMiscellaneous" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Miscellaneous</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsMiscellaneous" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsMiscellaneous"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsMiscellaneous" xlink:to="lab_us-gaap_OtherAssetsMiscellaneous" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_019bffd7-5158-766c-9425-d1de3aa51aa0_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets, Goodwill, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRetentionPolicyReinsuredRiskPercentage_019bffd7-515a-78a2-8cee-5add97b56433_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRetentionPolicyReinsuredRiskPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance, reinsured risk, percentage</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRetentionPolicyReinsuredRiskPercentage_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRetentionPolicyReinsuredRiskPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance, Reinsured Risk, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRetentionPolicyReinsuredRiskPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRetentionPolicyReinsuredRiskPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRetentionPolicyReinsuredRiskPercentage" xlink:to="lab_us-gaap_ReinsuranceRetentionPolicyReinsuredRiskPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_SentinelSecurityLifeInsuranceCompanySurplusNotesMember_019bffd7-515a-738b-b8f9-95feba262efb_terseLabel_en-US" xlink:label="lab_logan_SentinelSecurityLifeInsuranceCompanySurplusNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sentinel Security Life Insurance Company</link:label>
    <link:label id="lab_logan_SentinelSecurityLifeInsuranceCompanySurplusNotesMember_label_en-US" xlink:label="lab_logan_SentinelSecurityLifeInsuranceCompanySurplusNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sentinel Security Life Insurance Company Surplus Notes [Member]</link:label>
    <link:label id="lab_logan_SentinelSecurityLifeInsuranceCompanySurplusNotesMember_documentation_en-US" xlink:label="lab_logan_SentinelSecurityLifeInsuranceCompanySurplusNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sentinel Security Life Insurance Company Surplus Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_SentinelSecurityLifeInsuranceCompanySurplusNotesMember" xlink:href="logan-20251231.xsd#logan_SentinelSecurityLifeInsuranceCompanySurplusNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_SentinelSecurityLifeInsuranceCompanySurplusNotesMember" xlink:to="lab_logan_SentinelSecurityLifeInsuranceCompanySurplusNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFiveAndThereafter_019bffd7-5159-7c54-91eb-07e63a92045b_terseLabel_en-US" xlink:label="lab_logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFiveAndThereafter" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030 and thereafter</link:label>
    <link:label id="lab_logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFiveAndThereafter_label_en-US" xlink:label="lab_logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFiveAndThereafter" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Five and Thereafter</link:label>
    <link:label id="lab_logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFiveAndThereafter_documentation_en-US" xlink:label="lab_logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFiveAndThereafter" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Five and Thereafter</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFiveAndThereafter" xlink:href="logan-20251231.xsd#logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFiveAndThereafter"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFiveAndThereafter" xlink:to="lab_logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFiveAndThereafter" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_UnpaidPrincipalBalance_019bffd7-5159-79e9-9b2c-5e13e45775a6_terseLabel_en-US" xlink:label="lab_logan_UnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unpaid Principal Balance</link:label>
    <link:label id="lab_logan_UnpaidPrincipalBalance_label_en-US" xlink:label="lab_logan_UnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unpaid Principal Balance</link:label>
    <link:label id="lab_logan_UnpaidPrincipalBalance_documentation_en-US" xlink:label="lab_logan_UnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unpaid Principal Balance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_UnpaidPrincipalBalance" xlink:href="logan-20251231.xsd#logan_UnpaidPrincipalBalance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_UnpaidPrincipalBalance" xlink:to="lab_logan_UnpaidPrincipalBalance" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_019bffd7-5157-7e84-a2f8-26504b361946_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CededCreditRiskLineItems_019bffd7-515b-77e8-a75f-2d45a2ea9d4f_terseLabel_en-US" xlink:label="lab_us-gaap_CededCreditRiskLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ceded Credit Risk [Line Items]</link:label>
    <link:label id="lab_us-gaap_CededCreditRiskLineItems_label_en-US" xlink:label="lab_us-gaap_CededCreditRiskLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ceded Credit Risk [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CededCreditRiskLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CededCreditRiskLineItems" xlink:to="lab_us-gaap_CededCreditRiskLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostsAdditions_019bffd7-515a-70dd-a7bb-8f75d437f214_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostsAdditions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capitalization</link:label>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostsAdditions_label_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostsAdditions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Cost, Capitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredPolicyAcquisitionCostsAdditions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredPolicyAcquisitionCostsAdditions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredPolicyAcquisitionCostsAdditions" xlink:to="lab_us-gaap_DeferredPolicyAcquisitionCostsAdditions" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_019bffd7-5159-7d62-8315-af6354e965d0_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Maturities of Long-Term Debt</link:label>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Maturities of Long-Term Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Revenues_019bffd7-5157-73a8-bb87-a94b5742aa59_totalLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total revenues</link:label>
    <link:label id="lab_us-gaap_Revenues_019bffd7-515b-788c-80af-808e44640f1f_terseLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total revenues</link:label>
    <link:label id="lab_us-gaap_Revenues_label_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Revenues" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Revenues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Revenues" xlink:to="lab_us-gaap_Revenues" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_label_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:to="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InterestSensitiveContractLiabilitiesFairValue_019bffd7-5159-7b5a-8a7a-70ef952d1687_terseLabel_en-US" xlink:label="lab_logan_InterestSensitiveContractLiabilitiesFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest sensitive contract liabilities</link:label>
    <link:label id="lab_logan_InterestSensitiveContractLiabilitiesFairValue_label_en-US" xlink:label="lab_logan_InterestSensitiveContractLiabilitiesFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Sensitive Contract Liabilities, Fair Value</link:label>
    <link:label id="lab_logan_InterestSensitiveContractLiabilitiesFairValue_documentation_en-US" xlink:label="lab_logan_InterestSensitiveContractLiabilitiesFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Sensitive Contract Liabilities, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InterestSensitiveContractLiabilitiesFairValue" xlink:href="logan-20251231.xsd#logan_InterestSensitiveContractLiabilitiesFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InterestSensitiveContractLiabilitiesFairValue" xlink:to="lab_logan_InterestSensitiveContractLiabilitiesFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock_019bffd7-5158-7c79-9d3f-7154e73d92dd_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financing Receivable Credit Quality Indicators</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable Credit Quality Indicators [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:to="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_019bffd7-5159-784d-a137-7f81ee16c3f0_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning Balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_019bffd7-5159-74ff-aa5b-ec816191b3fa_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending Balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_019bffd7-5159-7c5e-b089-0e2f5a0ee8c3_totalLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total financial liabilities</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InternalCreditAssessmentLevelOneMember_019bffd7-5158-719f-9f8f-a14348850514_terseLabel_en-US" xlink:label="lab_logan_InternalCreditAssessmentLevelOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 1</link:label>
    <link:label id="lab_logan_InternalCreditAssessmentLevelOneMember_label_en-US" xlink:label="lab_logan_InternalCreditAssessmentLevelOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment Level One [Member]</link:label>
    <link:label id="lab_logan_InternalCreditAssessmentLevelOneMember_documentation_en-US" xlink:label="lab_logan_InternalCreditAssessmentLevelOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment Level One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InternalCreditAssessmentLevelOneMember" xlink:href="logan-20251231.xsd#logan_InternalCreditAssessmentLevelOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InternalCreditAssessmentLevelOneMember" xlink:to="lab_logan_InternalCreditAssessmentLevelOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_019bffd7-515b-7dcc-8de5-998db05d73dc_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheOneMember_019bffd7-5158-794b-be5d-b01f1da6ce85_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tranche One</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheOneMember_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Tranche One [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationAwardTrancheOneMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationAwardTrancheOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationAwardTrancheOneMember" xlink:to="lab_us-gaap_ShareBasedCompensationAwardTrancheOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_019bffd7-5159-7a11-b131-872b0ccb048d_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants exercise price(in usd per share)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_019c3794-4ce5-7807-ad7a-48bb8ae3171f_verboseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Warrants exercise price (in canadian per share)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Exercise Price of Warrants or Rights</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:to="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock_019bffd7-5159-7eeb-83ab-98406a43a4c0_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments in Statement of Financial Position, Fair Value</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments in Statement of Financial Position, Fair Value [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardExrcPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardExrcPrice" xlink:to="lab_ecd_AwardExrcPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_019bffd7-5157-712e-8d7c-209f92e0c778_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFilerCategory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFilerCategory" xlink:to="lab_dei_EntityFilerCategory" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_019c4bef-ffa4-7b61-a54f-eb8689bfa2be_verboseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Effective income tax rate reconciliation (as a percent)</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_019bffd7-515a-75c5-bfa9-08e66e3df0ca_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax expense at statutory tax rate</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, at Federal Statutory Income Tax Rate, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_019bffd7-515b-78ad-9eb8-d3c73579395e_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeAxis" xlink:to="lab_us-gaap_SubsequentEventTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonrelatedPartyMember_019bffd7-5159-7279-84a7-f9d3a1d8a31f_terseLabel_en-US" xlink:label="lab_us-gaap_NonrelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonrelated Party</link:label>
    <link:label id="lab_us-gaap_NonrelatedPartyMember_label_en-US" xlink:label="lab_us-gaap_NonrelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonrelated Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonrelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NonrelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonrelatedPartyMember" xlink:to="lab_us-gaap_NonrelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightDomain_019bffd7-5159-7d93-8adf-21a1aea27b78_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfWarrantOrRightDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightDomain" xlink:to="lab_us-gaap_ClassOfWarrantOrRightDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_019bffd7-5159-73b8-9eae-bea7c1a07705_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesReceivableGross_019bffd7-5158-7874-aa91-663e7d047273_terseLabel_en-US" xlink:label="lab_us-gaap_NotesReceivableGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing receivable, gross</link:label>
    <link:label id="lab_us-gaap_NotesReceivableGross_019bffd7-5158-7ae0-af3e-a5372fd20b60_totalLabel_en-US" xlink:label="lab_us-gaap_NotesReceivableGross" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_NotesReceivableGross_label_en-US" xlink:label="lab_us-gaap_NotesReceivableGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesReceivableGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NotesReceivableGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesReceivableGross" xlink:to="lab_us-gaap_NotesReceivableGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VestingDomain_019bffd7-5158-73fc-824c-9d485b677da3_terseLabel_en-US" xlink:label="lab_us-gaap_VestingDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting [Domain]</link:label>
    <link:label id="lab_us-gaap_VestingDomain_label_en-US" xlink:label="lab_us-gaap_VestingDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VestingDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VestingDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VestingDomain" xlink:to="lab_us-gaap_VestingDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_019bffd7-5159-7b46-a0ce-12137c128e60_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross carrying amount</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:to="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss_019bffd7-5158-74ad-b616-ce3e5cf914a2_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Cost or amortized cost</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_StockIssuedDuringPeriodSharesInvestments_019bffd7-5158-7700-9a1c-be52ddf9206b_terseLabel_en-US" xlink:label="lab_logan_StockIssuedDuringPeriodSharesInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common shares for investment purchases (in shares)</link:label>
    <link:label id="lab_logan_StockIssuedDuringPeriodSharesInvestments_label_en-US" xlink:label="lab_logan_StockIssuedDuringPeriodSharesInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Investments</link:label>
    <link:label id="lab_logan_StockIssuedDuringPeriodSharesInvestments_documentation_en-US" xlink:label="lab_logan_StockIssuedDuringPeriodSharesInvestments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_StockIssuedDuringPeriodSharesInvestments" xlink:href="logan-20251231.xsd#logan_StockIssuedDuringPeriodSharesInvestments"/>
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    <link:label id="lab_dei_EntityAddressAddressLine1_019c2cba-fadb-7e48-a182-c2f57611f1e9_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_019bffd7-5157-7b21-b522-efb419476c9b_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_019bffd7-5158-7eab-a110-18e22f7cccf7_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accrued Liabilities and Other Operating Liabilities</link:label>
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    <link:label id="lab_logan_FinancingReceivableNonaccrualWithAnAllowance_019bffd7-5159-7851-add0-717c290c0c5d_terseLabel_en-US" xlink:label="lab_logan_FinancingReceivableNonaccrualWithAnAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonaccrual loans with an allowance</link:label>
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    <link:label id="lab_logan_FinancingReceivableNonaccrualWithAnAllowance_documentation_en-US" xlink:label="lab_logan_FinancingReceivableNonaccrualWithAnAllowance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Nonaccrual, With an Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FinancingReceivableNonaccrualWithAnAllowance" xlink:href="logan-20251231.xsd#logan_FinancingReceivableNonaccrualWithAnAllowance"/>
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    <link:label id="lab_us-gaap_InternalCreditAssessmentAxis_019bffd7-5158-7bb8-b876-3a645ca5ec9d_terseLabel_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Axis]</link:label>
    <link:label id="lab_us-gaap_InternalCreditAssessmentAxis_label_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InternalCreditAssessmentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InternalCreditAssessmentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InternalCreditAssessmentAxis" xlink:to="lab_us-gaap_InternalCreditAssessmentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Asset Acquisition, Transaction between Entities under Common Control, and Joint Venture Formation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationAndAssetAcquisitionAbstract"/>
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    <link:label id="lab_srt_OwnershipAxis_019bffd7-515b-7b8b-92a1-85413f2f62b8_terseLabel_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:label id="lab_srt_OwnershipAxis_label_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipAxis"/>
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    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationDomesticationCapitalGainPercent_019c8fb2-f05f-7763-88b4-c4db79de1d3a_terseLabel_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationDomesticationCapitalGainPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Domestication capital gain</link:label>
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    <link:label id="lab_us-gaap_InternalCreditAssessmentDomain_019bffd7-5158-76ca-a722-ecb13585e220_terseLabel_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Domain]</link:label>
    <link:label id="lab_us-gaap_InternalCreditAssessmentDomain_label_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InternalCreditAssessmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InternalCreditAssessmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InternalCreditAssessmentDomain" xlink:to="lab_us-gaap_InternalCreditAssessmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_019bffd7-5159-73c5-93eb-24a21c6b8bc0_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock"/>
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    <link:label id="lab_logan_AdministrationAndServicingFeeExpense_019bffd7-5157-7f56-b398-9e5185573cb2_terseLabel_en-US" xlink:label="lab_logan_AdministrationAndServicingFeeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administration and servicing fees</link:label>
    <link:label id="lab_logan_AdministrationAndServicingFeeExpense_label_en-US" xlink:label="lab_logan_AdministrationAndServicingFeeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Administration And Servicing Fee Expense</link:label>
    <link:label id="lab_logan_AdministrationAndServicingFeeExpense_documentation_en-US" xlink:label="lab_logan_AdministrationAndServicingFeeExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Administration And Servicing Fee Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_AdministrationAndServicingFeeExpense" xlink:href="logan-20251231.xsd#logan_AdministrationAndServicingFeeExpense"/>
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    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
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    <link:label id="lab_logan_OtherTransactionsWithBCPAOrAffiliatesMember_019bffd7-515b-757b-9a7b-837e43af4cf9_terseLabel_en-US" xlink:label="lab_logan_OtherTransactionsWithBCPAOrAffiliatesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Transactions With BCPA or Affiliates</link:label>
    <link:label id="lab_logan_OtherTransactionsWithBCPAOrAffiliatesMember_label_en-US" xlink:label="lab_logan_OtherTransactionsWithBCPAOrAffiliatesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Transactions With BCPA or Affiliates [Member]</link:label>
    <link:label id="lab_logan_OtherTransactionsWithBCPAOrAffiliatesMember_documentation_en-US" xlink:label="lab_logan_OtherTransactionsWithBCPAOrAffiliatesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Transactions With BCPA or Affiliates</link:label>
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    <link:label id="lab_logan_ManagementFeesMember_019bffd7-5157-772a-9bd0-4a76d71e3001_terseLabel_en-US" xlink:label="lab_logan_ManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Management fees</link:label>
    <link:label id="lab_logan_ManagementFeesMember_label_en-US" xlink:label="lab_logan_ManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management Fees [Member]</link:label>
    <link:label id="lab_logan_ManagementFeesMember_documentation_en-US" xlink:label="lab_logan_ManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Management Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ManagementFeesMember" xlink:href="logan-20251231.xsd#logan_ManagementFeesMember"/>
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    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitCurrentWeightedAverageDiscountRate_019bffd7-515a-76ba-b8ca-5db8ac0f620d_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitCurrentWeightedAverageDiscountRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average interest rate at current rate</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitCurrentWeightedAverageDiscountRate_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitCurrentWeightedAverageDiscountRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Current Weighted-Average Discount Rate</link:label>
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    <link:label id="lab_logan_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleListNotDisclosedFlag_019cb9a4-32fc-7880-9de0-a8580785db70_terseLabel_en-US" xlink:label="lab_logan_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleListNotDisclosedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Asset Recurring Basis Still Held Unrealized Gain Loss Statement Of Income Extensible List Not Disclosed Flag</link:label>
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    <link:label id="lab_logan_AMBestNotRatedMember_019bffd7-515b-7068-b40d-6d0f035a3737_terseLabel_en-US" xlink:label="lab_logan_AMBestNotRatedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Not Rated</link:label>
    <link:label id="lab_logan_AMBestNotRatedMember_label_en-US" xlink:label="lab_logan_AMBestNotRatedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AM Best, Not Rated [Member]</link:label>
    <link:label id="lab_logan_AMBestNotRatedMember_documentation_en-US" xlink:label="lab_logan_AMBestNotRatedMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AM Best, Not Rated</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_019bffd7-5159-75a2-9d13-2f2377c44975_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Debt Obligations</link:label>
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    <link:label id="lab_us-gaap_LaborAndRelatedExpense_019bffd7-5157-7ca1-8280-2477ae9c28b9_verboseLabel_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Compensation and benefits</link:label>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_019bffd7-515b-79e4-a6db-ca55cef7d7af_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Compensation and benefits</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LaborAndRelatedExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LaborAndRelatedExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LaborAndRelatedExpense" xlink:to="lab_us-gaap_LaborAndRelatedExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_019bffd7-515a-72b7-8524-e001c98eecf1_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Granted (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireInvestments_019bffd7-5158-7c50-ac7d-8100827066ca_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of investments</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireInvestments_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireInvestments" xlink:to="lab_us-gaap_PaymentsToAcquireInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostsAndExpenses_019c7c3d-f0af-749d-ac50-ea2914093f22_terseLabel_en-US" xlink:label="lab_us-gaap_CostsAndExpenses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total expenses</link:label>
    <link:label id="lab_us-gaap_CostsAndExpenses_label_en-US" xlink:label="lab_us-gaap_CostsAndExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Costs and Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostsAndExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostsAndExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostsAndExpenses" xlink:to="lab_us-gaap_CostsAndExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_OtherGeographicalAreasMember_019bffd7-515b-7c57-88b8-e5404105aca4_terseLabel_en-US" xlink:label="lab_logan_OtherGeographicalAreasMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_logan_OtherGeographicalAreasMember_label_en-US" xlink:label="lab_logan_OtherGeographicalAreasMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Geographical Areas [Member]</link:label>
    <link:label id="lab_logan_OtherGeographicalAreasMember_documentation_en-US" xlink:label="lab_logan_OtherGeographicalAreasMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Geographical Areas</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_OtherGeographicalAreasMember" xlink:href="logan-20251231.xsd#logan_OtherGeographicalAreasMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_OtherGeographicalAreasMember" xlink:to="lab_logan_OtherGeographicalAreasMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_019bffd7-515a-73e4-8ea8-b6ca2b201565_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Forfeitures (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Forfeited in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_019bffd7-515b-7e46-aff2-beedc86d28cf_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:to="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal_019bffd7-515a-79a0-a60e-28d2c7626519_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision for credit losses for reinsurance recoverables</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable, Credit Loss Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal" xlink:to="lab_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months_019bffd7-5158-738b-a599-d6dd63a162f0_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less than 12 months</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, Less than 12 Months</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_019bffd7-5159-7f51-8acb-f9bc70d5bc52_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt obligation</link:label>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_label_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtFairValue" xlink:to="lab_us-gaap_LongTermDebtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_019bffd7-5159-7b6f-84c5-61392042fa5f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value Measurement Inputs and Valuation Techniques</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_label_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:to="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_019bffd7-5158-7b8b-99bb-5bad517ee92d_terseLabel_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_label_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RepurchaseAgreementCounterpartyNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ClassOfWarrantOrRightPeriodNotExercisableFromIssuance_019bffd7-5159-7843-a9a7-4cfa57a638e0_terseLabel_en-US" xlink:label="lab_logan_ClassOfWarrantOrRightPeriodNotExercisableFromIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrant period, not permitted to be exercised</link:label>
    <link:label id="lab_logan_ClassOfWarrantOrRightPeriodNotExercisableFromIssuance_label_en-US" xlink:label="lab_logan_ClassOfWarrantOrRightPeriodNotExercisableFromIssuance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Period Not Exercisable From Issuance</link:label>
    <link:label id="lab_logan_ClassOfWarrantOrRightPeriodNotExercisableFromIssuance_documentation_en-US" xlink:label="lab_logan_ClassOfWarrantOrRightPeriodNotExercisableFromIssuance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Period Not Exercisable From Issuance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ClassOfWarrantOrRightPeriodNotExercisableFromIssuance" xlink:href="logan-20251231.xsd#logan_ClassOfWarrantOrRightPeriodNotExercisableFromIssuance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ClassOfWarrantOrRightPeriodNotExercisableFromIssuance" xlink:to="lab_logan_ClassOfWarrantOrRightPeriodNotExercisableFromIssuance" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FiniteLivedIntangibleAssetsAccumulatedImpairment_019bffd7-5159-7d86-a0ff-e2824ce32998_negatedTerseLabel_en-US" xlink:label="lab_logan_FiniteLivedIntangibleAssetsAccumulatedImpairment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated impairment</link:label>
    <link:label id="lab_logan_FiniteLivedIntangibleAssetsAccumulatedImpairment_label_en-US" xlink:label="lab_logan_FiniteLivedIntangibleAssetsAccumulatedImpairment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Accumulated Impairment</link:label>
    <link:label id="lab_logan_FiniteLivedIntangibleAssetsAccumulatedImpairment_documentation_en-US" xlink:label="lab_logan_FiniteLivedIntangibleAssetsAccumulatedImpairment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Accumulated Impairment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FiniteLivedIntangibleAssetsAccumulatedImpairment" xlink:href="logan-20251231.xsd#logan_FiniteLivedIntangibleAssetsAccumulatedImpairment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FiniteLivedIntangibleAssetsAccumulatedImpairment" xlink:to="lab_logan_FiniteLivedIntangibleAssetsAccumulatedImpairment" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_AdministrativeFeesExpenseAdjusted_019bffd7-515b-7266-bb2d-cf73a701ae5c_negatedTerseLabel_en-US" xlink:label="lab_logan_AdministrativeFeesExpenseAdjusted" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Administration and servicing fees</link:label>
    <link:label id="lab_logan_AdministrativeFeesExpenseAdjusted_label_en-US" xlink:label="lab_logan_AdministrativeFeesExpenseAdjusted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Administrative Fees Expense, Adjusted</link:label>
    <link:label id="lab_logan_AdministrativeFeesExpenseAdjusted_documentation_en-US" xlink:label="lab_logan_AdministrativeFeesExpenseAdjusted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Administrative Fees Expense, Adjusted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_AdministrativeFeesExpenseAdjusted" xlink:href="logan-20251231.xsd#logan_AdministrativeFeesExpenseAdjusted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_AdministrativeFeesExpenseAdjusted" xlink:to="lab_logan_AdministrativeFeesExpenseAdjusted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsAllOtherInvestmentsAbstract_019bffd7-5157-7830-afbe-2a36d7fa6397_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsAllOtherInvestmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment and other income (loss) - Asset Management</link:label>
    <link:label id="lab_us-gaap_InvestmentsAllOtherInvestmentsAbstract_label_en-US" xlink:label="lab_us-gaap_InvestmentsAllOtherInvestmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, All Other Investments [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsAllOtherInvestmentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentsAllOtherInvestmentsAbstract"/>
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    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToPeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToPeoCompFnTextBlock" xlink:to="lab_ecd_AdjToPeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedInvestmentIncomeReceivable_019bffd7-515a-7e4b-bd56-b331f2248ac4_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedInvestmentIncomeReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued investment income</link:label>
    <link:label id="lab_us-gaap_AccruedInvestmentIncomeReceivable_label_en-US" xlink:label="lab_us-gaap_AccruedInvestmentIncomeReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Investment Income Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedInvestmentIncomeReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedInvestmentIncomeReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedInvestmentIncomeReceivable" xlink:to="lab_us-gaap_AccruedInvestmentIncomeReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParent_019cd2c4-014d-7ec0-9246-60cede8431b5_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized investment gains (losses) on available-for-sale securities</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Available-for-Sale Securities Adjustment, before Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParent"/>
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    <link:label id="lab_us-gaap_Investments_019bffd7-5157-7c6c-9c3e-f17565963612_terseLabel_en-US" xlink:label="lab_us-gaap_Investments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:label id="lab_us-gaap_Investments_019bffd7-515b-7c27-9694-7f92370a40d0_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_Investments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:label id="lab_us-gaap_Investments_label_en-US" xlink:label="lab_us-gaap_Investments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Investments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Investments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Investments" xlink:to="lab_us-gaap_Investments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_StockIssuedDuringPeriodSharesIssuedToSettleDebt_019bffd7-5157-7dec-a7c6-f41be2ce9649_terseLabel_en-US" xlink:label="lab_logan_StockIssuedDuringPeriodSharesIssuedToSettleDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity based compensation (in shares)</link:label>
    <link:label id="lab_logan_StockIssuedDuringPeriodSharesIssuedToSettleDebt_label_en-US" xlink:label="lab_logan_StockIssuedDuringPeriodSharesIssuedToSettleDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares Issued to Settle Debt</link:label>
    <link:label id="lab_logan_StockIssuedDuringPeriodSharesIssuedToSettleDebt_documentation_en-US" xlink:label="lab_logan_StockIssuedDuringPeriodSharesIssuedToSettleDebt" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares Issued to Settle Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_StockIssuedDuringPeriodSharesIssuedToSettleDebt" xlink:href="logan-20251231.xsd#logan_StockIssuedDuringPeriodSharesIssuedToSettleDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_StockIssuedDuringPeriodSharesIssuedToSettleDebt" xlink:to="lab_logan_StockIssuedDuringPeriodSharesIssuedToSettleDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_019bffd7-5158-758d-b336-0337d99be993_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Businesses, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireBusinessesGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:to="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_019bffd7-5158-78af-9b14-407517d5d2f1_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit loss</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FeeIncome_019bffd7-5157-7ea6-80c8-9953afd62a59_terseLabel_en-US" xlink:label="lab_us-gaap_FeeIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fee revenue</link:label>
    <link:label id="lab_us-gaap_FeeIncome_label_en-US" xlink:label="lab_us-gaap_FeeIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fee Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FeeIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FeeIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FeeIncome" xlink:to="lab_us-gaap_FeeIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_019bffd7-515a-76b6-9d11-525b6b28eb06_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_019c7c2c-c0ed-7c91-87d0-9b6a15342657_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:to="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_019bffd7-5158-7de0-9ec0-400f87725578_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross unrealized gains</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Gain, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax"/>
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    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLosses_019bffd7-5158-7a02-b419-6158cff13836_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLosses" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLosses_019bffd7-5159-7600-bdcf-fc36dda1a088_periodStartLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLosses" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLosses_019bffd7-5159-78cc-bfe8-c7dc62f3296f_periodEndLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLosses" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLosses_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAllowanceForCreditLosses"/>
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    <link:label id="lab_us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability_019bffd7-5159-777d-9f39-b87a01ba2496_terseLabel_en-US" xlink:label="lab_us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ceded reinsurance - embedded derivative</link:label>
    <link:label id="lab_us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability_label_en-US" xlink:label="lab_us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Embedded Derivative, Fair Value of Embedded Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019bffd7-5158-7ec1-8067-aa308d45a16f_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
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    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjsMember"/>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
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    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisaggregationOfRevenueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:to="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherIncome_019bffd7-5157-7d0d-aac6-f0d10254308a_terseLabel_en-US" xlink:label="lab_us-gaap_OtherIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net investment income (loss) on funds withheld</link:label>
    <link:label id="lab_us-gaap_OtherIncome_019bffd7-5157-7e36-83cb-d288806dd846_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherIncome" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other income (loss), net</link:label>
    <link:label id="lab_us-gaap_OtherIncome_label_en-US" xlink:label="lab_us-gaap_OtherIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherIncome" xlink:to="lab_us-gaap_OtherIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_country_CA_019bffd7-515a-77e6-9cd4-df235bbc818f_terseLabel_en-US" xlink:label="lab_country_CA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Canada</link:label>
    <link:label id="lab_country_CA_label_en-US" xlink:label="lab_country_CA" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CANADA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_CA" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_CA"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_CA" xlink:to="lab_country_CA" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract_019bffd7-515a-74e5-8094-da36c842fbcc_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit), Continuing Operations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:to="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_019bffd7-5159-7e4b-9a34-6487a0fdb99f_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_019bffd7-5158-797c-8cfb-05e207f16db3_terseLabel_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value</link:label>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Estimate of Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EstimateOfFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureBenefitOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange_019bffd7-515a-722a-b28e-faae6609f3bf_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureBenefitOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Adjusted balance, beginning of year</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureBenefitOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureBenefitOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Future Benefit, Original Discount Rate, before Reinsurance, after Cash Flow Change</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureBenefitOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureBenefitOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureBenefitOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureBenefitOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReportingUnitDomain_019c77dd-785f-794e-a28f-0784da1b61a9_terseLabel_en-US" xlink:label="lab_us-gaap_ReportingUnitDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reporting Unit [Domain]</link:label>
    <link:label id="lab_us-gaap_ReportingUnitDomain_label_en-US" xlink:label="lab_us-gaap_ReportingUnitDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reporting Unit [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReportingUnitDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReportingUnitDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReportingUnitDomain" xlink:to="lab_us-gaap_ReportingUnitDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_019bffd7-5158-73d9-89f2-974ac157f70b_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year One Through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_019c7c0b-a191-72ee-9181-947cf67f9d8a_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of foreign tax rate differential</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential"/>
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    <link:label id="lab_logan_OtherInvestedAssetsFairValue_019bffd7-5159-7000-8a49-b2d1f6b41f95_terseLabel_en-US" xlink:label="lab_logan_OtherInvestedAssetsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other invested assets</link:label>
    <link:label id="lab_logan_OtherInvestedAssetsFairValue_label_en-US" xlink:label="lab_logan_OtherInvestedAssetsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Invested Assets, Fair Value</link:label>
    <link:label id="lab_logan_OtherInvestedAssetsFairValue_documentation_en-US" xlink:label="lab_logan_OtherInvestedAssetsFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Invested Assets, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_OtherInvestedAssetsFairValue" xlink:href="logan-20251231.xsd#logan_OtherInvestedAssetsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_OtherInvestedAssetsFairValue" xlink:to="lab_logan_OtherInvestedAssetsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenuesAbstract_019bffd7-5157-7fdc-ad99-160ecc055c58_terseLabel_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">REVENUES</link:label>
    <link:label id="lab_us-gaap_RevenuesAbstract_label_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenuesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenuesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenuesAbstract" xlink:to="lab_us-gaap_RevenuesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentsIncorporatedByReferenceTextBlock_019c7b3d-7013-7670-bd4a-02402893697a_terseLabel_en-US" xlink:label="lab_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Documents Incorporated by Reference</link:label>
    <link:label id="lab_dei_DocumentsIncorporatedByReferenceTextBlock_label_en-US" xlink:label="lab_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Documents Incorporated by Reference [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentsIncorporatedByReferenceTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:to="lab_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_019bffd7-5158-71b9-8a4d-7fd25d861f3e_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitActivityTableTextBlock_019bffd7-515a-7c23-a157-888c28510a80_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Activity</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitActivityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Activity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitActivityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitActivityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitActivityTableTextBlock" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitActivityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions_019bffd7-5158-7cb6-bc91-b592a56510d0_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AFS securities with continuous loss position for more than 12 months (security)</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, 12 Months or Longer, Number of Positions</link:label>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_019bffd7-5157-708f-ba9b-3b99ba9cf8bd_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive income (loss)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
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    <link:label id="lab_us-gaap_GoodwillGross_label_en-US" xlink:label="lab_us-gaap_GoodwillGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillGross" xlink:to="lab_us-gaap_GoodwillGross" xlink:type="arc" order="1"/>
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    <link:label id="lab_logan_ScheduleOfDeferredAcquisitionCostFutureAmortizationExpenseTableTextBlock_label_en-US" xlink:label="lab_logan_ScheduleOfDeferredAcquisitionCostFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Deferred Acquisition Cost Future Amortization Expense [Table Text Block]</link:label>
    <link:label id="lab_logan_ScheduleOfDeferredAcquisitionCostFutureAmortizationExpenseTableTextBlock_documentation_en-US" xlink:label="lab_logan_ScheduleOfDeferredAcquisitionCostFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule Of Deferred Acquisition Cost Future Amortization Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ScheduleOfDeferredAcquisitionCostFutureAmortizationExpenseTableTextBlock" xlink:href="logan-20251231.xsd#logan_ScheduleOfDeferredAcquisitionCostFutureAmortizationExpenseTableTextBlock"/>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_019bffd7-5159-708f-8cf1-b44c09be1cc5_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths"/>
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    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_019bffd7-5158-7057-8820-fd0a8cc33b41_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
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    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_019bffd7-515a-757f-94cd-c7fe4123ecaa_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Total deferred tax liabilities</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxLiabilities" xlink:to="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_019bffd7-5159-7166-99e2-65cc89a4352a_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchases</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_019c7bd7-e641-784b-b89f-7aa86b2632b7_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive"/>
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    <link:label id="lab_us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTableTextBlock_019bffd7-5159-7db1-b240-9cdb0235480e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Indefinite-Lived Intangible Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Indefinite-Lived Intangible Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTableTextBlock"/>
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    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtPnsnAdjsSvcCstMember"/>
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    <link:label id="lab_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_019bffd7-5158-758c-b2e3-559e5385b6d3_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Investment Income [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Investment Income [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems"/>
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    <link:label id="lab_logan_ValuationTechniqueVolatilityMember_label_en-US" xlink:label="lab_logan_ValuationTechniqueVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Volatility [Member]</link:label>
    <link:label id="lab_logan_ValuationTechniqueVolatilityMember_documentation_en-US" xlink:label="lab_logan_ValuationTechniqueVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Valuation Technique, Volatility</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_019bffd7-5159-70b8-bad3-20e35d8dfae7_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis"/>
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    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
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    <link:label id="lab_us-gaap_RepaymentsOfNotesPayable_019c4c63-1021-705d-8e9e-cad393bb2b88_terseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfNotesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repayments of notes payable</link:label>
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    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange_019c52ea-b86c-7607-bf35-e25f7c5f5d40_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Adjusted balance</link:label>
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    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
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    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_019bffd7-5159-7189-9723-acfccd5a803f_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt obligations</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSaleOfInvestments_019bffd7-5157-7a75-8d28-2908ce3b82bb_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net gains (losses) from investment activities</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfInvestments_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Sale of Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSaleOfInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnSaleOfInvestments" xlink:to="lab_us-gaap_GainLossOnSaleOfInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ArrangementWarrantsMember_019bffd7-515a-7cda-aded-05c65e574994_terseLabel_en-US" xlink:label="lab_logan_ArrangementWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Warrants</link:label>
    <link:label id="lab_logan_ArrangementWarrantsMember_label_en-US" xlink:label="lab_logan_ArrangementWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Arrangement Warrants [Member]</link:label>
    <link:label id="lab_logan_ArrangementWarrantsMember_documentation_en-US" xlink:label="lab_logan_ArrangementWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Arrangement Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ArrangementWarrantsMember" xlink:href="logan-20251231.xsd#logan_ArrangementWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ArrangementWarrantsMember" xlink:to="lab_logan_ArrangementWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AociLiabilityForFuturePolicyBenefitParentMember_019bffd7-515a-7a85-a939-1840590f5fa8_terseLabel_en-US" xlink:label="lab_us-gaap_AociLiabilityForFuturePolicyBenefitParentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remeasurement gains (losses) on future policy benefits related to discount rate</link:label>
    <link:label id="lab_us-gaap_AociLiabilityForFuturePolicyBenefitParentMember_label_en-US" xlink:label="lab_us-gaap_AociLiabilityForFuturePolicyBenefitParentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI, Liability for Future Policy Benefit, Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AociLiabilityForFuturePolicyBenefitParentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AociLiabilityForFuturePolicyBenefitParentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AociLiabilityForFuturePolicyBenefitParentMember" xlink:to="lab_us-gaap_AociLiabilityForFuturePolicyBenefitParentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CurrentForeignTaxExpenseBenefit_019bffd7-515a-761c-a748-bbe71c10e490_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign</link:label>
    <link:label id="lab_us-gaap_CurrentForeignTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Foreign Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentForeignTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:to="lab_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillRollForward_019bffd7-5159-71f9-b10c-4e0612c69fe3_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_GoodwillRollForward_label_en-US" xlink:label="lab_us-gaap_GoodwillRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillRollForward" xlink:to="lab_us-gaap_GoodwillRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseCurrentAndFiveSucceedingFiscalYearsAbstract_019bffd7-5159-7a76-b2cc-4104d8309c65_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseCurrentAndFiveSucceedingFiscalYearsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization Expense, Maturity Schedule</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseCurrentAndFiveSucceedingFiscalYearsAbstract_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseCurrentAndFiveSucceedingFiscalYearsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Amortization Expense, Maturity Schedule [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseCurrentAndFiveSucceedingFiscalYearsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseCurrentAndFiveSucceedingFiscalYearsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseCurrentAndFiveSucceedingFiscalYearsAbstract" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseCurrentAndFiveSucceedingFiscalYearsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_019bffd7-515b-71e8-8410-48e621550b07_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitRollForward_019bffd7-515a-7886-aa3c-2cc7594e47f2_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Present value of Expected Future Policy Benefits</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitRollForward_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Future Policy Benefit [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitRollForward" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember_019bffd7-5158-76d0-b875-ce20b3e61933_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tranche Two</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Tranche Two [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationAwardTrancheTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:to="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019bffd7-5157-7147-823c-75daefe213b1_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average shares outstanding &#8211; Diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019c4640-8fd0-7adc-99fd-1002bd95f50d_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average number of diluted common shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_label_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonGaapMeasureDescriptionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:to="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_SingleLargestInvestmentMember_019bffd7-5158-7584-bf22-fca10de726e8_terseLabel_en-US" xlink:label="lab_logan_SingleLargestInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Single Largest Investment</link:label>
    <link:label id="lab_logan_SingleLargestInvestmentMember_label_en-US" xlink:label="lab_logan_SingleLargestInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Single Largest Investment [Member]</link:label>
    <link:label id="lab_logan_SingleLargestInvestmentMember_documentation_en-US" xlink:label="lab_logan_SingleLargestInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Single Largest Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_SingleLargestInvestmentMember" xlink:href="logan-20251231.xsd#logan_SingleLargestInvestmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_SingleLargestInvestmentMember" xlink:to="lab_logan_SingleLargestInvestmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeTable_019bffd7-5159-7174-93b5-de53a82396b9_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:label id="lab_us-gaap_DerivativeTable_label_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeTable" xlink:to="lab_us-gaap_DerivativeTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitActivityLineItems_019bffd7-515a-775a-8c61-c505b9f14568_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitActivityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Activity [Line Items]</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitActivityLineItems_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitActivityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Activity [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitActivityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitActivityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitActivityLineItems" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitActivityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ClassOfWarrantOrRightExercisablePeriod_019bffd7-5159-71f9-b71c-c0c8fd2e094e_terseLabel_en-US" xlink:label="lab_logan_ClassOfWarrantOrRightExercisablePeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrant exercise period</link:label>
    <link:label id="lab_logan_ClassOfWarrantOrRightExercisablePeriod_label_en-US" xlink:label="lab_logan_ClassOfWarrantOrRightExercisablePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Exercisable Period</link:label>
    <link:label id="lab_logan_ClassOfWarrantOrRightExercisablePeriod_documentation_en-US" xlink:label="lab_logan_ClassOfWarrantOrRightExercisablePeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Exercisable Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ClassOfWarrantOrRightExercisablePeriod" xlink:href="logan-20251231.xsd#logan_ClassOfWarrantOrRightExercisablePeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ClassOfWarrantOrRightExercisablePeriod" xlink:to="lab_logan_ClassOfWarrantOrRightExercisablePeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_019bffd7-5157-7013-a39e-ce4552e043e3_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_019bffd7-5158-713e-8fb0-a806690653ca_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity interest acquired, percentage</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_019bffd7-5158-7660-9999-3b2c6e15846b_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Percentage Ownership</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Voting Equity Interest Acquired, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:to="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:to="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_MLCSCMember_019bffd7-515b-7df8-8602-d1d1f852436d_terseLabel_en-US" xlink:label="lab_logan_MLCSCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MLCSC</link:label>
    <link:label id="lab_logan_MLCSCMember_label_en-US" xlink:label="lab_logan_MLCSCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MLCSC [Member]</link:label>
    <link:label id="lab_logan_MLCSCMember_documentation_en-US" xlink:label="lab_logan_MLCSCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">MLCSC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_MLCSCMember" xlink:href="logan-20251231.xsd#logan_MLCSCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_MLCSCMember" xlink:to="lab_logan_MLCSCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_TURNMember_019bffd7-5158-758d-916c-6f699c53c296_terseLabel_en-US" xlink:label="lab_logan_TURNMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">TURN shareholders</link:label>
    <link:label id="lab_logan_TURNMember_label_en-US" xlink:label="lab_logan_TURNMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">TURN [Member]</link:label>
    <link:label id="lab_logan_TURNMember_documentation_en-US" xlink:label="lab_logan_TURNMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">TURN</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_TURNMember" xlink:href="logan-20251231.xsd#logan_TURNMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_TURNMember" xlink:to="lab_logan_TURNMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_StaffingAndResourceAgreementMember_019cf4aa-c13a-7135-a6eb-c80396ab64b6_terseLabel_en-US" xlink:label="lab_logan_StaffingAndResourceAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Staffing and Resource Agreement</link:label>
    <link:label id="lab_logan_StaffingAndResourceAgreementMember_label_en-US" xlink:label="lab_logan_StaffingAndResourceAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Staffing And Resource Agreement [Member]</link:label>
    <link:label id="lab_logan_StaffingAndResourceAgreementMember_documentation_en-US" xlink:label="lab_logan_StaffingAndResourceAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Staffing And Resource Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_StaffingAndResourceAgreementMember" xlink:href="logan-20251231.xsd#logan_StaffingAndResourceAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_StaffingAndResourceAgreementMember" xlink:to="lab_logan_StaffingAndResourceAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit_019cf498-1311-7deb-aa0d-8dcc41a526d7_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State</link:label>
    <link:label id="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current State and Local Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentStateAndLocalTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:to="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFiveAndThereafter_019bffd7-5158-7452-b051-d2da97552f69_terseLabel_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFiveAndThereafter" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2031 and thereafter</link:label>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFiveAndThereafter_label_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFiveAndThereafter" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss, Maturity Year Five and Thereafter</link:label>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFiveAndThereafter_documentation_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFiveAndThereafter" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss, Maturity Year Five and Thereafter</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFiveAndThereafter" xlink:href="logan-20251231.xsd#logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFiveAndThereafter"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFiveAndThereafter" xlink:to="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFiveAndThereafter" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_019c2cb5-ff04-73a1-baf9-9bc429faaa88_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_019bffd7-5158-7d76-a3ee-fa6d65f2cd2a_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year One Through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_CapitalaAcquisitionMember_019bffd7-515b-7ee4-bce1-54d756478c0c_terseLabel_en-US" xlink:label="lab_logan_CapitalaAcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capitala Acquisition</link:label>
    <link:label id="lab_logan_CapitalaAcquisitionMember_label_en-US" xlink:label="lab_logan_CapitalaAcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capitala Acquisition [Member]</link:label>
    <link:label id="lab_logan_CapitalaAcquisitionMember_documentation_en-US" xlink:label="lab_logan_CapitalaAcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Capitala Acquisition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_CapitalaAcquisitionMember" xlink:href="logan-20251231.xsd#logan_CapitalaAcquisitionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_CapitalaAcquisitionMember" xlink:to="lab_logan_CapitalaAcquisitionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock_019bffd7-515b-70fa-9f97-00327ace3410_terseLabel_en-US" xlink:label="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedules of investment concentration risk</link:label>
    <link:label id="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock_label_en-US" xlink:label="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedules of Concentration of Risk, by Risk Factor [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:to="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_terseLabel_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Securities</link:label>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_label_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Underlying Securities Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardUndrlygSecuritiesAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:to="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_019bffd7-5157-7a9d-b3f8-0ea7e6e5bc8e_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_019c2cb5-32e3-7c4f-8176-dbd09397889c_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentPeriodEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentPeriodEndDate" xlink:to="lab_dei_DocumentPeriodEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumCumulativeIncreaseDecreaseFromCashFlowChange_019bffd7-515a-74ba-873d-21daec70c161_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumCumulativeIncreaseDecreaseFromCashFlowChange" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in effect in cashflow assumptions</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumCumulativeIncreaseDecreaseFromCashFlowChange_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumCumulativeIncreaseDecreaseFromCashFlowChange" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Net Premium, Cumulative Increase (Decrease) from Cash Flow Change</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumCumulativeIncreaseDecreaseFromCashFlowChange" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumCumulativeIncreaseDecreaseFromCashFlowChange"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumCumulativeIncreaseDecreaseFromCashFlowChange" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumCumulativeIncreaseDecreaseFromCashFlowChange" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_019bffd7-515a-721a-9c22-61e19fa874b7_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:to="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_RevenuesAdjusted_019bffd7-515b-7f6a-8455-31c024fcc6bf_terseLabel_en-US" xlink:label="lab_logan_RevenuesAdjusted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenues, adjusted</link:label>
    <link:label id="lab_logan_RevenuesAdjusted_label_en-US" xlink:label="lab_logan_RevenuesAdjusted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues, Adjusted</link:label>
    <link:label id="lab_logan_RevenuesAdjusted_documentation_en-US" xlink:label="lab_logan_RevenuesAdjusted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenues, Adjusted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_RevenuesAdjusted" xlink:href="logan-20251231.xsd#logan_RevenuesAdjusted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_RevenuesAdjusted" xlink:to="lab_logan_RevenuesAdjusted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitInterestExpense_019bffd7-515a-772c-a1ae-26dbabb1cefa_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitInterestExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest accrual</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitInterestExpense_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitInterestExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Future Policy Benefit, Interest Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitInterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitInterestExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitInterestExpense" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitInterestExpense" xlink:type="arc" order="1"/>
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    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearOne_documentation_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearOne" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense, Year One</link:label>
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    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_CapitalizationOfDeferredPolicyAcquisitionCostsPolicy_019bffd7-5158-7848-8603-50103b0ac8a1_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalizationOfDeferredPolicyAcquisitionCostsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred acquisition costs ("DAC")</link:label>
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    <link:label id="lab_logan_LaborAndRelatedExpenseAdjusted_label_en-US" xlink:label="lab_logan_LaborAndRelatedExpenseAdjusted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Labor And Related Expense, Adjusted</link:label>
    <link:label id="lab_logan_LaborAndRelatedExpenseAdjusted_documentation_en-US" xlink:label="lab_logan_LaborAndRelatedExpenseAdjusted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Labor And Related Expense, Adjusted</link:label>
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    <link:label id="lab_us-gaap_RisksAndUncertaintiesAbstract_label_en-US" xlink:label="lab_us-gaap_RisksAndUncertaintiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Risks and Uncertainties [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RisksAndUncertaintiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RisksAndUncertaintiesAbstract"/>
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    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet_019bffd7-5159-7f29-b1d6-5e69974249a3_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage loans</link:label>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet_label_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans on Real Estate, Commercial and Consumer, Net</link:label>
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    <link:label id="lab_dei_DocumentType_019bffd7-5157-7fb3-963b-40a04f78c079_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_019bffd7-5159-78ab-9377-3a6558d43862_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 3</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableforSaleUnrealizedLossPositionAbstract_019bffd7-5158-749c-b644-e722e2dcd7f8_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableforSaleUnrealizedLossPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair&#160;value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableforSaleUnrealizedLossPositionAbstract_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableforSaleUnrealizedLossPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Loss Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableforSaleUnrealizedLossPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableforSaleUnrealizedLossPositionAbstract"/>
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    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_019bffd7-515b-798e-be42-ca611b511775_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings per share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Text Block]</link:label>
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    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
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    <link:label id="lab_us-gaap_AdditionalPaidInCapital_019bffd7-5157-7f92-b0d9-79a2cf498cc5_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in-capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapital" xlink:to="lab_us-gaap_AdditionalPaidInCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductOrServiceAxis_019bffd7-5157-7336-bb85-bae65f6ba645_terseLabel_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:label id="lab_srt_ProductOrServiceAxis_label_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductOrServiceAxis"/>
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    <link:label id="lab_us-gaap_AssetAcquisitionDomain_019bffd7-515b-7742-83b2-3c29ce5e74b3_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Domain]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionDomain_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionDomain"/>
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    <link:label id="lab_us-gaap_CededCreditRiskReinsurerDomain_label_en-US" xlink:label="lab_us-gaap_CededCreditRiskReinsurerDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurer, Name [Domain]</link:label>
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    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer, Excluding Assessed Tax</link:label>
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    <link:label id="lab_us-gaap_AssumedPremiumsEarned_label_en-US" xlink:label="lab_us-gaap_AssumedPremiumsEarned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assumed Premiums Earned</link:label>
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    <link:label id="lab_logan_FinancingReceivableCollateralDependentLoans_label_en-US" xlink:label="lab_logan_FinancingReceivableCollateralDependentLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Collateral Dependent Loans</link:label>
    <link:label id="lab_logan_FinancingReceivableCollateralDependentLoans_documentation_en-US" xlink:label="lab_logan_FinancingReceivableCollateralDependentLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Collateral Dependent Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FinancingReceivableCollateralDependentLoans" xlink:href="logan-20251231.xsd#logan_FinancingReceivableCollateralDependentLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FinancingReceivableCollateralDependentLoans" xlink:to="lab_logan_FinancingReceivableCollateralDependentLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_019bffd7-5158-77db-abf6-280b3e345a17_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StockRepurchaseProgramAuthorizedAmount1_019caddc-0da0-7a3e-8463-3418ac007089_terseLabel_en-US" xlink:label="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share repurchase program, authorized, amount</link:label>
    <link:label id="lab_srt_StockRepurchaseProgramAuthorizedAmount1_label_en-US" xlink:label="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program, Authorized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StockRepurchaseProgramAuthorizedAmount1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:to="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FinancingReceivableCreditLossExpenseReversalNet_019bffd7-5158-7520-88c3-ba614110bdb5_terseLabel_en-US" xlink:label="lab_logan_FinancingReceivableCreditLossExpenseReversalNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (decrease) in estimated credit losses</link:label>
    <link:label id="lab_logan_FinancingReceivableCreditLossExpenseReversalNet_label_en-US" xlink:label="lab_logan_FinancingReceivableCreditLossExpenseReversalNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Loss, Expense (Reversal), Net</link:label>
    <link:label id="lab_logan_FinancingReceivableCreditLossExpenseReversalNet_documentation_en-US" xlink:label="lab_logan_FinancingReceivableCreditLossExpenseReversalNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Loss, Expense (Reversal), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FinancingReceivableCreditLossExpenseReversalNet" xlink:href="logan-20251231.xsd#logan_FinancingReceivableCreditLossExpenseReversalNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FinancingReceivableCreditLossExpenseReversalNet" xlink:to="lab_logan_FinancingReceivableCreditLossExpenseReversalNet" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_UnsecuredNotesDueJanuary2031Member_019c7c33-8c9f-70b5-8231-d07363f8d6d7_terseLabel_en-US" xlink:label="lab_logan_UnsecuredNotesDueJanuary2031Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured Notes Due January 2031</link:label>
    <link:label id="lab_logan_UnsecuredNotesDueJanuary2031Member_label_en-US" xlink:label="lab_logan_UnsecuredNotesDueJanuary2031Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Notes Due January 2031 [Member]</link:label>
    <link:label id="lab_logan_UnsecuredNotesDueJanuary2031Member_documentation_en-US" xlink:label="lab_logan_UnsecuredNotesDueJanuary2031Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unsecured Notes Due January 2031</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_UnsecuredNotesDueJanuary2031Member" xlink:href="logan-20251231.xsd#logan_UnsecuredNotesDueJanuary2031Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_UnsecuredNotesDueJanuary2031Member" xlink:to="lab_logan_UnsecuredNotesDueJanuary2031Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitCumulativeIncreaseDecreaseFromCashFlowChange_019bffd7-515a-79a1-bcda-7b3322c34c57_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitCumulativeIncreaseDecreaseFromCashFlowChange" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of foreign currency</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitCumulativeIncreaseDecreaseFromCashFlowChange_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitCumulativeIncreaseDecreaseFromCashFlowChange" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Future Policy Benefit, Cumulative Increase (Decrease) from Cash Flow Change</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitCumulativeIncreaseDecreaseFromCashFlowChange" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitCumulativeIncreaseDecreaseFromCashFlowChange"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitCumulativeIncreaseDecreaseFromCashFlowChange" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitCumulativeIncreaseDecreaseFromCashFlowChange" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ProceedsReceivedFromReverseAcquisitionOfBusiness_019bffd7-5158-7a27-bb92-3d2e0340e4b1_terseLabel_en-US" xlink:label="lab_logan_ProceedsReceivedFromReverseAcquisitionOfBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds received from reverse acquisition of business</link:label>
    <link:label id="lab_logan_ProceedsReceivedFromReverseAcquisitionOfBusiness_label_en-US" xlink:label="lab_logan_ProceedsReceivedFromReverseAcquisitionOfBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds Received From Reverse Acquisition Of Business</link:label>
    <link:label id="lab_logan_ProceedsReceivedFromReverseAcquisitionOfBusiness_documentation_en-US" xlink:label="lab_logan_ProceedsReceivedFromReverseAcquisitionOfBusiness" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds Received From Reverse Acquisition Of Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ProceedsReceivedFromReverseAcquisitionOfBusiness" xlink:href="logan-20251231.xsd#logan_ProceedsReceivedFromReverseAcquisitionOfBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ProceedsReceivedFromReverseAcquisitionOfBusiness" xlink:to="lab_logan_ProceedsReceivedFromReverseAcquisitionOfBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_019bffd7-5159-7504-9195-fce3bbaea3df_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ScheduleOfCollateralDependentLoansTableTextBlock_019bffd7-5158-79bf-97af-8929787e6daa_terseLabel_en-US" xlink:label="lab_logan_ScheduleOfCollateralDependentLoansTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Collateral Dependent Loans</link:label>
    <link:label id="lab_logan_ScheduleOfCollateralDependentLoansTableTextBlock_label_en-US" xlink:label="lab_logan_ScheduleOfCollateralDependentLoansTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Collateral Dependent Loans [Table Text Block]</link:label>
    <link:label id="lab_logan_ScheduleOfCollateralDependentLoansTableTextBlock_documentation_en-US" xlink:label="lab_logan_ScheduleOfCollateralDependentLoansTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Collateral Dependent Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ScheduleOfCollateralDependentLoansTableTextBlock" xlink:href="logan-20251231.xsd#logan_ScheduleOfCollateralDependentLoansTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ScheduleOfCollateralDependentLoansTableTextBlock" xlink:to="lab_logan_ScheduleOfCollateralDependentLoansTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ProbabilityWeightedExpectedReturnMethodDependentProbabilitiesMember_019bffd7-5159-7882-92c0-341628978bfe_terseLabel_en-US" xlink:label="lab_logan_ProbabilityWeightedExpectedReturnMethodDependentProbabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Probability-Weighted Expected Return Method Dependent Probabilities</link:label>
    <link:label id="lab_logan_ProbabilityWeightedExpectedReturnMethodDependentProbabilitiesMember_label_en-US" xlink:label="lab_logan_ProbabilityWeightedExpectedReturnMethodDependentProbabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Probability-Weighted Expected Return Method Dependent Probabilities [Member]</link:label>
    <link:label id="lab_logan_ProbabilityWeightedExpectedReturnMethodDependentProbabilitiesMember_documentation_en-US" xlink:label="lab_logan_ProbabilityWeightedExpectedReturnMethodDependentProbabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Probability-Weighted Expected Return Method Dependent Probabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ProbabilityWeightedExpectedReturnMethodDependentProbabilitiesMember" xlink:href="logan-20251231.xsd#logan_ProbabilityWeightedExpectedReturnMethodDependentProbabilitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ProbabilityWeightedExpectedReturnMethodDependentProbabilitiesMember" xlink:to="lab_logan_ProbabilityWeightedExpectedReturnMethodDependentProbabilitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfOtherAssetsTableTextBlock_019bffd7-515a-7988-ae1c-20aef947b224_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfOtherAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Other Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleOfOtherAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfOtherAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Other Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfOtherAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfOtherAssetsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfOtherAssetsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfOtherAssetsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_CorporateLoansMember_019bffd7-5158-72a9-9047-245048f406c1_terseLabel_en-US" xlink:label="lab_logan_CorporateLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate loans</link:label>
    <link:label id="lab_logan_CorporateLoansMember_label_en-US" xlink:label="lab_logan_CorporateLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Corporate Loans [Member]</link:label>
    <link:label id="lab_logan_CorporateLoansMember_documentation_en-US" xlink:label="lab_logan_CorporateLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Corporate Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_CorporateLoansMember" xlink:href="logan-20251231.xsd#logan_CorporateLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_CorporateLoansMember" xlink:to="lab_logan_CorporateLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:to="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ReinsuranceRecoverableNetCreditExposure_019bffd7-515b-7028-837f-2f82d1da62f3_terseLabel_en-US" xlink:label="lab_logan_ReinsuranceRecoverableNetCreditExposure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net reinsurance credit exposure</link:label>
    <link:label id="lab_logan_ReinsuranceRecoverableNetCreditExposure_label_en-US" xlink:label="lab_logan_ReinsuranceRecoverableNetCreditExposure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable, Net Credit Exposure</link:label>
    <link:label id="lab_logan_ReinsuranceRecoverableNetCreditExposure_documentation_en-US" xlink:label="lab_logan_ReinsuranceRecoverableNetCreditExposure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable, Net Credit Exposure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ReinsuranceRecoverableNetCreditExposure" xlink:href="logan-20251231.xsd#logan_ReinsuranceRecoverableNetCreditExposure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ReinsuranceRecoverableNetCreditExposure" xlink:to="lab_logan_ReinsuranceRecoverableNetCreditExposure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_019bffd7-5157-7986-8c59-628a7e454849_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionSharePrice_019bffd7-5158-7bb0-8e0f-990d7ee2d587_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionSharePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share price (in usd per share)</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionSharePrice_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionSharePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionSharePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionSharePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionSharePrice" xlink:to="lab_us-gaap_BusinessAcquisitionSharePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_019bffd7-5159-7ecb-9f5e-2ae6010ec440_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 1</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InternalCreditAssessmentLevelThreeMember_019bffd7-5158-76dd-a7b2-4da23ca40327_terseLabel_en-US" xlink:label="lab_logan_InternalCreditAssessmentLevelThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 3</link:label>
    <link:label id="lab_logan_InternalCreditAssessmentLevelThreeMember_label_en-US" xlink:label="lab_logan_InternalCreditAssessmentLevelThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment Level Three [Member]</link:label>
    <link:label id="lab_logan_InternalCreditAssessmentLevelThreeMember_documentation_en-US" xlink:label="lab_logan_InternalCreditAssessmentLevelThreeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment Level Three</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_019bffd7-515b-75f5-bcb4-2f226e554220_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
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    <link:label id="lab_us-gaap_EarningsPerShareDiluted_019c4640-bdda-784e-8c2f-1cccabafd1a2_verboseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Diluted earnings (loss) per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareDiluted"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_019bffd7-5158-7494-8e72-e3c2ae65c3aa_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through ten years</link:label>
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    <link:label id="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward_019c379b-6d9c-73d9-9731-8fc984219752_terseLabel_en-US" xlink:label="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent, Net of Tax [Roll Forward]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AOCIAttributableToParentNetOfTaxRollForward"/>
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    <link:label id="lab_logan_ProceedsFromBorrowingsOfAssetManagementBusiness_019bffd7-5158-7dd0-8172-42eddcc138c4_terseLabel_en-US" xlink:label="lab_logan_ProceedsFromBorrowingsOfAssetManagementBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from borrowings of asset management business</link:label>
    <link:label id="lab_logan_ProceedsFromBorrowingsOfAssetManagementBusiness_label_en-US" xlink:label="lab_logan_ProceedsFromBorrowingsOfAssetManagementBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Borrowings Of Asset Management Business</link:label>
    <link:label id="lab_logan_ProceedsFromBorrowingsOfAssetManagementBusiness_documentation_en-US" xlink:label="lab_logan_ProceedsFromBorrowingsOfAssetManagementBusiness" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Borrowings Of Asset Management Business</link:label>
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    <link:label id="lab_logan_DeferredTaxAssetsTaxBenefitOfExpenditurePools_019bffd7-515a-7084-adb7-e1f1df67b78d_terseLabel_en-US" xlink:label="lab_logan_DeferredTaxAssetsTaxBenefitOfExpenditurePools" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tax benefit of expenditure pools</link:label>
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    <link:label id="lab_logan_DeferredTaxAssetsTaxBenefitOfExpenditurePools_documentation_en-US" xlink:label="lab_logan_DeferredTaxAssetsTaxBenefitOfExpenditurePools" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Tax Benefit Of Expenditure Pools</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DeferredTaxAssetsTaxBenefitOfExpenditurePools" xlink:href="logan-20251231.xsd#logan_DeferredTaxAssetsTaxBenefitOfExpenditurePools"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DeferredTaxAssetsTaxBenefitOfExpenditurePools" xlink:to="lab_logan_DeferredTaxAssetsTaxBenefitOfExpenditurePools" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_019c7c28-9792-726c-9d26-21b82a081966_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of stock, number of shares issued in transaction (in shares)</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Number of Shares Issued in Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:to="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_country_KY_019bffd7-515b-7c96-87d9-1e86fed20783_terseLabel_en-US" xlink:label="lab_country_KY" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cayman Islands</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_country_KY" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_KY"/>
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    <link:label id="lab_us-gaap_PolicyholderAccountBalanceTable_019bffd7-515a-7cdc-a4be-38f6597ad7f0_terseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance [Table]</link:label>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceTable_label_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderAccountBalanceTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderAccountBalanceTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyholderAccountBalanceTable" xlink:to="lab_us-gaap_PolicyholderAccountBalanceTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceAccountingPolicy_019bffd7-5158-7f06-b485-b45d4de381ef_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceAccountingPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance</link:label>
    <link:label id="lab_us-gaap_ReinsuranceAccountingPolicy_label_en-US" xlink:label="lab_us-gaap_ReinsuranceAccountingPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Accounting Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceAccountingPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceAccountingPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceAccountingPolicy" xlink:to="lab_us-gaap_ReinsuranceAccountingPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherAccountsPayable_019bffd7-5158-7a43-9bd0-70f8fbbd9ac0_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherAccountsPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due to related parties</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherAccountsPayable" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherAccountsPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodFairValue_019bffd7-515a-7710-b01a-81bb01ba1f3f_terseLabel_en-US" xlink:label="lab_logan_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value</link:label>
    <link:label id="lab_logan_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodFairValue_label_en-US" xlink:label="lab_logan_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants In Period, Fair Value</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived_019c7c1d-d183-7077-892c-fd641452332f_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State and Local</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, State and Local, after Refund Received</link:label>
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    <link:label id="lab_srt_ConsolidationItemsDomain_label_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
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    <link:label id="lab_us-gaap_SeniorDebtObligationsMember_019bffd7-5158-7a4b-8b06-2f4fc9ffd4a2_terseLabel_en-US" xlink:label="lab_us-gaap_SeniorDebtObligationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt obligation</link:label>
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    <link:label id="lab_logan_First10YearsMember_documentation_en-US" xlink:label="lab_logan_First10YearsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">First 10 Years</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_First10YearsMember" xlink:href="logan-20251231.xsd#logan_First10YearsMember"/>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:to="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AuditorLocation_019cfdb5-09ac-7c28-8607-2244b001dedb_terseLabel_en-US" xlink:label="lab_dei_AuditorLocation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Location</link:label>
    <link:label id="lab_dei_AuditorLocation_label_en-US" xlink:label="lab_dei_AuditorLocation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Location</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorLocation" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AuditorLocation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AuditorLocation" xlink:to="lab_dei_AuditorLocation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember_019bffd7-5159-7360-8181-3e0d5320efec_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Not Primary Beneficiary</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Not Primary Beneficiary [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:to="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CededCreditRiskAxis_019bffd7-515a-7da6-b1c9-807f23a23b2c_terseLabel_en-US" xlink:label="lab_us-gaap_CededCreditRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurer, Name [Axis]</link:label>
    <link:label id="lab_us-gaap_CededCreditRiskAxis_label_en-US" xlink:label="lab_us-gaap_CededCreditRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurer, Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CededCreditRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CededCreditRiskAxis" xlink:to="lab_us-gaap_CededCreditRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DeferredCostsCapitalizedPrepaidAndOtherAssetsAndLiabilitiesDisclosureAbstract_label_en-US" xlink:label="lab_logan_DeferredCostsCapitalizedPrepaidAndOtherAssetsAndLiabilitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Costs, Capitalized, Prepaid, and Other Assets And Liabilities Disclosure [Abstract]</link:label>
    <link:label id="lab_logan_DeferredCostsCapitalizedPrepaidAndOtherAssetsAndLiabilitiesDisclosureAbstract_documentation_en-US" xlink:label="lab_logan_DeferredCostsCapitalizedPrepaidAndOtherAssetsAndLiabilitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Costs, Capitalized, Prepaid, and Other Assets And Liabilities Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DeferredCostsCapitalizedPrepaidAndOtherAssetsAndLiabilitiesDisclosureAbstract" xlink:href="logan-20251231.xsd#logan_DeferredCostsCapitalizedPrepaidAndOtherAssetsAndLiabilitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DeferredCostsCapitalizedPrepaidAndOtherAssetsAndLiabilitiesDisclosureAbstract" xlink:to="lab_logan_DeferredCostsCapitalizedPrepaidAndOtherAssetsAndLiabilitiesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue_019bffd7-5157-7d9c-b88a-a02f8cd413ab_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Common shares repurchased</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased and Retired During Period, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRepurchasedAndRetiredDuringPeriodValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:to="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverables_019bffd7-5157-7295-8f42-632231991bdf_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverables" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverables_019bffd7-515a-7da6-a509-74acf1f49d6e_totalLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverables" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total reinsurance recoverable</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverables_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverables, Including Reinsurance Premium Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverables" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverables" xlink:to="lab_us-gaap_ReinsuranceRecoverables" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablePortfolioSegmentAxis_019bffd7-5158-7762-8f4e-2a10fa0f58e5_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablePortfolioSegmentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable Portfolio Segment [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablePortfolioSegmentAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablePortfolioSegmentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable Portfolio Segment [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablePortfolioSegmentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablePortfolioSegmentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablePortfolioSegmentAxis" xlink:to="lab_us-gaap_FinancingReceivablePortfolioSegmentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DomesticCountryMember_019c77a5-5c9c-7fb7-9148-38c38e801d44_terseLabel_en-US" xlink:label="lab_us-gaap_DomesticCountryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Domestic Tax Jurisdiction [Member]</link:label>
    <link:label id="lab_us-gaap_DomesticCountryMember_label_en-US" xlink:label="lab_us-gaap_DomesticCountryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Domestic Tax Jurisdiction [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DomesticCountryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DomesticCountryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DomesticCountryMember" xlink:to="lab_us-gaap_DomesticCountryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumUndiscountedBeforeReinsurance_019bffd7-515a-7bcd-8b90-73538c39104f_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumUndiscountedBeforeReinsurance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected future gross premiums, Undiscounted</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumUndiscountedBeforeReinsurance_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumUndiscountedBeforeReinsurance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Future Gross Premium, Undiscounted, before Reinsurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumUndiscountedBeforeReinsurance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumUndiscountedBeforeReinsurance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumUndiscountedBeforeReinsurance" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumUndiscountedBeforeReinsurance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_019bffd7-5158-7d6a-8a85-6b334ac59711_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income taxes paid</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_019c7c1e-a95a-7573-aa86-74212580adf8_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income taxes paid</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Taxes Paid, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxesPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaidNet" xlink:to="lab_us-gaap_IncomeTaxesPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_LegacyMountLoganShareholdersMember_019bffd7-5158-7934-8e8d-67d563b21a94_terseLabel_en-US" xlink:label="lab_logan_LegacyMountLoganShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legacy Mount Logan shareholders</link:label>
    <link:label id="lab_logan_LegacyMountLoganShareholdersMember_label_en-US" xlink:label="lab_logan_LegacyMountLoganShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legacy Mount Logan Shareholders [Member]</link:label>
    <link:label id="lab_logan_LegacyMountLoganShareholdersMember_documentation_en-US" xlink:label="lab_logan_LegacyMountLoganShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Legacy Mount Logan Shareholders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_LegacyMountLoganShareholdersMember" xlink:href="logan-20251231.xsd#logan_LegacyMountLoganShareholdersMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_LegacyMountLoganShareholdersMember" xlink:to="lab_logan_LegacyMountLoganShareholdersMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_019bffd7-5159-79a5-b5ae-8bd57d91799d_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherInsuranceProductLineMember_019bffd7-515a-7ffd-935e-f67611cb9d8b_terseLabel_en-US" xlink:label="lab_us-gaap_OtherInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_OtherInsuranceProductLineMember_label_en-US" xlink:label="lab_us-gaap_OtherInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance, Other [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInsuranceProductLineMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherInsuranceProductLineMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherInsuranceProductLineMember" xlink:to="lab_us-gaap_OtherInsuranceProductLineMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesPurchaseOfAssets_019bffd7-5157-720c-ab17-52e68a049e50_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesPurchaseOfAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share issuance for investment purchase (shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesPurchaseOfAssets_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesPurchaseOfAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Purchase of Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesPurchaseOfAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesPurchaseOfAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesPurchaseOfAssets" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesPurchaseOfAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_019bffd7-5159-7619-a5e8-d1603d26c129_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Outstanding balance</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_019bffd7-5159-7f9a-a634-1b0800238827_totalLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Gross</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_019bffd7-515b-7be1-a715-3ee17fe8681d_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Promissory note</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:to="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityWellKnownSeasonedIssuer_019c2cbf-ba87-7771-9758-164e6bfed6e1_terseLabel_en-US" xlink:label="lab_dei_EntityWellKnownSeasonedIssuer" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Well-known Seasoned Issuer</link:label>
    <link:label id="lab_dei_EntityWellKnownSeasonedIssuer_label_en-US" xlink:label="lab_dei_EntityWellKnownSeasonedIssuer" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Well-known Seasoned Issuer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityWellKnownSeasonedIssuer" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityWellKnownSeasonedIssuer"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityWellKnownSeasonedIssuer" xlink:to="lab_dei_EntityWellKnownSeasonedIssuer" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_LongTermCareInsuranceMember_019bffd7-515a-795c-b6da-36ab9d11fef5_terseLabel_en-US" xlink:label="lab_logan_LongTermCareInsuranceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long term care reinsurance</link:label>
    <link:label id="lab_logan_LongTermCareInsuranceMember_label_en-US" xlink:label="lab_logan_LongTermCareInsuranceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Care Insurance [Member]</link:label>
    <link:label id="lab_logan_LongTermCareInsuranceMember_documentation_en-US" xlink:label="lab_logan_LongTermCareInsuranceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Care Insurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_LongTermCareInsuranceMember" xlink:href="logan-20251231.xsd#logan_LongTermCareInsuranceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_LongTermCareInsuranceMember" xlink:to="lab_logan_LongTermCareInsuranceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesGrossAbstract_019bffd7-515a-761f-8a3f-faced3a178d9_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesGrossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesGrossAbstract_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesGrossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverables, Gross [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesGrossAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverablesGrossAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverablesGrossAbstract" xlink:to="lab_us-gaap_ReinsuranceRecoverablesGrossAbstract" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_OtherCommitmentsDomain_019bffd7-515b-75bf-98f9-0e97ba94d02e_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Commitments [Domain]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignGovernmentDebtSecuritiesMember" xlink:to="lab_us-gaap_ForeignGovernmentDebtSecuritiesMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_PolicyholderAccountBalanceBenefitPayment_019bffd7-515a-7adc-88b5-56588b88a84d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceBenefitPayment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Benefit payments</link:label>
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    <link:label id="lab_logan_VistaModcoMember_019bffd7-515a-768e-859d-d6f5fdf5c0f1_terseLabel_en-US" xlink:label="lab_logan_VistaModcoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vista Modco Funds Withheld</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_logan_VistaModcoMember" xlink:href="logan-20251231.xsd#logan_VistaModcoMember"/>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredProfitSharingMember" xlink:to="lab_us-gaap_DeferredProfitSharingMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss"/>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes_019c7c0b-a191-747d-9099-c10888d77f44_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State and local income taxes, net of federal (national) income tax effect</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, State and Local Income Taxes, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes"/>
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    <link:label id="lab_logan_UnsecuredReinsuranceRecoverable_019bffd7-515a-73d8-aa95-7f16f55b0e61_terseLabel_en-US" xlink:label="lab_logan_UnsecuredReinsuranceRecoverable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured reinsurance recoverable</link:label>
    <link:label id="lab_logan_UnsecuredReinsuranceRecoverable_label_en-US" xlink:label="lab_logan_UnsecuredReinsuranceRecoverable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Reinsurance Recoverable</link:label>
    <link:label id="lab_logan_UnsecuredReinsuranceRecoverable_documentation_en-US" xlink:label="lab_logan_UnsecuredReinsuranceRecoverable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unsecured Reinsurance Recoverable</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanAccumulatedBenefitObligation_019bffd7-515a-76e1-ac9a-8c08f25ff3d9_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanAccumulatedBenefitObligation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined benefit plan, accumulated benefit obligation</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanAccumulatedBenefitObligation_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanAccumulatedBenefitObligation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Accumulated Benefit Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanAccumulatedBenefitObligation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanAccumulatedBenefitObligation"/>
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    <link:label id="lab_dei_CurrentFiscalYearEndDate_019c2cb5-82d4-73ee-be70-71e1e3175f05_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight_019bffd7-515a-71bd-8c88-0bad9711176d_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants callable by each right (in shares)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight"/>
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    <link:label id="lab_logan_AuditorInformationAbstract_documentation_en-US" xlink:label="lab_logan_AuditorInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Auditor Information</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_AuditorInformationAbstract" xlink:href="logan-20251231.xsd#logan_AuditorInformationAbstract"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss_019bffd7-5158-7cde-a0a0-cc3a3a6e1f92_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less than 12 months</link:label>
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    <link:label id="lab_us-gaap_ServiceAgreementsMember_019bffd7-515b-751a-a81c-86f738dda140_terseLabel_en-US" xlink:label="lab_us-gaap_ServiceAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Service Agreements</link:label>
    <link:label id="lab_us-gaap_ServiceAgreementsMember_label_en-US" xlink:label="lab_us-gaap_ServiceAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Service Agreements [Member]</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_019bffd7-5159-78d6-b3d6-133cc93348ea_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain"/>
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    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_019bffd7-5158-77a9-aafd-d0255feae4c4_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Mortgage and Corporate Loans</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_019bffd7-515b-7d9e-acf3-a1924e62a12b_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average grant date fair value</link:label>
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    <link:label id="lab_logan_IncreaseDecreaseInFairValueOfDebtObligation_documentation_en-US" xlink:label="lab_logan_IncreaseDecreaseInFairValueOfDebtObligation" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Fair Value Of Debt Obligation</link:label>
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    <link:label id="lab_us-gaap_DerivativeLiabilities_019bffd7-5157-7e58-b534-6e0f7ab7ba1a_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_019bffd7-5159-711d-92cb-d3690eb7adef_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_019bffd7-5159-7c87-bbbc-1ddbb4b4854c_netLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Interest rate swaps</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilities"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYear"/>
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    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in Compensation Table</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss_019bffd7-5158-7462-93e3-485a9d53e6f9_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Loss Position, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss"/>
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    <link:label id="lab_us-gaap_EquityMethodInvestmentDividendsOrDistributions_019bffd7-5158-7ed0-866f-bd3505ac5424_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributions from equity method investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentDividendsOrDistributions_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Equity Method Investment, Distribution</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentDividendsOrDistributions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:to="lab_us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_PromissoryNoteMember_019bffd7-5159-7eb3-864e-234a33757c18_terseLabel_en-US" xlink:label="lab_logan_PromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Promissory Note</link:label>
    <link:label id="lab_logan_PromissoryNoteMember_label_en-US" xlink:label="lab_logan_PromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Promissory Note [Member]</link:label>
    <link:label id="lab_logan_PromissoryNoteMember_documentation_en-US" xlink:label="lab_logan_PromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Promissory Note</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_PromissoryNoteMember" xlink:href="logan-20251231.xsd#logan_PromissoryNoteMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_PromissoryNoteMember" xlink:to="lab_logan_PromissoryNoteMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions_019bffd7-5157-7cfb-8ced-4f1ac540a2b9_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share issuance for reverse acquisition</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueAcquisitions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_MLCUSHoldingsCreditFacilityMember_019bffd7-5159-75c9-9e45-aa64820c5318_terseLabel_en-US" xlink:label="lab_logan_MLCUSHoldingsCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MLC US Holdings Credit Facility</link:label>
    <link:label id="lab_logan_MLCUSHoldingsCreditFacilityMember_label_en-US" xlink:label="lab_logan_MLCUSHoldingsCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MLC US Holdings Credit Facility [Member]</link:label>
    <link:label id="lab_logan_MLCUSHoldingsCreditFacilityMember_documentation_en-US" xlink:label="lab_logan_MLCUSHoldingsCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">MLC US Holdings Credit Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_MLCUSHoldingsCreditFacilityMember" xlink:href="logan-20251231.xsd#logan_MLCUSHoldingsCreditFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_MLCUSHoldingsCreditFacilityMember" xlink:to="lab_logan_MLCUSHoldingsCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearOne_019bffd7-5158-7983-b368-2f1cddd859f0_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearOne" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearOne_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearOne" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss, Maturity, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearOne" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearOne"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearOne" xlink:to="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearOne" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_019bffd7-5158-7ae5-8b84-1a754b1893c6_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquired net assets</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired to Liability Assumed, Excess (Less)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet"/>
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    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_019bffd7-515b-7cfb-aab2-8f5e09b2fc0d_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive securities (in shares)</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_CapitalaAcquisitionSellerNoteMember_019bffd7-5159-7684-8ef7-3a2a90e53523_terseLabel_en-US" xlink:label="lab_logan_CapitalaAcquisitionSellerNoteMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capitala Acquisition Seller Note</link:label>
    <link:label id="lab_logan_CapitalaAcquisitionSellerNoteMember_label_en-US" xlink:label="lab_logan_CapitalaAcquisitionSellerNoteMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capitala Acquisition Seller Note [Member]</link:label>
    <link:label id="lab_logan_CapitalaAcquisitionSellerNoteMember_documentation_en-US" xlink:label="lab_logan_CapitalaAcquisitionSellerNoteMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Capitala Acquisition Seller Note</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_CapitalaAcquisitionSellerNoteMember" xlink:href="logan-20251231.xsd#logan_CapitalaAcquisitionSellerNoteMember"/>
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    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_019bffd7-5159-7f69-a0a1-21d9ff13f299_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial liabilities</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
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    <link:label id="lab_logan_DebtInstrumentInterestRatePayablePeriodDomain_019bffd7-515b-755a-a007-fa15b04ee2d8_terseLabel_en-US" xlink:label="lab_logan_DebtInstrumentInterestRatePayablePeriodDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate Payable, Period [Domain]</link:label>
    <link:label id="lab_logan_DebtInstrumentInterestRatePayablePeriodDomain_label_en-US" xlink:label="lab_logan_DebtInstrumentInterestRatePayablePeriodDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate Payable, Period [Domain]</link:label>
    <link:label id="lab_logan_DebtInstrumentInterestRatePayablePeriodDomain_documentation_en-US" xlink:label="lab_logan_DebtInstrumentInterestRatePayablePeriodDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate Payable, Period [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DebtInstrumentInterestRatePayablePeriodDomain" xlink:href="logan-20251231.xsd#logan_DebtInstrumentInterestRatePayablePeriodDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DebtInstrumentInterestRatePayablePeriodDomain" xlink:to="lab_logan_DebtInstrumentInterestRatePayablePeriodDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_019bffd7-5159-7564-9613-b2d499a24ca5_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo"/>
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    <link:label id="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock_019bffd7-5158-7523-8a46-75664ae454ff_terseLabel_en-US" xlink:label="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financing Receivable, Past Due</link:label>
    <link:label id="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PastDueFinancingReceivablesTableTextBlock"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_019bffd7-5158-7fb1-a44e-a0e864bbdc0c_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by (used in) financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
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    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MeasureAxis"/>
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    <link:label id="lab_us-gaap_ProvisionForLoanLossesExpensed_019bffd7-5159-776b-9490-35ed451f1106_verboseLabel_en-US" xlink:label="lab_us-gaap_ProvisionForLoanLossesExpensed" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Provision for credit losses</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProvisionForLoanLossesExpensed" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProvisionForLoanLossesExpensed"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProvisionForLoanLossesExpensed" xlink:to="lab_us-gaap_ProvisionForLoanLossesExpensed" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_019bffd7-5159-70ec-a7b8-7675fed6dfcc_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueAxis" xlink:to="lab_us-gaap_ValuationTechniqueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromDividendsReceived_019bffd7-5158-7890-b69e-a95a6796cc31_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromDividendsReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends received</link:label>
    <link:label id="lab_us-gaap_ProceedsFromDividendsReceived_label_en-US" xlink:label="lab_us-gaap_ProceedsFromDividendsReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Dividends Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromDividendsReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromDividendsReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromDividendsReceived" xlink:to="lab_us-gaap_ProceedsFromDividendsReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract_019bffd7-5159-7330-a7db-78b785c1cc41_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial liabilities</link:label>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Liabilities Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:to="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock_019bffd7-5158-7a52-bccd-45db51ea46e1_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of significant accounting policies</link:label>
    <link:label id="lab_us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis of Presentation and Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashSurrenderValueDuePolicyholdersAmount_019bffd7-515a-70fc-a8d4-32ced259fd09_terseLabel_en-US" xlink:label="lab_us-gaap_CashSurrenderValueDuePolicyholdersAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash surrender value</link:label>
    <link:label id="lab_us-gaap_CashSurrenderValueDuePolicyholdersAmount_label_en-US" xlink:label="lab_us-gaap_CashSurrenderValueDuePolicyholdersAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance, Cash Surrender Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashSurrenderValueDuePolicyholdersAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashSurrenderValueDuePolicyholdersAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashSurrenderValueDuePolicyholdersAmount" xlink:to="lab_us-gaap_CashSurrenderValueDuePolicyholdersAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendAndInterestReceivable_019bffd7-515a-733f-bc7e-88a1f8076c1f_terseLabel_en-US" xlink:label="lab_us-gaap_DividendAndInterestReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest and dividends receivable - related parties</link:label>
    <link:label id="lab_us-gaap_DividendAndInterestReceivable_label_en-US" xlink:label="lab_us-gaap_DividendAndInterestReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividend and Interest Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendAndInterestReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendAndInterestReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendAndInterestReceivable" xlink:to="lab_us-gaap_DividendAndInterestReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InternalCreditAssessmentLevelFiveMember_019bffd7-5158-7027-8f7b-3c0ccdb0a89b_terseLabel_en-US" xlink:label="lab_logan_InternalCreditAssessmentLevelFiveMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 5</link:label>
    <link:label id="lab_logan_InternalCreditAssessmentLevelFiveMember_label_en-US" xlink:label="lab_logan_InternalCreditAssessmentLevelFiveMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment Level Five [Member]</link:label>
    <link:label id="lab_logan_InternalCreditAssessmentLevelFiveMember_documentation_en-US" xlink:label="lab_logan_InternalCreditAssessmentLevelFiveMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment Level Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InternalCreditAssessmentLevelFiveMember" xlink:href="logan-20251231.xsd#logan_InternalCreditAssessmentLevelFiveMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InternalCreditAssessmentLevelFiveMember" xlink:to="lab_logan_InternalCreditAssessmentLevelFiveMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PvpTableTextBlock"/>
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    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_019bffd7-5158-76aa-84b0-d207288035bd_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of debt issuance costs</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfFinancingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfFinancingCosts" xlink:to="lab_us-gaap_AmortizationOfFinancingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeInvestmentExpense_019bffd7-5158-7c41-bef3-9aa38ae67e54_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInvestmentExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Investment expense</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInvestmentExpense_019c47f8-3622-724c-9b89-98179066a2b6_negatedLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInvestmentExpense" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Cost of funds</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInvestmentExpense_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInvestmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Investment Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInvestmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeInvestmentExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeInvestmentExpense" xlink:to="lab_us-gaap_InvestmentIncomeInvestmentExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_019c2cb9-32b1-70bf-8a22-283a41e523fe_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityTaxIdentificationNumber"/>
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    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_019bffd7-5159-7a54-81e3-219f30e91933_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discounted cash flow</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Discounted Cash Flow [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueDiscountedCashFlowMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:to="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomePercent_019c7c0b-a191-7541-9aeb-12735fd71445_terseLabel_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomePercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign accrual property income impact</link:label>
    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomePercent_label_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomePercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Foreign Accrual Property Income, Percent</link:label>
    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomePercent_documentation_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomePercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Foreign Accrual Property Income, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomePercent" xlink:href="logan-20251231.xsd#logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomePercent"/>
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    <link:label id="lab_logan_AssetManagementExpenseAbstract_019bffd7-5157-7680-b7cc-133c1337bb7d_terseLabel_en-US" xlink:label="lab_logan_AssetManagementExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Management</link:label>
    <link:label id="lab_logan_AssetManagementExpenseAbstract_label_en-US" xlink:label="lab_logan_AssetManagementExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Management, Expense [Abstract]</link:label>
    <link:label id="lab_logan_AssetManagementExpenseAbstract_documentation_en-US" xlink:label="lab_logan_AssetManagementExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Management, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_AssetManagementExpenseAbstract" xlink:href="logan-20251231.xsd#logan_AssetManagementExpenseAbstract"/>
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    <link:label id="lab_us-gaap_AssetAcquisitionAxis_019bffd7-515b-76b9-acd3-cd01cc169ff1_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Axis]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionAxis_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionAxis" xlink:to="lab_us-gaap_AssetAcquisitionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_019bffd7-5159-73c4-827f-243996674b4b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTextBlock"/>
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    <link:label id="lab_us-gaap_DerivativeMember_019bffd7-5158-75eb-8297-9e3f876f52fb_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativeMember_label_en-US" xlink:label="lab_us-gaap_DerivativeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeMember" xlink:to="lab_us-gaap_DerivativeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableTradeCurrent_019cf4a9-613e-711e-be89-d798bcecd870_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableTradeCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding payables</link:label>
    <link:label id="lab_us-gaap_AccountsPayableTradeCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableTradeCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable, Trade, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableTradeCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableTradeCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableTradeCurrent" xlink:to="lab_us-gaap_AccountsPayableTradeCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesGrossUnrealizedLoss_019bffd7-5158-7d95-9569-c6769bf18367_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesGrossUnrealizedLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AFS, unrealized loss</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesGrossUnrealizedLoss_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesGrossUnrealizedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesGrossUnrealizedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleDebtSecuritiesGrossUnrealizedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleDebtSecuritiesGrossUnrealizedLoss" xlink:to="lab_us-gaap_AvailableForSaleDebtSecuritiesGrossUnrealizedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_GainOnReverseAcquisitionOfBusiness_019bffd7-5158-76c7-a92c-7ee2e57be34d_negatedTerseLabel_en-US" xlink:label="lab_logan_GainOnReverseAcquisitionOfBusiness" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gain on reverse acquisition of business</link:label>
    <link:label id="lab_logan_GainOnReverseAcquisitionOfBusiness_label_en-US" xlink:label="lab_logan_GainOnReverseAcquisitionOfBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain On Reverse Acquisition Of Business</link:label>
    <link:label id="lab_logan_GainOnReverseAcquisitionOfBusiness_documentation_en-US" xlink:label="lab_logan_GainOnReverseAcquisitionOfBusiness" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain On Reverse Acquisition Of Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_GainOnReverseAcquisitionOfBusiness" xlink:href="logan-20251231.xsd#logan_GainOnReverseAcquisitionOfBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_GainOnReverseAcquisitionOfBusiness" xlink:to="lab_logan_GainOnReverseAcquisitionOfBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_019bffd7-5157-71e2-b7a4-1dc40525cecf_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_019bffd7-5159-780b-941a-13b1ca530f31_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_019bffd7-5159-7ee3-9738-d8a1b2f009a7_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill and intangible assets</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitReinsuranceRecoverableAfterAllowance_019bffd7-515a-767d-8364-443db10abb93_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitReinsuranceRecoverableAfterAllowance" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: Reinsurance recoverables, net of allowance for credit losses</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitReinsuranceRecoverableAfterAllowance_019bffd7-515a-78f8-a8fa-c55ab130d102_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitReinsuranceRecoverableAfterAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance assumed</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitReinsuranceRecoverableAfterAllowance_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitReinsuranceRecoverableAfterAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Reinsurance Recoverable, after Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitReinsuranceRecoverableAfterAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitReinsuranceRecoverableAfterAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitReinsuranceRecoverableAfterAllowance" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitReinsuranceRecoverableAfterAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_MarketApproachMember_019bffd7-5159-75ad-823d-d69c67f179e9_terseLabel_en-US" xlink:label="lab_logan_MarketApproachMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Market approach</link:label>
    <link:label id="lab_logan_MarketApproachMember_label_en-US" xlink:label="lab_logan_MarketApproachMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Market Approach [Member]</link:label>
    <link:label id="lab_logan_MarketApproachMember_documentation_en-US" xlink:label="lab_logan_MarketApproachMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Market Approach</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_MarketApproachMember" xlink:href="logan-20251231.xsd#logan_MarketApproachMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_MarketApproachMember" xlink:to="lab_logan_MarketApproachMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityPublicFloat_019cd2ad-dec6-7651-96a7-1e165c40926f_terseLabel_en-US" xlink:label="lab_dei_EntityPublicFloat" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Public Float</link:label>
    <link:label id="lab_dei_EntityPublicFloat_label_en-US" xlink:label="lab_dei_EntityPublicFloat" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Public Float</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityPublicFloat" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityPublicFloat"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityPublicFloat" xlink:to="lab_dei_EntityPublicFloat" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ValuationTechniqueYearsToExerciseMember_019bffd7-5159-7bfa-b4a0-9a23f07a6b43_terseLabel_en-US" xlink:label="lab_logan_ValuationTechniqueYearsToExerciseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Technique, Years To Exercise</link:label>
    <link:label id="lab_logan_ValuationTechniqueYearsToExerciseMember_label_en-US" xlink:label="lab_logan_ValuationTechniqueYearsToExerciseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Years To Exercise [Member]</link:label>
    <link:label id="lab_logan_ValuationTechniqueYearsToExerciseMember_documentation_en-US" xlink:label="lab_logan_ValuationTechniqueYearsToExerciseMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Valuation Technique, Years To Exercise</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ValuationTechniqueYearsToExerciseMember" xlink:href="logan-20251231.xsd#logan_ValuationTechniqueYearsToExerciseMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ValuationTechniqueYearsToExerciseMember" xlink:to="lab_logan_ValuationTechniqueYearsToExerciseMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTextBlock_019bffd7-5159-7eb6-86d0-d4f5f605399e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Goodwill</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Goodwill [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGoodwillTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfGoodwillTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGoodwillTextBlock" xlink:to="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TradingArrAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrAxis" xlink:to="lab_ecd_TradingArrAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnAmt" xlink:to="lab_ecd_TotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationDeductionsDividends_019c8fe1-a6ab-78e9-a7b7-3fe1b93fea5a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationDeductionsDividends" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends Received Deduction</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationDeductionsDividends_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationDeductionsDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Deduction, Dividends, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationDeductionsDividends" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationDeductionsDividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationDeductionsDividends" xlink:to="lab_us-gaap_IncomeTaxReconciliationDeductionsDividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationBeforeTaxParent_019bffd7-5157-720a-90b6-59c67c06d273_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationBeforeTaxParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gains (losses) on hedging instruments</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationBeforeTaxParent_019c7b92-4729-746e-a4c5-99b339ebbcaa_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationBeforeTaxParent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gains (losses) on hedging instruments</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationBeforeTaxParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationBeforeTaxParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), after Reclassification, before Tax, Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationBeforeTaxParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationBeforeTaxParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationBeforeTaxParent" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationBeforeTaxParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings_019bffd7-5159-7ff1-a464-dc164c50f783_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Included in income</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Gain (Loss) Included in Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_019bffd7-515b-7461-b635-73c532f3a240_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate allocations</link:label>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_label_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Reconciling Item, Corporate Nonsegment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateNonSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CorporateNonSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateNonSegmentMember" xlink:to="lab_us-gaap_CorporateNonSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_019c2cbf-4158-777f-b95a-ec08e204bc20_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTextBlock_019bffd7-515b-7794-a299-2f8d98e860ef_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation of Revenue from Segments to Consolidated</link:label>
    <link:label id="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTextBlock_label_en-US" xlink:label="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reconciliation of Revenue from Segments to Consolidated [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTextBlock" xlink:to="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPaidForeignAfterRefundReceived_019c7c1d-d183-7ff5-9b0e-a1ebeb3d65be_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidForeignAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPaidForeignAfterRefundReceived_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidForeignAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, Foreign, after Refund Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPaidForeignAfterRefundReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidForeignAfterRefundReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPaidForeignAfterRefundReceived" xlink:to="lab_us-gaap_IncomeTaxPaidForeignAfterRefundReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesAllowance_019bffd7-515a-746f-88b8-a553b73be148_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable, credit loss allowance</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesAllowance_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverablesAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverablesAllowance" xlink:to="lab_us-gaap_ReinsuranceRecoverablesAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpense_019c8fd2-db51-79b3-b34f-20f0d82194da_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nondeductible Differences</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpense_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationNondeductibleExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationNondeductibleExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationNondeductibleExpense" xlink:to="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_019bffd7-5159-7d46-b27c-02832b474b11_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit facility, maximum borrowing capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CededPremiumsEarned_019bffd7-515a-7287-913d-3391eebfd640_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_CededPremiumsEarned" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance ceded</link:label>
    <link:label id="lab_us-gaap_CededPremiumsEarned_label_en-US" xlink:label="lab_us-gaap_CededPremiumsEarned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ceded Premiums Earned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededPremiumsEarned" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CededPremiumsEarned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CededPremiumsEarned" xlink:to="lab_us-gaap_CededPremiumsEarned" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_019bffd7-515a-7495-9005-d7c8152b0826_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock repurchased during period (in shares)</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRepurchasedDuringPeriodShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:to="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain_019bffd7-5159-7b72-82b6-c4430110d0a5_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain_label_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_019bffd7-5159-7b74-9c0d-4c22dba6b329_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearThree_019bffd7-5158-7635-8429-dbeb7f4ede13_terseLabel_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearThree_label_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss,Maturity, Year Three</link:label>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearThree_documentation_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearThree" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss,Maturity, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearThree" xlink:href="logan-20251231.xsd#logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearThree" xlink:to="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AociLiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeTax_019bffd7-515a-75cc-bf8f-aff5b8057f80_terseLabel_en-US" xlink:label="lab_us-gaap_AociLiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of changes in discount rate assumptions</link:label>
    <link:label id="lab_us-gaap_AociLiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeTax_label_en-US" xlink:label="lab_us-gaap_AociLiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI, Liability for Future Policy Benefit, Expected Net Premium, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AociLiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AociLiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AociLiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeTax" xlink:to="lab_us-gaap_AociLiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseFromCashFlowChange_019bffd7-515a-70d6-80f7-ad2dc78fbc06_terseLabel_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseFromCashFlowChange" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in effect in cashflow assumptions</link:label>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseFromCashFlowChange_label_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseFromCashFlowChange" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Future Policy Benefit, Increase (Decrease) from Cash Flow Change</link:label>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseFromCashFlowChange_documentation_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseFromCashFlowChange" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Future Policy Benefit, Increase (Decrease) from Cash Flow Change</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseFromCashFlowChange" xlink:href="logan-20251231.xsd#logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseFromCashFlowChange"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseFromCashFlowChange" xlink:to="lab_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseFromCashFlowChange" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1_019bffd7-5159-73d4-ac42-00369b708715_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Included in income</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Gain (Loss) Included in Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_IncomeFromProfitSharingAgreement_019bffd7-515b-7030-a253-2f313b1b4acb_terseLabel_en-US" xlink:label="lab_logan_IncomeFromProfitSharingAgreement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income from profit sharing agreement</link:label>
    <link:label id="lab_logan_IncomeFromProfitSharingAgreement_label_en-US" xlink:label="lab_logan_IncomeFromProfitSharingAgreement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income From Profit Sharing Agreement</link:label>
    <link:label id="lab_logan_IncomeFromProfitSharingAgreement_documentation_en-US" xlink:label="lab_logan_IncomeFromProfitSharingAgreement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income From Profit Sharing Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_IncomeFromProfitSharingAgreement" xlink:href="logan-20251231.xsd#logan_IncomeFromProfitSharingAgreement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_IncomeFromProfitSharingAgreement" xlink:to="lab_logan_IncomeFromProfitSharingAgreement" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FeeIncomeAdjusted_019bffd7-515b-7c68-bf11-80981d0d9264_terseLabel_en-US" xlink:label="lab_logan_FeeIncomeAdjusted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Management fees</link:label>
    <link:label id="lab_logan_FeeIncomeAdjusted_label_en-US" xlink:label="lab_logan_FeeIncomeAdjusted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fee Income, Adjusted</link:label>
    <link:label id="lab_logan_FeeIncomeAdjusted_documentation_en-US" xlink:label="lab_logan_FeeIncomeAdjusted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fee Income, Adjusted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FeeIncomeAdjusted" xlink:href="logan-20251231.xsd#logan_FeeIncomeAdjusted"/>
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    <link:label id="lab_us-gaap_InterestSensitiveLifeMember_019bffd7-515a-7aa9-b2bc-1678af30eb69_terseLabel_en-US" xlink:label="lab_us-gaap_InterestSensitiveLifeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Sensitive Life</link:label>
    <link:label id="lab_us-gaap_InterestSensitiveLifeMember_label_en-US" xlink:label="lab_us-gaap_InterestSensitiveLifeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Sensitive Life [Member]</link:label>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_019bffd7-515a-7e4b-b3ae-3b65d4e19b20_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitsPaymentForBenefits_019bffd7-515a-7e93-a2ba-3cc58474078a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitsPaymentForBenefits" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Benefit payments</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitsPaymentForBenefits_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitsPaymentForBenefits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Future Policy Benefit, Benefit Payment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitsPaymentForBenefits" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitsPaymentForBenefits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitsPaymentForBenefits" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitsPaymentForBenefits" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DebentureWarrantsMember_019bffd7-5159-7d00-a509-b42231f1d30d_terseLabel_en-US" xlink:label="lab_logan_DebentureWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debenture Warrants</link:label>
    <link:label id="lab_logan_DebentureWarrantsMember_019c37f6-2508-7c19-ad00-10e53f1d3964_verboseLabel_en-US" xlink:label="lab_logan_DebentureWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Debenture Units</link:label>
    <link:label id="lab_logan_DebentureWarrantsMember_label_en-US" xlink:label="lab_logan_DebentureWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debenture Warrants [Member]</link:label>
    <link:label id="lab_logan_DebentureWarrantsMember_documentation_en-US" xlink:label="lab_logan_DebentureWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debenture Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DebentureWarrantsMember" xlink:href="logan-20251231.xsd#logan_DebentureWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DebentureWarrantsMember" xlink:to="lab_logan_DebentureWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill_019bffd7-5159-73c9-96c9-27ba2edfe9c5_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross carrying amount</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Assets, Gross (Excluding Goodwill)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IntangibleAssetsGrossExcludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:to="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByAssetClassAxis_019bffd7-5159-7234-8f66-bb84d3278009_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByAssetClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByAssetClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByAssetClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByAssetClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByAssetClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByAssetClassAxis" xlink:to="lab_us-gaap_FairValueByAssetClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_019bffd7-5159-7f03-af1d-9eb956c1622a_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDomain" xlink:to="lab_us-gaap_ValuationTechniqueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateSwapMember_019bffd7-5159-7359-a2bb-ff3ae32f5c2c_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateSwapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate swaps</link:label>
    <link:label id="lab_us-gaap_InterestRateSwapMember_label_en-US" xlink:label="lab_us-gaap_InterestRateSwapMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateSwapMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestRateSwapMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateSwapMember" xlink:to="lab_us-gaap_InterestRateSwapMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtPolicyTextBlock_019bffd7-5158-7d91-b15f-bbdf4ed8ea3c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt issuance costs</link:label>
    <link:label id="lab_us-gaap_DebtPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtPolicyTextBlock" xlink:to="lab_us-gaap_DebtPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss_019bffd7-5159-7ac9-a231-80bbc8fa71ad_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Included in OCI</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Gain (Loss) Included in Other Comprehensive Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_019bffd7-5157-7258-bc2e-0c20db019501_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity investment earning</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_019bffd7-5158-7f3d-a01b-5a732b39896d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Equity investment earnings</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromEquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:to="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_RelatedPartyTransactionDueToAffiliatesPayable_019bffd7-515b-7796-a72d-0f5b967f07ee_terseLabel_en-US" xlink:label="lab_logan_RelatedPartyTransactionDueToAffiliatesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payable to affiliate</link:label>
    <link:label id="lab_logan_RelatedPartyTransactionDueToAffiliatesPayable_label_en-US" xlink:label="lab_logan_RelatedPartyTransactionDueToAffiliatesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Due to Affiliates, Payable</link:label>
    <link:label id="lab_logan_RelatedPartyTransactionDueToAffiliatesPayable_documentation_en-US" xlink:label="lab_logan_RelatedPartyTransactionDueToAffiliatesPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Due to Affiliates, Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_RelatedPartyTransactionDueToAffiliatesPayable" xlink:href="logan-20251231.xsd#logan_RelatedPartyTransactionDueToAffiliatesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_RelatedPartyTransactionDueToAffiliatesPayable" xlink:to="lab_logan_RelatedPartyTransactionDueToAffiliatesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_019bffd7-515b-7d7b-918d-149d439e38cb_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic earnings per share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareBasicAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:to="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYear_019bffd7-5159-7392-9fba-c5001c403740_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year two</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Year Two, Originated, Fiscal Year before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_019bffd7-5158-7e15-9a06-24cfb6c6d5dc_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity interest issued (in shares)</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_019bffd7-5158-7cf8-9860-9813f467ca2c_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Number of Legacy Mount Logan shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Equity Interest, Share Issued, Number of Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:to="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InsuranceSolutionsRevenueAbstract_019bffd7-5157-797d-83bc-63e66cc7c184_terseLabel_en-US" xlink:label="lab_logan_InsuranceSolutionsRevenueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance Solutions</link:label>
    <link:label id="lab_logan_InsuranceSolutionsRevenueAbstract_label_en-US" xlink:label="lab_logan_InsuranceSolutionsRevenueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance Solutions, Revenue [Abstract]</link:label>
    <link:label id="lab_logan_InsuranceSolutionsRevenueAbstract_documentation_en-US" xlink:label="lab_logan_InsuranceSolutionsRevenueAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Insurance Solutions, Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InsuranceSolutionsRevenueAbstract" xlink:href="logan-20251231.xsd#logan_InsuranceSolutionsRevenueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InsuranceSolutionsRevenueAbstract" xlink:to="lab_logan_InsuranceSolutionsRevenueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_NetInvestmentIncomeAndRealizedGainLossNet_019bffd7-515b-7194-8393-cd8e2fafe59c_terseLabel_en-US" xlink:label="lab_logan_NetInvestmentIncomeAndRealizedGainLossNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net investment income and realized gain (loss), net</link:label>
    <link:label id="lab_logan_NetInvestmentIncomeAndRealizedGainLossNet_label_en-US" xlink:label="lab_logan_NetInvestmentIncomeAndRealizedGainLossNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Investment Income And Realized Gain (Loss), Net</link:label>
    <link:label id="lab_logan_NetInvestmentIncomeAndRealizedGainLossNet_documentation_en-US" xlink:label="lab_logan_NetInvestmentIncomeAndRealizedGainLossNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Investment Income And Realized Gain (Loss), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_NetInvestmentIncomeAndRealizedGainLossNet" xlink:href="logan-20251231.xsd#logan_NetInvestmentIncomeAndRealizedGainLossNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_NetInvestmentIncomeAndRealizedGainLossNet" xlink:to="lab_logan_NetInvestmentIncomeAndRealizedGainLossNet" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_CashlessRepaymentOnBorrowings_019bffd7-5158-7b2f-8018-008f06f50c70_terseLabel_en-US" xlink:label="lab_logan_CashlessRepaymentOnBorrowings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cashless repayment on borrowings</link:label>
    <link:label id="lab_logan_CashlessRepaymentOnBorrowings_label_en-US" xlink:label="lab_logan_CashlessRepaymentOnBorrowings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cashless Repayment On Borrowings</link:label>
    <link:label id="lab_logan_CashlessRepaymentOnBorrowings_documentation_en-US" xlink:label="lab_logan_CashlessRepaymentOnBorrowings" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cashless Repayment On Borrowings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_CashlessRepaymentOnBorrowings" xlink:href="logan-20251231.xsd#logan_CashlessRepaymentOnBorrowings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_CashlessRepaymentOnBorrowings" xlink:to="lab_logan_CashlessRepaymentOnBorrowings" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeInterestEarningAsset_019bffd7-5157-7bc8-952d-9749cf65b5da_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeInterestEarningAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income</link:label>
    <link:label id="lab_us-gaap_InterestIncomeInterestEarningAsset_label_en-US" xlink:label="lab_us-gaap_InterestIncomeInterestEarningAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income, Interest-Earning Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeInterestEarningAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeInterestEarningAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeInterestEarningAsset" xlink:to="lab_us-gaap_InterestIncomeInterestEarningAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_MedcoInsuranceCompanyMember_019bffd7-515a-7050-8717-dcdd053e9b74_terseLabel_en-US" xlink:label="lab_logan_MedcoInsuranceCompanyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Medico Insurance Company</link:label>
    <link:label id="lab_logan_MedcoInsuranceCompanyMember_label_en-US" xlink:label="lab_logan_MedcoInsuranceCompanyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Medco Insurance Company [Member]</link:label>
    <link:label id="lab_logan_MedcoInsuranceCompanyMember_documentation_en-US" xlink:label="lab_logan_MedcoInsuranceCompanyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Medco Insurance Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_MedcoInsuranceCompanyMember" xlink:href="logan-20251231.xsd#logan_MedcoInsuranceCompanyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_MedcoInsuranceCompanyMember" xlink:to="lab_logan_MedcoInsuranceCompanyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_019bffd7-5158-7443-b493-552c0ee66dd6_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gross unrealized losses</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Loss, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:to="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrByIndTable_terseLabel_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual</link:label>
    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrByIndTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TradingArrByIndTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrByIndTable" xlink:to="lab_ecd_TradingArrByIndTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightOutstanding_019bffd7-515a-7dac-8b25-0a17133a2b08_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of warrant or right, outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightOutstanding_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfWarrantOrRightOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:to="lab_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_019bffd7-5157-7ef8-a9f5-b0c9582c5092_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to common shareholders - basic (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_019c4647-3b7d-7a6a-9c16-ad0687fd8fc6_verboseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Basic earnings (loss) per share - basic (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasic" xlink:to="lab_us-gaap_EarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommercialPaperMember_019bffd7-515b-7377-88bd-7e90662125ae_terseLabel_en-US" xlink:label="lab_us-gaap_CommercialPaperMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Paper</link:label>
    <link:label id="lab_us-gaap_CommercialPaperMember_label_en-US" xlink:label="lab_us-gaap_CommercialPaperMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Paper [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommercialPaperMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommercialPaperMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommercialPaperMember" xlink:to="lab_us-gaap_CommercialPaperMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsGross_019bffd7-515a-763e-ab76-16427c38f8c5_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsGross" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total deferred tax assets</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsGross_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsGross" xlink:to="lab_us-gaap_DeferredTaxAssetsGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_019bffd7-5159-78e2-9ad1-65dbd0e640f2_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount rate</link:label>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Discount Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputDiscountRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:to="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_019bffd7-515b-7802-9cd0-a575b5c6e608_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_019bffd7-5159-7a79-a3c7-f3fe743d62fe_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeDomain" xlink:to="lab_us-gaap_MeasurementInputTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceLineItems_019bffd7-515a-7aef-aab4-5b1ffe737dd5_terseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance [Line Items]</link:label>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceLineItems_label_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderAccountBalanceLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderAccountBalanceLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyholderAccountBalanceLineItems" xlink:to="lab_us-gaap_PolicyholderAccountBalanceLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_AffiliatedEntityMember_019bffd7-515b-724e-ab8b-9d8f9a5ae257_terseLabel_en-US" xlink:label="lab_srt_AffiliatedEntityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Affiliated Entity</link:label>
    <link:label id="lab_srt_AffiliatedEntityMember_label_en-US" xlink:label="lab_srt_AffiliatedEntityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Affiliated Entity [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_AffiliatedEntityMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_AffiliatedEntityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_AffiliatedEntityMember" xlink:to="lab_srt_AffiliatedEntityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DeferredTaxAssetsUnrealizedLossesOnRemeasurementOfInvestments_019bffd7-515a-7573-9e34-8e8f8de86b27_terseLabel_en-US" xlink:label="lab_logan_DeferredTaxAssetsUnrealizedLossesOnRemeasurementOfInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized losses on remeasurement of investments</link:label>
    <link:label id="lab_logan_DeferredTaxAssetsUnrealizedLossesOnRemeasurementOfInvestments_label_en-US" xlink:label="lab_logan_DeferredTaxAssetsUnrealizedLossesOnRemeasurementOfInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Unrealized Losses On Remeasurement Of Investments</link:label>
    <link:label id="lab_logan_DeferredTaxAssetsUnrealizedLossesOnRemeasurementOfInvestments_documentation_en-US" xlink:label="lab_logan_DeferredTaxAssetsUnrealizedLossesOnRemeasurementOfInvestments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Unrealized Losses On Remeasurement Of Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DeferredTaxAssetsUnrealizedLossesOnRemeasurementOfInvestments" xlink:href="logan-20251231.xsd#logan_DeferredTaxAssetsUnrealizedLossesOnRemeasurementOfInvestments"/>
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    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisChangeInUnrealizedGainLoss_019bffd7-5159-7b24-b181-8cd44b680afd_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in unrealized gains (losses) included in income on Level 3 assets and liabilities still held</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisChangeInUnrealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Asset, Recurring Basis, Still Held, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisChangeInUnrealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_OtherAssetsAndOtherLiabilitiesTable_019bffd7-515a-735c-96a2-0d024f090477_terseLabel_en-US" xlink:label="lab_logan_OtherAssetsAndOtherLiabilitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Assets and Other Liabilities [Table]</link:label>
    <link:label id="lab_logan_OtherAssetsAndOtherLiabilitiesTable_label_en-US" xlink:label="lab_logan_OtherAssetsAndOtherLiabilitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets and Other Liabilities [Table]</link:label>
    <link:label id="lab_logan_OtherAssetsAndOtherLiabilitiesTable_documentation_en-US" xlink:label="lab_logan_OtherAssetsAndOtherLiabilitiesTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Assets and Other Liabilities [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_OtherAssetsAndOtherLiabilitiesTable" xlink:href="logan-20251231.xsd#logan_OtherAssetsAndOtherLiabilitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_OtherAssetsAndOtherLiabilitiesTable" xlink:to="lab_logan_OtherAssetsAndOtherLiabilitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossConcentrationPercentage_019bffd7-5158-7294-95a8-a293e1c758d9_terseLabel_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossConcentrationPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing receivable concentration (as a percent)</link:label>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossConcentrationPercentage_label_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossConcentrationPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss, Concentration Percentage</link:label>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossConcentrationPercentage_documentation_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossConcentrationPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss, Concentration Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FinancingReceivableBeforeAllowanceForCreditLossConcentrationPercentage" xlink:href="logan-20251231.xsd#logan_FinancingReceivableBeforeAllowanceForCreditLossConcentrationPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FinancingReceivableBeforeAllowanceForCreditLossConcentrationPercentage" xlink:to="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossConcentrationPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyholderAccountBalancePolicyCharge_019bffd7-515a-7320-a9fe-9a7231edfcd0_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalancePolicyCharge" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Product charges</link:label>
    <link:label id="lab_us-gaap_PolicyholderAccountBalancePolicyCharge_label_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalancePolicyCharge" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance, Policy Charge</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderAccountBalancePolicyCharge" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderAccountBalancePolicyCharge"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyholderAccountBalancePolicyCharge" xlink:to="lab_us-gaap_PolicyholderAccountBalancePolicyCharge" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassLineItems_019bffd7-5159-7682-9d4e-6acfd2727142_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets [Line Items]</link:label>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassLineItems_label_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassLineItems" xlink:to="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ProbabilityWeightedExpectedReturnMethodYearsToCashFlowsMember_019bffd7-5159-7009-ba24-deb21f67c8a2_terseLabel_en-US" xlink:label="lab_logan_ProbabilityWeightedExpectedReturnMethodYearsToCashFlowsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Probability-Weighted Expected Return Method Years To Cash Flows</link:label>
    <link:label id="lab_logan_ProbabilityWeightedExpectedReturnMethodYearsToCashFlowsMember_label_en-US" xlink:label="lab_logan_ProbabilityWeightedExpectedReturnMethodYearsToCashFlowsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Probability-Weighted Expected Return Method Years To Cash Flows [Member]</link:label>
    <link:label id="lab_logan_ProbabilityWeightedExpectedReturnMethodYearsToCashFlowsMember_documentation_en-US" xlink:label="lab_logan_ProbabilityWeightedExpectedReturnMethodYearsToCashFlowsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Probability-Weighted Expected Return Method Years To Cash Flows</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ProbabilityWeightedExpectedReturnMethodYearsToCashFlowsMember" xlink:href="logan-20251231.xsd#logan_ProbabilityWeightedExpectedReturnMethodYearsToCashFlowsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ProbabilityWeightedExpectedReturnMethodYearsToCashFlowsMember" xlink:to="lab_logan_ProbabilityWeightedExpectedReturnMethodYearsToCashFlowsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCededCreditRiskByReinsurerTextBlock_019bffd7-515b-7152-ab63-12ef12d3c534_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCededCreditRiskByReinsurerTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of credit risk related to recoverable reinsurance</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCededCreditRiskByReinsurerTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCededCreditRiskByReinsurerTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ceded Credit Risk [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCededCreditRiskByReinsurerTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfCededCreditRiskByReinsurerTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfCededCreditRiskByReinsurerTextBlock" xlink:to="lab_us-gaap_ScheduleOfCededCreditRiskByReinsurerTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:to="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InterestSensitiveContractBenefitExpense_019bffd7-5157-7cb4-876e-6436bd44e7fb_terseLabel_en-US" xlink:label="lab_logan_InterestSensitiveContractBenefitExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest sensitive contract benefits</link:label>
    <link:label id="lab_logan_InterestSensitiveContractBenefitExpense_label_en-US" xlink:label="lab_logan_InterestSensitiveContractBenefitExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Sensitive Contract Benefit Expense</link:label>
    <link:label id="lab_logan_InterestSensitiveContractBenefitExpense_documentation_en-US" xlink:label="lab_logan_InterestSensitiveContractBenefitExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Sensitive Contract Benefit Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InterestSensitiveContractBenefitExpense" xlink:href="logan-20251231.xsd#logan_InterestSensitiveContractBenefitExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InterestSensitiveContractBenefitExpense" xlink:to="lab_logan_InterestSensitiveContractBenefitExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_019bffd7-5157-74e1-9e88-fdd029d1ec90_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Primary Beneficiary</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Primary Beneficiary [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableInterestEntityPrimaryBeneficiaryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:to="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_MergersMember_019bffd7-5158-79f9-afcc-138016b0732c_terseLabel_en-US" xlink:label="lab_logan_MergersMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mergers</link:label>
    <link:label id="lab_logan_MergersMember_label_en-US" xlink:label="lab_logan_MergersMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mergers [Member]</link:label>
    <link:label id="lab_logan_MergersMember_documentation_en-US" xlink:label="lab_logan_MergersMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mergers</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_MergersMember" xlink:href="logan-20251231.xsd#logan_MergersMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_MergersMember" xlink:to="lab_logan_MergersMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_019bffd7-515a-789c-8220-4457b046acec_terseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity-based compensation</link:label>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_019cadd0-1ae5-7cdd-a852-74756578573a_negatedLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Equity-based compensation</link:label>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_label_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllocatedShareBasedCompensationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:to="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingDesignationDomain_019bffd7-5159-740e-8917-e9fb9ae6ed14_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:label id="lab_us-gaap_HedgingDesignationDomain_label_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HedgingDesignationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingDesignationDomain" xlink:to="lab_us-gaap_HedgingDesignationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAndWarrantsIssuedDuringPeriodValuePreferredStockAndWarrants_019bffd7-5157-7474-8670-00c062ea61cd_terseLabel_en-US" xlink:label="lab_us-gaap_StockAndWarrantsIssuedDuringPeriodValuePreferredStockAndWarrants" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of warrants</link:label>
    <link:label id="lab_us-gaap_StockAndWarrantsIssuedDuringPeriodValuePreferredStockAndWarrants_label_en-US" xlink:label="lab_us-gaap_StockAndWarrantsIssuedDuringPeriodValuePreferredStockAndWarrants" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock and Warrants Issued During Period, Value, Preferred Stock and Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAndWarrantsIssuedDuringPeriodValuePreferredStockAndWarrants" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockAndWarrantsIssuedDuringPeriodValuePreferredStockAndWarrants"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAndWarrantsIssuedDuringPeriodValuePreferredStockAndWarrants" xlink:to="lab_us-gaap_StockAndWarrantsIssuedDuringPeriodValuePreferredStockAndWarrants" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_AtlanticCoastLifeInsuranceCompanySurplusNotesMember_019bffd7-515a-7a1b-8923-eb83c21a7f58_terseLabel_en-US" xlink:label="lab_logan_AtlanticCoastLifeInsuranceCompanySurplusNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Atlantic Coast Life Insurance Company</link:label>
    <link:label id="lab_logan_AtlanticCoastLifeInsuranceCompanySurplusNotesMember_label_en-US" xlink:label="lab_logan_AtlanticCoastLifeInsuranceCompanySurplusNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Atlantic Coast Life Insurance Company Surplus Notes [Member]</link:label>
    <link:label id="lab_logan_AtlanticCoastLifeInsuranceCompanySurplusNotesMember_documentation_en-US" xlink:label="lab_logan_AtlanticCoastLifeInsuranceCompanySurplusNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Atlantic Coast Life Insurance Company Surplus Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_AtlanticCoastLifeInsuranceCompanySurplusNotesMember" xlink:href="logan-20251231.xsd#logan_AtlanticCoastLifeInsuranceCompanySurplusNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_AtlanticCoastLifeInsuranceCompanySurplusNotesMember" xlink:to="lab_logan_AtlanticCoastLifeInsuranceCompanySurplusNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_019bffd7-5157-7a7c-83aa-50acf9ecde2f_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities and equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_019bffd7-5158-799d-8a53-846cdefea2d1_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency translation and transactions</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Currency Transactions and Translations Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:to="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_019bffd7-515b-773a-8928-316ed9bdae06_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems"/>
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    <link:label id="lab_us-gaap_ObligationsMember_019bffd7-5159-79b3-aa91-b6aa979a464d_terseLabel_en-US" xlink:label="lab_us-gaap_ObligationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt obligations</link:label>
    <link:label id="lab_us-gaap_ObligationsMember_label_en-US" xlink:label="lab_us-gaap_ObligationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Obligations [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ObligationsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ObligationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ObligationsMember" xlink:to="lab_us-gaap_ObligationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions_019bffd7-5157-7f35-a2cd-13c4c1275352_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share issuance for acquisition (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions_019c3791-3743-75d5-b8eb-3641e009b094_netLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Share issuance for acquisition (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesAcquisitions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCosts_019bffd7-5157-7385-b13f-aa4e668f3fd9_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred acquisition costs</link:label>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCosts_019bffd7-515a-721e-bb1e-85edc19835f7_periodStartLabel_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCosts" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCosts_019bffd7-515a-7f62-9f22-1c49d3ae019c_periodEndLabel_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCosts" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCosts_019bffd7-515a-724b-bfae-740e4e43703a_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCosts" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCosts_label_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredPolicyAcquisitionCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredPolicyAcquisitionCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredPolicyAcquisitionCosts" xlink:to="lab_us-gaap_DeferredPolicyAcquisitionCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_019bffd7-515b-7fc8-a7bd-c0e21ed2ca45_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:to="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_PortmanLoganMember_019bffd7-515b-7acd-aaf8-a62216e9fa51_terseLabel_en-US" xlink:label="lab_logan_PortmanLoganMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portman-Logan</link:label>
    <link:label id="lab_logan_PortmanLoganMember_label_en-US" xlink:label="lab_logan_PortmanLoganMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portman-Logan [Member]</link:label>
    <link:label id="lab_logan_PortmanLoganMember_documentation_en-US" xlink:label="lab_logan_PortmanLoganMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Portman-Logan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_PortmanLoganMember" xlink:href="logan-20251231.xsd#logan_PortmanLoganMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_PortmanLoganMember" xlink:to="lab_logan_PortmanLoganMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LicensingAgreementsMember_019bffd7-5159-7dc5-80ca-63f7f7973aff_terseLabel_en-US" xlink:label="lab_us-gaap_LicensingAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Licensing Agreements</link:label>
    <link:label id="lab_us-gaap_LicensingAgreementsMember_label_en-US" xlink:label="lab_us-gaap_LicensingAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Licensing Agreements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LicensingAgreementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LicensingAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LicensingAgreementsMember" xlink:to="lab_us-gaap_LicensingAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesDeferredExpenseReservesAndAccruals_019bffd7-515a-78de-8492-324b8434d8dc_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesDeferredExpenseReservesAndAccruals" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Insurance reserves</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesDeferredExpenseReservesAndAccruals_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesDeferredExpenseReservesAndAccruals" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Deferred Expense, Reserves and Accruals</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesDeferredExpenseReservesAndAccruals" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesDeferredExpenseReservesAndAccruals"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesDeferredExpenseReservesAndAccruals" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesDeferredExpenseReservesAndAccruals" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOther_019bffd7-515a-76ab-b695-f6096ca4cc04_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets tax value in excess of book value</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOther_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOther" xlink:to="lab_us-gaap_DeferredTaxAssetsOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_019bffd7-515b-7a7e-ae9b-dd0ed9ff89eb_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:to="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DebtObligationMember_019bffd7-5159-7105-9949-4ea6e0449b5a_terseLabel_en-US" xlink:label="lab_logan_DebtObligationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt obligation</link:label>
    <link:label id="lab_logan_DebtObligationMember_label_en-US" xlink:label="lab_logan_DebtObligationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Obligation [Member]</link:label>
    <link:label id="lab_logan_DebtObligationMember_documentation_en-US" xlink:label="lab_logan_DebtObligationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DebtObligationMember" xlink:href="logan-20251231.xsd#logan_DebtObligationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DebtObligationMember" xlink:to="lab_logan_DebtObligationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdministrativeFeePayable_019bffd7-515b-75e8-a75d-b446af6ed77c_terseLabel_en-US" xlink:label="lab_us-gaap_AdministrativeFeePayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administrative fees payable</link:label>
    <link:label id="lab_us-gaap_AdministrativeFeePayable_label_en-US" xlink:label="lab_us-gaap_AdministrativeFeePayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Administrative Fee Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdministrativeFeePayable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdministrativeFeePayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdministrativeFeePayable" xlink:to="lab_us-gaap_AdministrativeFeePayable" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InsurancePolicyBenefitsAndClaimsNet_019bffd7-5157-7fe1-84c4-1fc57c6bb2bf_negatedTerseLabel_en-US" xlink:label="lab_logan_InsurancePolicyBenefitsAndClaimsNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net policy benefit and claims (remeasurement gain on policy liabilities of $9,872 and $16,237 for the year ended December 31, 2025 and 2024, respectively)</link:label>
    <link:label id="lab_logan_InsurancePolicyBenefitsAndClaimsNet_label_en-US" xlink:label="lab_logan_InsurancePolicyBenefitsAndClaimsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance Policy Benefits And Claims, Net</link:label>
    <link:label id="lab_logan_InsurancePolicyBenefitsAndClaimsNet_documentation_en-US" xlink:label="lab_logan_InsurancePolicyBenefitsAndClaimsNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Insurance Policy Benefits And Claims, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InsurancePolicyBenefitsAndClaimsNet" xlink:href="logan-20251231.xsd#logan_InsurancePolicyBenefitsAndClaimsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InsurancePolicyBenefitsAndClaimsNet" xlink:to="lab_logan_InsurancePolicyBenefitsAndClaimsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ProfitSharingInterestMember_019bffd7-5159-7fc9-91a9-91dccb0fc53b_terseLabel_en-US" xlink:label="lab_logan_ProfitSharingInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Profit Sharing Interest</link:label>
    <link:label id="lab_logan_ProfitSharingInterestMember_label_en-US" xlink:label="lab_logan_ProfitSharingInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Profit Sharing Interest [Member]</link:label>
    <link:label id="lab_logan_ProfitSharingInterestMember_documentation_en-US" xlink:label="lab_logan_ProfitSharingInterestMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Profit Sharing Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ProfitSharingInterestMember" xlink:href="logan-20251231.xsd#logan_ProfitSharingInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ProfitSharingInterestMember" xlink:to="lab_logan_ProfitSharingInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_IncentiveFeeReceivable_019bffd7-515a-79b9-9609-cb7730378aae_terseLabel_en-US" xlink:label="lab_logan_IncentiveFeeReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Incentive fee receivable - related parties</link:label>
    <link:label id="lab_logan_IncentiveFeeReceivable_label_en-US" xlink:label="lab_logan_IncentiveFeeReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incentive Fee Receivable</link:label>
    <link:label id="lab_logan_IncentiveFeeReceivable_documentation_en-US" xlink:label="lab_logan_IncentiveFeeReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Incentive Fee Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_IncentiveFeeReceivable" xlink:href="logan-20251231.xsd#logan_IncentiveFeeReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_IncentiveFeeReceivable" xlink:to="lab_logan_IncentiveFeeReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightAxis_019bffd7-5159-72ff-850c-c37cb54fe68a_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Axis]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightAxis_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfWarrantOrRightAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightAxis" xlink:to="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_019bffd7-515a-7545-a505-4c039db7c7cf_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiability" xlink:to="lab_us-gaap_OperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices_019bffd7-515a-7998-872d-ad79ebe7d0a5_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares issued for services (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Issued for Services</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesIssuedForServices"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectsOfReinsuranceTable_019bffd7-515a-70ce-9714-61ed9f2e1a0e_terseLabel_en-US" xlink:label="lab_us-gaap_EffectsOfReinsuranceTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effects of Reinsurance [Table]</link:label>
    <link:label id="lab_us-gaap_EffectsOfReinsuranceTable_label_en-US" xlink:label="lab_us-gaap_EffectsOfReinsuranceTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effects of Reinsurance [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectsOfReinsuranceTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectsOfReinsuranceTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectsOfReinsuranceTable" xlink:to="lab_us-gaap_EffectsOfReinsuranceTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_019bffd7-5159-76ab-9af5-652fbcecd366_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans 90 days or more past due</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Equal to or Greater than 90 Days Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:to="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_019bffd7-5157-7619-a8fe-e0a23b315df7_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LIABILITIES</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAbstract" xlink:to="lab_us-gaap_LiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_019bffd7-5158-72c0-854f-7a80bc3c8d96_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business combinations</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:to="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure_019bffd7-5159-7718-88e7-be53d9ff957f_totalLabel_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Liabilities</link:label>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Liabilities Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialLiabilitiesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:to="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_KeyManagementPersonnelCompensationMember_019bffd7-515b-75aa-9cf5-8aecea1ac992_terseLabel_en-US" xlink:label="lab_logan_KeyManagementPersonnelCompensationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Key Management Personnel Compensation</link:label>
    <link:label id="lab_logan_KeyManagementPersonnelCompensationMember_label_en-US" xlink:label="lab_logan_KeyManagementPersonnelCompensationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Key Management Personnel Compensation [Member]</link:label>
    <link:label id="lab_logan_KeyManagementPersonnelCompensationMember_documentation_en-US" xlink:label="lab_logan_KeyManagementPersonnelCompensationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Key Management Personnel Compensation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_KeyManagementPersonnelCompensationMember" xlink:href="logan-20251231.xsd#logan_KeyManagementPersonnelCompensationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_KeyManagementPersonnelCompensationMember" xlink:to="lab_logan_KeyManagementPersonnelCompensationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_IndefiniteLivedIntangibleAssetsAccumulatedImpairment_019cade0-5e59-7f12-a1d9-8a4656f25c51_negatedLabel_en-US" xlink:label="lab_logan_IndefiniteLivedIntangibleAssetsAccumulatedImpairment" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Accumulated impairment</link:label>
    <link:label id="lab_logan_IndefiniteLivedIntangibleAssetsAccumulatedImpairment_label_en-US" xlink:label="lab_logan_IndefiniteLivedIntangibleAssetsAccumulatedImpairment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets, Accumulated Impairment</link:label>
    <link:label id="lab_logan_IndefiniteLivedIntangibleAssetsAccumulatedImpairment_documentation_en-US" xlink:label="lab_logan_IndefiniteLivedIntangibleAssetsAccumulatedImpairment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets, Accumulated Impairment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_IndefiniteLivedIntangibleAssetsAccumulatedImpairment" xlink:href="logan-20251231.xsd#logan_IndefiniteLivedIntangibleAssetsAccumulatedImpairment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_IndefiniteLivedIntangibleAssetsAccumulatedImpairment" xlink:to="lab_logan_IndefiniteLivedIntangibleAssetsAccumulatedImpairment" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DebtInstrumentInterestRatePayablePeriodAxis_019bffd7-515b-7314-8d38-c2749bdc6029_terseLabel_en-US" xlink:label="lab_logan_DebtInstrumentInterestRatePayablePeriodAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate Payable, Period [Axis]</link:label>
    <link:label id="lab_logan_DebtInstrumentInterestRatePayablePeriodAxis_label_en-US" xlink:label="lab_logan_DebtInstrumentInterestRatePayablePeriodAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate Payable, Period [Axis]</link:label>
    <link:label id="lab_logan_DebtInstrumentInterestRatePayablePeriodAxis_documentation_en-US" xlink:label="lab_logan_DebtInstrumentInterestRatePayablePeriodAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate Payable, Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DebtInstrumentInterestRatePayablePeriodAxis" xlink:href="logan-20251231.xsd#logan_DebtInstrumentInterestRatePayablePeriodAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DebtInstrumentInterestRatePayablePeriodAxis" xlink:to="lab_logan_DebtInstrumentInterestRatePayablePeriodAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_019bffd7-5159-7a32-a4d7-176ae7fb64be_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial assets</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_019c371d-c53b-732a-a106-f3859e585a6d_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill impairment</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_019c4b63-4a6a-7c44-87fa-1e276d183287_verboseLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Goodwill Impairment</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_019c5307-b36e-72be-bef4-e14e50a7c1ef_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Goodwill impairment</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_019cadcc-198c-78ae-9846-b08f69407644_negatedNetLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2009/role/negatedNetLabel" xlink:type="resource" xml:lang="en-US">Impairment loss - Goodwill</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_label_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Impairment Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillImpairmentLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillImpairmentLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillImpairmentLoss" xlink:to="lab_us-gaap_GoodwillImpairmentLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock_019bffd7-515b-791c-b540-88577232dfcb_terseLabel_en-US" xlink:label="lab_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital management and regulatory requirements</link:label>
    <link:label id="lab_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock_label_en-US" xlink:label="lab_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Regulatory Capital Requirements under Banking Regulations [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock" xlink:to="lab_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_019bffd7-5158-795d-9ea4-df578573513e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightUnissued_019bffd7-515a-7b7e-bdfa-126ad5663390_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightUnissued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of warrant or right, unissued (in shares)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightUnissued_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightUnissued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Unissued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightUnissued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfWarrantOrRightUnissued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightUnissued" xlink:to="lab_us-gaap_ClassOfWarrantOrRightUnissued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_NumberOfProductLines_019bffd7-515b-7c86-a4c4-140193037ede_terseLabel_en-US" xlink:label="lab_logan_NumberOfProductLines" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of product lines</link:label>
    <link:label id="lab_logan_NumberOfProductLines_label_en-US" xlink:label="lab_logan_NumberOfProductLines" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Product Lines</link:label>
    <link:label id="lab_logan_NumberOfProductLines_documentation_en-US" xlink:label="lab_logan_NumberOfProductLines" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Product Lines</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_NumberOfProductLines" xlink:href="logan-20251231.xsd#logan_NumberOfProductLines"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_NumberOfProductLines" xlink:to="lab_logan_NumberOfProductLines" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumRollForward_019bffd7-515a-77f8-970a-d5ec626fc984_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Present value of expected net premiums</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumRollForward_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Net Premium [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumRollForward" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_019bffd7-5157-7f5d-a6a4-5685c67773b7_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive income (loss)</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_019bffd7-5159-7c76-837f-beaef20f292f_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeAxis" xlink:to="lab_us-gaap_MeasurementInputTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_AdditionalLiabilityLongDurationInsuranceWeightedAverageDurationAtOriginalRate_019bffd7-515a-789a-ad89-4ec410cd8b6b_terseLabel_en-US" xlink:label="lab_logan_AdditionalLiabilityLongDurationInsuranceWeightedAverageDurationAtOriginalRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average duration of liability (years) at original rate</link:label>
    <link:label id="lab_logan_AdditionalLiabilityLongDurationInsuranceWeightedAverageDurationAtOriginalRate_label_en-US" xlink:label="lab_logan_AdditionalLiabilityLongDurationInsuranceWeightedAverageDurationAtOriginalRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Liability, Long-Duration Insurance, Weighted Average Duration At Original Rate</link:label>
    <link:label id="lab_logan_AdditionalLiabilityLongDurationInsuranceWeightedAverageDurationAtOriginalRate_documentation_en-US" xlink:label="lab_logan_AdditionalLiabilityLongDurationInsuranceWeightedAverageDurationAtOriginalRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Additional Liability, Long-Duration Insurance, Weighted Average Duration At Original Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_AdditionalLiabilityLongDurationInsuranceWeightedAverageDurationAtOriginalRate" xlink:href="logan-20251231.xsd#logan_AdditionalLiabilityLongDurationInsuranceWeightedAverageDurationAtOriginalRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_AdditionalLiabilityLongDurationInsuranceWeightedAverageDurationAtOriginalRate" xlink:to="lab_logan_AdditionalLiabilityLongDurationInsuranceWeightedAverageDurationAtOriginalRate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock_019bffd7-515a-7ab7-bc2c-764dfb1fef06_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Income (Loss) Before Income Taxes by Jurisdiction</link:label>
    <link:label id="lab_us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Income before Income Tax, Domestic and Foreign [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_019bffd7-5158-7d7b-a160-13b30a5735ad_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due in one year or less</link:label>
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    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_019bffd7-5159-7350-94e5-53d4a39f7e47_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent_019bffd7-5157-73a7-9b71-89fa9452fa3d_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss), before tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent_019bffd7-5157-7a58-92c1-7a8d2e5bc236_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), before Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent"/>
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    <link:label id="lab_us-gaap_ClassOfStockLineItems_019bffd7-515a-71bc-842b-47b89f26fca1_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_label_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockLineItems" xlink:to="lab_us-gaap_ClassOfStockLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InternalCreditAssessmentLevelFourMember_019bffd7-5158-788f-a368-36ad60227b21_terseLabel_en-US" xlink:label="lab_logan_InternalCreditAssessmentLevelFourMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 4</link:label>
    <link:label id="lab_logan_InternalCreditAssessmentLevelFourMember_label_en-US" xlink:label="lab_logan_InternalCreditAssessmentLevelFourMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment Level Four [Member]</link:label>
    <link:label id="lab_logan_InternalCreditAssessmentLevelFourMember_documentation_en-US" xlink:label="lab_logan_InternalCreditAssessmentLevelFourMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment Level Four</link:label>
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    <link:label id="lab_us-gaap_OtherLiabilitiesTableTextBlock_019bffd7-515a-714e-9f65-c9b00b5b4b2c_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_OtherLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_StockIssuedDuringPeriodSharesShareBasedPaymentArrangement_019bffd7-5158-7429-bc9a-4ea1e5b52d5a_terseLabel_en-US" xlink:label="lab_logan_StockIssuedDuringPeriodSharesShareBasedPaymentArrangement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common shares for share based compensation</link:label>
    <link:label id="lab_logan_StockIssuedDuringPeriodSharesShareBasedPaymentArrangement_label_en-US" xlink:label="lab_logan_StockIssuedDuringPeriodSharesShareBasedPaymentArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Share-Based Payment Arrangement</link:label>
    <link:label id="lab_logan_StockIssuedDuringPeriodSharesShareBasedPaymentArrangement_documentation_en-US" xlink:label="lab_logan_StockIssuedDuringPeriodSharesShareBasedPaymentArrangement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Share-Based Payment Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_StockIssuedDuringPeriodSharesShareBasedPaymentArrangement" xlink:href="logan-20251231.xsd#logan_StockIssuedDuringPeriodSharesShareBasedPaymentArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_StockIssuedDuringPeriodSharesShareBasedPaymentArrangement" xlink:to="lab_logan_StockIssuedDuringPeriodSharesShareBasedPaymentArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ScheduleOfFuturePolicyBenefitsAndReinsuranceRecoverableTableTextBlock_019bffd7-515a-766e-b90a-009e0deec53c_terseLabel_en-US" xlink:label="lab_logan_ScheduleOfFuturePolicyBenefitsAndReinsuranceRecoverableTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule Of Future Policy Benefits And Reinsurance Recoverable</link:label>
    <link:label id="lab_logan_ScheduleOfFuturePolicyBenefitsAndReinsuranceRecoverableTableTextBlock_label_en-US" xlink:label="lab_logan_ScheduleOfFuturePolicyBenefitsAndReinsuranceRecoverableTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Future Policy Benefits And Reinsurance Recoverable [Table Text Block]</link:label>
    <link:label id="lab_logan_ScheduleOfFuturePolicyBenefitsAndReinsuranceRecoverableTableTextBlock_documentation_en-US" xlink:label="lab_logan_ScheduleOfFuturePolicyBenefitsAndReinsuranceRecoverableTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule Of Future Policy Benefits And Reinsurance Recoverable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ScheduleOfFuturePolicyBenefitsAndReinsuranceRecoverableTableTextBlock" xlink:href="logan-20251231.xsd#logan_ScheduleOfFuturePolicyBenefitsAndReinsuranceRecoverableTableTextBlock"/>
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    <link:label id="lab_us-gaap_LongTermDebt_019bffd7-5159-7824-a6da-965bf4c62e7c_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt obligations</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_019bffd7-5159-797d-862a-85816b628393_totalLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_019bffd7-515a-756d-b143-017fb8318890_netLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Carrying value of note</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LegalEntityAxis_019bffd7-5157-7b8c-8f6d-1962f9056ddc_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LegalEntityAxis"/>
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    <link:label id="lab_us-gaap_Assets_019bffd7-5157-7b38-8499-b93aab24e85c_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_Assets_019bffd7-5159-779d-a896-7900d9e6133d_verboseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Carrying amount</link:label>
    <link:label id="lab_us-gaap_Assets_019bffd7-5159-75ec-a415-4a58dc799059_terseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total financial assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract_019bffd7-5158-71fd-a41e-c7eb2c1e4b69_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investing Activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Continuing Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_019bffd7-5159-7abb-a802-892c33ddec4d_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths"/>
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    <link:label id="lab_us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember_019bffd7-5158-7001-b9e5-caba8d8d43d8_verboseLabel_en-US" xlink:label="lab_us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair value option</link:label>
    <link:label id="lab_us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember_019bffd7-5158-7d87-9754-2f41fcbae407_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other than Fair Value Measurement</link:label>
    <link:label id="lab_us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Other than Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue"/>
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    <link:label id="lab_logan_PromissoryNoteDueOctober2040Member_label_en-US" xlink:label="lab_logan_PromissoryNoteDueOctober2040Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Promissory Note due October 2040 [Member]</link:label>
    <link:label id="lab_logan_PromissoryNoteDueOctober2040Member_documentation_en-US" xlink:label="lab_logan_PromissoryNoteDueOctober2040Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Promissory Note due October 2040</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_PromissoryNoteDueOctober2040Member" xlink:href="logan-20251231.xsd#logan_PromissoryNoteDueOctober2040Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_PromissoryNoteDueOctober2040Member" xlink:to="lab_logan_PromissoryNoteDueOctober2040Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_019bffd7-5158-7d99-94bd-d9ace6e94ef3_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents and Restricted cash</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Restricted Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:to="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_SegmentGeographicalDomain_019bffd7-515a-75ab-bca8-0045db74b3ca_terseLabel_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:label id="lab_srt_SegmentGeographicalDomain_label_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_SegmentGeographicalDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_SegmentGeographicalDomain" xlink:to="lab_srt_SegmentGeographicalDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_CanadianFixedIncomeManagerMember_019bffd7-515a-7aa8-9291-4bd918daec31_terseLabel_en-US" xlink:label="lab_logan_CanadianFixedIncomeManagerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Canadian Fixed Income Manager</link:label>
    <link:label id="lab_logan_CanadianFixedIncomeManagerMember_label_en-US" xlink:label="lab_logan_CanadianFixedIncomeManagerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Canadian Fixed Income Manager [Member]</link:label>
    <link:label id="lab_logan_CanadianFixedIncomeManagerMember_documentation_en-US" xlink:label="lab_logan_CanadianFixedIncomeManagerMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Canadian Fixed Income Manager</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_CanadianFixedIncomeManagerMember" xlink:href="logan-20251231.xsd#logan_CanadianFixedIncomeManagerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_CanadianFixedIncomeManagerMember" xlink:to="lab_logan_CanadianFixedIncomeManagerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_019bffd7-5158-7f50-9a5c-f66f260624dc_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:to="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward_019bffd7-5159-791b-9bea-772b2f54229c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:to="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivableInvestmentSale_019bffd7-515a-781c-a639-7243e8796197_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivableInvestmentSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable for investments sold</link:label>
    <link:label id="lab_us-gaap_ReceivableInvestmentSale_label_en-US" xlink:label="lab_us-gaap_ReceivableInvestmentSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable, Investment, Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivableInvestmentSale" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReceivableInvestmentSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivableInvestmentSale" xlink:to="lab_us-gaap_ReceivableInvestmentSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_019bffd7-515b-7b8b-b044-43eb16e17a1d_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:to="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_YieldstreetAlternativeIncomeFundMember_019d0539-d121-79f6-9ce7-415ac0cf5fb9_terseLabel_en-US" xlink:label="lab_logan_YieldstreetAlternativeIncomeFundMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Yieldstreet Alternative Income Fund</link:label>
    <link:label id="lab_logan_YieldstreetAlternativeIncomeFundMember_label_en-US" xlink:label="lab_logan_YieldstreetAlternativeIncomeFundMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Yieldstreet Alternative Income Fund [Member]</link:label>
    <link:label id="lab_logan_YieldstreetAlternativeIncomeFundMember_documentation_en-US" xlink:label="lab_logan_YieldstreetAlternativeIncomeFundMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Yieldstreet Alternative Income Fund</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_YieldstreetAlternativeIncomeFundMember" xlink:href="logan-20251231.xsd#logan_YieldstreetAlternativeIncomeFundMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_YieldstreetAlternativeIncomeFundMember" xlink:to="lab_logan_YieldstreetAlternativeIncomeFundMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InsuranceSolutionsSegmentMember_019bffd7-5157-7f9f-9f7f-0227e1d382e9_terseLabel_en-US" xlink:label="lab_logan_InsuranceSolutionsSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance Solutions</link:label>
    <link:label id="lab_logan_InsuranceSolutionsSegmentMember_019c4b5b-bcee-7015-8fb1-9f58d834b234_verboseLabel_en-US" xlink:label="lab_logan_InsuranceSolutionsSegmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Insurance Solutions</link:label>
    <link:label id="lab_logan_InsuranceSolutionsSegmentMember_label_en-US" xlink:label="lab_logan_InsuranceSolutionsSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance Solutions Segment [Member]</link:label>
    <link:label id="lab_logan_InsuranceSolutionsSegmentMember_documentation_en-US" xlink:label="lab_logan_InsuranceSolutionsSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Insurance Solutions Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InsuranceSolutionsSegmentMember" xlink:href="logan-20251231.xsd#logan_InsuranceSolutionsSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InsuranceSolutionsSegmentMember" xlink:to="lab_logan_InsuranceSolutionsSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_019bffd7-5159-78f0-8618-2ae0d43b70bd_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial assets</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:to="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_019bffd7-5159-7e84-89eb-205f5b5620ba_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_019bffd7-5158-70f3-bd42-bccab5504bcb_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableInterestEntityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityLineItems" xlink:to="lab_us-gaap_VariableInterestEntityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_019bffd7-515a-7fed-bc55-c33820850e94_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends declared (per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Declared</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockDividendsPerShareDeclared"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:to="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationVariableInterestEntityPolicy_019bffd7-5158-7c3e-b534-0349b8c82819_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationVariableInterestEntityPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial instruments held by consolidated VIEs</link:label>
    <link:label id="lab_us-gaap_ConsolidationVariableInterestEntityPolicy_label_en-US" xlink:label="lab_us-gaap_ConsolidationVariableInterestEntityPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Variable Interest Entity, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationVariableInterestEntityPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConsolidationVariableInterestEntityPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationVariableInterestEntityPolicy" xlink:to="lab_us-gaap_ConsolidationVariableInterestEntityPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WarrantMember_019bffd7-515b-71ca-808b-f8970ecd0897_terseLabel_en-US" xlink:label="lab_us-gaap_WarrantMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average number of unexcercised warrants</link:label>
    <link:label id="lab_us-gaap_WarrantMember_label_en-US" xlink:label="lab_us-gaap_WarrantMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrant [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WarrantMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WarrantMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WarrantMember" xlink:to="lab_us-gaap_WarrantMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_019bffd7-5157-7086-8f13-b5bbba989b56_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_019bffd7-5159-7d64-9335-e2ef9104592d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 2</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFinStmtErrorCorrectionFlag_019c7b3a-4c1e-7a24-bff6-2a6f3d89fe91_terseLabel_en-US" xlink:label="lab_dei_DocumentFinStmtErrorCorrectionFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Financial Statement Error Correction [Flag]</link:label>
    <link:label id="lab_dei_DocumentFinStmtErrorCorrectionFlag_label_en-US" xlink:label="lab_dei_DocumentFinStmtErrorCorrectionFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Financial Statement Error Correction [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFinStmtErrorCorrectionFlag" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFinStmtErrorCorrectionFlag"/>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes_019bffd7-515a-7732-bc74-0f8dd6a0e19c_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State and local income taxes, net of federal (national) income tax effect</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_019bffd7-5157-7f84-b7cf-8e3a641a78cf_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:to="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyMember_019bffd7-5157-7c2f-84e1-98e671fca996_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party</link:label>
    <link:label id="lab_us-gaap_RelatedPartyMember_label_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyMember" xlink:to="lab_us-gaap_RelatedPartyMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_EquityMethodInvestmentsMember_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsMember" xlink:to="lab_us-gaap_EquityMethodInvestmentsMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock_019bffd7-515a-772b-ae59-aa1cabd08f09_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Income Tax Provision by Jurisdiction</link:label>
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    <link:label id="lab_logan_PaidInKindInterestNet_019bffd7-5158-7177-bc66-48c30c2cb999_terseLabel_en-US" xlink:label="lab_logan_PaidInKindInterestNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payment in-kind interest</link:label>
    <link:label id="lab_logan_PaidInKindInterestNet_label_en-US" xlink:label="lab_logan_PaidInKindInterestNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Paid-in-Kind Interest, Net</link:label>
    <link:label id="lab_logan_PaidInKindInterestNet_documentation_en-US" xlink:label="lab_logan_PaidInKindInterestNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Paid-in-Kind Interest, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_PaidInKindInterestNet" xlink:href="logan-20251231.xsd#logan_PaidInKindInterestNet"/>
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    <link:label id="lab_dei_DocumentInformationTable_019c7b21-3fa1-754c-932d-500f1e2c7aa9_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
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    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
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    <link:label id="lab_logan_ProfitSharingInterestDistributionEntitlementPercentage_019bffd7-515b-723c-beb2-318d05a323f0_terseLabel_en-US" xlink:label="lab_logan_ProfitSharingInterestDistributionEntitlementPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Profit sharing interest, distribution entitlement percentage</link:label>
    <link:label id="lab_logan_ProfitSharingInterestDistributionEntitlementPercentage_label_en-US" xlink:label="lab_logan_ProfitSharingInterestDistributionEntitlementPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Profit Sharing Interest, Distribution Entitlement Percentage</link:label>
    <link:label id="lab_logan_ProfitSharingInterestDistributionEntitlementPercentage_documentation_en-US" xlink:label="lab_logan_ProfitSharingInterestDistributionEntitlementPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Profit Sharing Interest, Distribution Entitlement Percentage</link:label>
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    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3_019bffd7-5159-71ca-b307-373feb015ba5_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfer in</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromSaleMaturityAndCollectionsOfInvestments_019bffd7-5158-7bc4-b220-897682d52328_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleMaturityAndCollectionsOfInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sales and repayments of investments</link:label>
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    <link:label id="lab_us-gaap_InvestmentIncomeInterest_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeInterest"/>
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    <link:label id="lab_logan_RelatedPartyInterestIncomeMember_label_en-US" xlink:label="lab_logan_RelatedPartyInterestIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Interest Income [Member]</link:label>
    <link:label id="lab_logan_RelatedPartyInterestIncomeMember_documentation_en-US" xlink:label="lab_logan_RelatedPartyInterestIncomeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Interest Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_RelatedPartyInterestIncomeMember" xlink:href="logan-20251231.xsd#logan_RelatedPartyInterestIncomeMember"/>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance_019bffd7-515a-7bc8-b39b-ae9fd13a590d_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax assets not recognized (valuation allowance)</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:to="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsMember_019bffd7-5157-79e2-bf8c-affacdc7acb5_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsMember" xlink:to="lab_us-gaap_RetainedEarningsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_019bffd7-515a-7701-962c-f85335415b9f_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxAuthorityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxAuthorityAxis" xlink:to="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_UnsecuredPromissoryNoteMember_019bffd7-5159-72a1-862b-a44de6cd4075_terseLabel_en-US" xlink:label="lab_logan_UnsecuredPromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured Promissory Note</link:label>
    <link:label id="lab_logan_UnsecuredPromissoryNoteMember_label_en-US" xlink:label="lab_logan_UnsecuredPromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Promissory Note [Member]</link:label>
    <link:label id="lab_logan_UnsecuredPromissoryNoteMember_documentation_en-US" xlink:label="lab_logan_UnsecuredPromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unsecured Promissory Note</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_UnsecuredPromissoryNoteMember" xlink:href="logan-20251231.xsd#logan_UnsecuredPromissoryNoteMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_UnsecuredPromissoryNoteMember" xlink:to="lab_logan_UnsecuredPromissoryNoteMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:to="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019bffd7-5158-72fa-84d8-8d920a590892_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents and restricted cash, and cash and cash equivalents of consolidated VIEs, beginning of the period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019bffd7-5158-77e3-94e2-de8126d2be71_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents and restricted cash, and cash and cash equivalents of consolidated VIEs, end of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_OtherInvestedAssetsMeasurementInputs_019bffd7-5159-7054-a3cf-ed2c8591e18f_terseLabel_en-US" xlink:label="lab_logan_OtherInvestedAssetsMeasurementInputs" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other invested assets , measurement input</link:label>
    <link:label id="lab_logan_OtherInvestedAssetsMeasurementInputs_label_en-US" xlink:label="lab_logan_OtherInvestedAssetsMeasurementInputs" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Invested Assets, Measurement Inputs</link:label>
    <link:label id="lab_logan_OtherInvestedAssetsMeasurementInputs_documentation_en-US" xlink:label="lab_logan_OtherInvestedAssetsMeasurementInputs" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Invested Assets, Measurement Inputs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_OtherInvestedAssetsMeasurementInputs" xlink:href="logan-20251231.xsd#logan_OtherInvestedAssetsMeasurementInputs"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_OtherInvestedAssetsMeasurementInputs" xlink:to="lab_logan_OtherInvestedAssetsMeasurementInputs" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssets_019bffd7-5159-7451-beda-cf14e09fa44d_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_019c7c36-88e5-761a-9c06-667cae78cf76_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_label_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssets" xlink:to="lab_us-gaap_DerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_IncomeLossFromContinuingOperationsBeforeIncomeTaxesNoncontrollingInterestAdjusted_019bffd7-515b-7b50-901c-d89eebd2ed05_totalLabel_en-US" xlink:label="lab_logan_IncomeLossFromContinuingOperationsBeforeIncomeTaxesNoncontrollingInterestAdjusted" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Segment income</link:label>
    <link:label id="lab_logan_IncomeLossFromContinuingOperationsBeforeIncomeTaxesNoncontrollingInterestAdjusted_label_en-US" xlink:label="lab_logan_IncomeLossFromContinuingOperationsBeforeIncomeTaxesNoncontrollingInterestAdjusted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) From Continuing Operations Before Income Taxes, Noncontrolling Interest, Adjusted</link:label>
    <link:label id="lab_logan_IncomeLossFromContinuingOperationsBeforeIncomeTaxesNoncontrollingInterestAdjusted_documentation_en-US" xlink:label="lab_logan_IncomeLossFromContinuingOperationsBeforeIncomeTaxesNoncontrollingInterestAdjusted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income (Loss) From Continuing Operations Before Income Taxes, Noncontrolling Interest, Adjusted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_IncomeLossFromContinuingOperationsBeforeIncomeTaxesNoncontrollingInterestAdjusted" xlink:href="logan-20251231.xsd#logan_IncomeLossFromContinuingOperationsBeforeIncomeTaxesNoncontrollingInterestAdjusted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_IncomeLossFromContinuingOperationsBeforeIncomeTaxesNoncontrollingInterestAdjusted" xlink:to="lab_logan_IncomeLossFromContinuingOperationsBeforeIncomeTaxesNoncontrollingInterestAdjusted" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearTwo_019bffd7-5158-7b20-ab92-1f0334ab5653_terseLabel_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearTwo_label_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss Maturity, Year Two</link:label>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearTwo_documentation_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearTwo" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss Maturity, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearTwo" xlink:href="logan-20251231.xsd#logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearTwo" xlink:to="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger_019bffd7-5158-7cb2-99eb-3a44188879eb_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">12 months or more</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, 12 Months or Longer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent_019bffd7-515a-7758-b94b-1f0d6dab5d06_terseLabel_en-US" xlink:label="lab_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss), before reclassifications</link:label>
    <link:label id="lab_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OCI, before Reclassifications, before Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent" xlink:to="lab_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_019c7c2c-c0ed-7cea-81ce-19ad31deed64_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleOfStockNameOfTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_019bffd7-5157-71d1-b1ff-d6b6d8f7a4da_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_019bffd7-5159-7950-91d7-7d3f5860c7d3_totalLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net carrying amount</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Assets, Net (Excluding Goodwill)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IntangibleAssetsNetExcludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:to="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductsAndServicesDomain_019bffd7-5157-72fe-b1bb-b2b31b4cb168_terseLabel_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:label id="lab_srt_ProductsAndServicesDomain_label_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductsAndServicesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductsAndServicesDomain" xlink:to="lab_srt_ProductsAndServicesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesAbstract_019bffd7-5158-71f9-8da2-5fca0f6971b5_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt securities:</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromInterestReceived_019bffd7-5158-7e74-9baa-64520af17b30_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromInterestReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest received</link:label>
    <link:label id="lab_us-gaap_ProceedsFromInterestReceived_label_en-US" xlink:label="lab_us-gaap_ProceedsFromInterestReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Interest Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromInterestReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromInterestReceived"/>
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    <link:label id="lab_us-gaap_ReinsurerConcentrationRiskMember_019bffd7-515b-739d-8775-bab7b9928fbc_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsurerConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurer Concentration Risk</link:label>
    <link:label id="lab_us-gaap_ReinsurerConcentrationRiskMember_label_en-US" xlink:label="lab_us-gaap_ReinsurerConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurer Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsurerConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsurerConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsurerConcentrationRiskMember" xlink:to="lab_us-gaap_ReinsurerConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetInvestmentIncome_019bffd7-5157-73be-b596-dda7b8716c87_terseLabel_en-US" xlink:label="lab_us-gaap_NetInvestmentIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net investment income</link:label>
    <link:label id="lab_us-gaap_NetInvestmentIncome_019bffd7-5158-7259-a8a3-348a2b7e6326_totalLabel_en-US" xlink:label="lab_us-gaap_NetInvestmentIncome" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net investment income</link:label>
    <link:label id="lab_us-gaap_NetInvestmentIncome_label_en-US" xlink:label="lab_us-gaap_NetInvestmentIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Investment Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetInvestmentIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetInvestmentIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetInvestmentIncome" xlink:to="lab_us-gaap_NetInvestmentIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ManagementFeeReceivable_019bffd7-515a-77a6-842e-d9912f7b5ad2_terseLabel_en-US" xlink:label="lab_logan_ManagementFeeReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Management fee receivable - related parties</link:label>
    <link:label id="lab_logan_ManagementFeeReceivable_label_en-US" xlink:label="lab_logan_ManagementFeeReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management Fee Receivable</link:label>
    <link:label id="lab_logan_ManagementFeeReceivable_documentation_en-US" xlink:label="lab_logan_ManagementFeeReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Management Fee Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ManagementFeeReceivable" xlink:href="logan-20251231.xsd#logan_ManagementFeeReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ManagementFeeReceivable" xlink:to="lab_logan_ManagementFeeReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiMeasurementInput_019bffd7-5159-7144-820e-23c8c245651c_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity securities, measurement input</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiMeasurementInput_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNiMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNiMeasurementInput" xlink:to="lab_us-gaap_EquitySecuritiesFvNiMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_019bffd7-5159-78b1-b793-fa49c3b0864f_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total financial liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:to="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_019bffd7-5158-71d5-906b-d731a6c88f49_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:to="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_019bffd7-5159-7cbd-ae2b-3f4cd4fd3b34_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notional amount</link:label>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNotionalAmount" xlink:to="lab_us-gaap_DerivativeNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
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    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationDomesticationCapitalGainAmount_019c8fb2-7be8-7217-8592-0cc3a72310a6_terseLabel_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationDomesticationCapitalGainAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Domestication capital gain</link:label>
    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationDomesticationCapitalGainAmount_label_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationDomesticationCapitalGainAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Domestication Capital Gain, Amount</link:label>
    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationDomesticationCapitalGainAmount_documentation_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationDomesticationCapitalGainAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Domestication Capital Gain, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_EffectiveIncomeTaxRateReconciliationDomesticationCapitalGainAmount" xlink:href="logan-20251231.xsd#logan_EffectiveIncomeTaxRateReconciliationDomesticationCapitalGainAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_EffectiveIncomeTaxRateReconciliationDomesticationCapitalGainAmount" xlink:to="lab_logan_EffectiveIncomeTaxRateReconciliationDomesticationCapitalGainAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable_019c7c1d-d183-7abb-81ba-04512af8b4df_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Paid, by Individual Jurisdiction [Table]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, by Individual Jurisdiction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidByIndividualJurisdictionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:to="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_019c2cbd-60f9-753a-ae44-35ba51b2d954_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CityAreaCode"/>
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    <link:label id="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_019bffd7-5158-7f4f-9c10-a191f9a34514_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financing Receivable, Allowance for Credit Loss</link:label>
    <link:label id="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:to="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesOnPaidLosses_019bffd7-515a-7c17-84e5-288f0a911d60_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesOnPaidLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net ceded reinsurance recoverable</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesOnPaidLosses_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesOnPaidLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable for Paid Claims and Claims Adjustments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesOnPaidLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverablesOnPaidLosses"/>
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    <link:label id="lab_us-gaap_InvestmentTextBlock_019bffd7-5158-7f60-9c79-74004d5ae9d9_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:label id="lab_us-gaap_InvestmentTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentTextBlock" xlink:to="lab_us-gaap_InvestmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansHeldForSaleMeasurementInput_019bffd7-5159-7287-b437-caf436a00ce9_terseLabel_en-US" xlink:label="lab_us-gaap_LoansHeldForSaleMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate loans, measurement input</link:label>
    <link:label id="lab_us-gaap_LoansHeldForSaleMeasurementInput_label_en-US" xlink:label="lab_us-gaap_LoansHeldForSaleMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan, Held-for-Sale, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansHeldForSaleMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansHeldForSaleMeasurementInput"/>
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    <link:label id="lab_logan_SeniorNotesDue2031Member_documentation_en-US" xlink:label="lab_logan_SeniorNotesDue2031Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Senior Notes Due 2031</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable_019bffd7-5158-7d65-a82d-5a640f9af40b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, and Equity Securities, FV-NI [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, and Equity Securities, FV-NI [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable"/>
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    <link:label id="lab_logan_ModcoInvestmentsVistaMember_019bffd7-515a-7ad0-8485-cbf90eac4d4e_terseLabel_en-US" xlink:label="lab_logan_ModcoInvestmentsVistaMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Modco investments Vista</link:label>
    <link:label id="lab_logan_ModcoInvestmentsVistaMember_label_en-US" xlink:label="lab_logan_ModcoInvestmentsVistaMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Modco Investments Vista [Member]</link:label>
    <link:label id="lab_logan_ModcoInvestmentsVistaMember_documentation_en-US" xlink:label="lab_logan_ModcoInvestmentsVistaMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Modco Investments Vista</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ModcoInvestmentsVistaMember" xlink:href="logan-20251231.xsd#logan_ModcoInvestmentsVistaMember"/>
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    <link:label id="lab_logan_IncreaseDecreaseGuaranteedInterestContracts_019bffd7-5158-796c-8f51-1613b9742f8f_terseLabel_en-US" xlink:label="lab_logan_IncreaseDecreaseGuaranteedInterestContracts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest sensitive contract liabilities</link:label>
    <link:label id="lab_logan_IncreaseDecreaseGuaranteedInterestContracts_label_en-US" xlink:label="lab_logan_IncreaseDecreaseGuaranteedInterestContracts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase Decrease Guaranteed Interest Contracts</link:label>
    <link:label id="lab_logan_IncreaseDecreaseGuaranteedInterestContracts_documentation_en-US" xlink:label="lab_logan_IncreaseDecreaseGuaranteedInterestContracts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase Decrease Guaranteed Interest Contracts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_IncreaseDecreaseGuaranteedInterestContracts" xlink:href="logan-20251231.xsd#logan_IncreaseDecreaseGuaranteedInterestContracts"/>
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    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PvpTable"/>
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    <link:label id="lab_us-gaap_InterestReceivable_019cbd67-d285-7aa5-95e0-4f8c985ee55b_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Purchase receivables</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_label_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestReceivable" xlink:to="lab_us-gaap_InterestReceivable" xlink:type="arc" order="1"/>
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    <link:label id="lab_logan_ValuationTechniqueEnterpriseValueMember_label_en-US" xlink:label="lab_logan_ValuationTechniqueEnterpriseValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Enterprise Value [Member]</link:label>
    <link:label id="lab_logan_ValuationTechniqueEnterpriseValueMember_documentation_en-US" xlink:label="lab_logan_ValuationTechniqueEnterpriseValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Valuation Technique, Enterprise Value</link:label>
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    <link:label id="lab_us-gaap_AdditionalLiabilityLongDurationInsuranceWeightedAverageDuration_019bffd7-515a-7bfb-b214-363d83a4b9a5_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalLiabilityLongDurationInsuranceWeightedAverageDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average duration of liability (years) at current rate</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalLiabilityLongDurationInsuranceWeightedAverageDuration" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalLiabilityLongDurationInsuranceWeightedAverageDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalLiabilityLongDurationInsuranceWeightedAverageDuration" xlink:to="lab_us-gaap_AdditionalLiabilityLongDurationInsuranceWeightedAverageDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:to="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems_019bffd7-515a-7f71-b7fc-958a73d1ac65_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation [Line Items]</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationLineItems"/>
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    <link:label id="lab_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent_019bffd7-5159-746a-a245-cba477a30cfa_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity securities</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:to="lab_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashFlowHedgingMember_019bffd7-5159-7ae2-93f4-6181933e20bc_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowHedgingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Flow Hedging</link:label>
    <link:label id="lab_us-gaap_CashFlowHedgingMember_label_en-US" xlink:label="lab_us-gaap_CashFlowHedgingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Flow Hedging [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashFlowHedgingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashFlowHedgingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashFlowHedgingMember" xlink:to="lab_us-gaap_CashFlowHedgingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Goodwill_019bffd7-5157-78bd-a4c6-da3f545d4131_terseLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_Goodwill_019bffd7-5159-7495-91eb-0d06c1d80872_periodStartLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance, beginning of period</link:label>
    <link:label id="lab_us-gaap_Goodwill_019bffd7-5159-77b0-9730-44c80c18d715_periodEndLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance, end of period</link:label>
    <link:label id="lab_us-gaap_Goodwill_label_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Goodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Goodwill"/>
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    <link:label id="lab_us-gaap_GainLossOnInvestments_019bffd7-5158-7338-ba20-a6cca691739f_totalLabel_en-US" xlink:label="lab_us-gaap_GainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net gains (losses) from investment activities</link:label>
    <link:label id="lab_us-gaap_GainLossOnInvestments_label_en-US" xlink:label="lab_us-gaap_GainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnInvestments" xlink:to="lab_us-gaap_GainLossOnInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit_019cf499-9881-7769-975d-e93c4d50bf9b_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal</link:label>
    <link:label id="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Federal Income Tax Expense (Benefit)</link:label>
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    <link:label id="lab_dei_AuditorName_019cfdb3-5f56-75a3-8179-13f5d48ad83f_terseLabel_en-US" xlink:label="lab_dei_AuditorName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Name</link:label>
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    <link:label id="lab_us-gaap_ConcentrationRiskTable_019bffd7-515b-7996-bb78-9ed8adab6c2d_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTable_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskTable"/>
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    <link:label id="lab_srt_FinancingReceivableBeforeAllowanceForCreditLossMaturityTableTextBlock_019bffd7-5158-7f72-9f61-d3d5aa2313c6_terseLabel_en-US" xlink:label="lab_srt_FinancingReceivableBeforeAllowanceForCreditLossMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Maturity of Finance Receivables</link:label>
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    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationPartnershipDifferencesAmount_documentation_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationPartnershipDifferencesAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Partnership Differences, Amount</link:label>
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    <link:label id="lab_us-gaap_GuarantyAssets_019bffd7-515a-7f92-9c67-af88b35a0388_terseLabel_en-US" xlink:label="lab_us-gaap_GuarantyAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guaranty funds on deposit</link:label>
    <link:label id="lab_us-gaap_GuarantyAssets_label_en-US" xlink:label="lab_us-gaap_GuarantyAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guaranty Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuarantyAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GuarantyAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuarantyAssets" xlink:to="lab_us-gaap_GuarantyAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_019bffd7-5158-744e-8020-ac45ec19c24d_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental disclosures of cash flow information</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SupplementalCashFlowInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_019bffd7-5159-7b81-8f95-9ca161d31a19_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt securities:</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:to="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss_019c5307-7174-7ebc-b05a-5ff754bdf683_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated impairment losses&#185;</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss_label_en-US" xlink:label="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Impaired, Accumulated Impairment Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillImpairedAccumulatedImpairmentLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:to="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_RestrictedStockUnitsAndDividendEquivalentUnitsMember_019bffd7-515a-7f62-a048-64a8570cc159_terseLabel_en-US" xlink:label="lab_logan_RestrictedStockUnitsAndDividendEquivalentUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average number RSUs outstanding, inclusive of DEUs</link:label>
    <link:label id="lab_logan_RestrictedStockUnitsAndDividendEquivalentUnitsMember_label_en-US" xlink:label="lab_logan_RestrictedStockUnitsAndDividendEquivalentUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock Units And Dividend Equivalent Units [Member]</link:label>
    <link:label id="lab_logan_RestrictedStockUnitsAndDividendEquivalentUnitsMember_documentation_en-US" xlink:label="lab_logan_RestrictedStockUnitsAndDividendEquivalentUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Stock Units And Dividend Equivalent Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_RestrictedStockUnitsAndDividendEquivalentUnitsMember" xlink:href="logan-20251231.xsd#logan_RestrictedStockUnitsAndDividendEquivalentUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_RestrictedStockUnitsAndDividendEquivalentUnitsMember" xlink:to="lab_logan_RestrictedStockUnitsAndDividendEquivalentUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_019bffd7-5159-72ed-8a25-15a6e0e63dc0_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt issuance costs paid to lenders</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDebtIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:to="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_USTreasuryAndGovernmentMember_019bffd7-5158-7000-91f3-7dd57697919a_terseLabel_en-US" xlink:label="lab_us-gaap_USTreasuryAndGovernmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. government and agency</link:label>
    <link:label id="lab_us-gaap_USTreasuryAndGovernmentMember_019c4c24-4e13-7e7b-a6c0-4167acbd0950_verboseLabel_en-US" xlink:label="lab_us-gaap_USTreasuryAndGovernmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">U.S. government and agency</link:label>
    <link:label id="lab_us-gaap_USTreasuryAndGovernmentMember_label_en-US" xlink:label="lab_us-gaap_USTreasuryAndGovernmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Treasury and Government [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USTreasuryAndGovernmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_USTreasuryAndGovernmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USTreasuryAndGovernmentMember" xlink:to="lab_us-gaap_USTreasuryAndGovernmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DependentProbabilitiesMember_019bffd7-5159-7ffe-b55d-efadea408c0c_terseLabel_en-US" xlink:label="lab_logan_DependentProbabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dependent Probabilities</link:label>
    <link:label id="lab_logan_DependentProbabilitiesMember_label_en-US" xlink:label="lab_logan_DependentProbabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dependent Probabilities [Member]</link:label>
    <link:label id="lab_logan_DependentProbabilitiesMember_documentation_en-US" xlink:label="lab_logan_DependentProbabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Dependent Probabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DependentProbabilitiesMember" xlink:href="logan-20251231.xsd#logan_DependentProbabilitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DependentProbabilitiesMember" xlink:to="lab_logan_DependentProbabilitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongDurationInsuranceContractsDisclosureTextBlock_019bffd7-515a-7c0d-bc28-ece004c77430_terseLabel_en-US" xlink:label="lab_us-gaap_LongDurationInsuranceContractsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future policy benefits and related reinsurance recoverable</link:label>
    <link:label id="lab_us-gaap_LongDurationInsuranceContractsDisclosureTextBlock_019bffd7-515a-73ab-87e4-48bb22f45d41_verboseLabel_en-US" xlink:label="lab_us-gaap_LongDurationInsuranceContractsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest sensitive contract liabilities</link:label>
    <link:label id="lab_us-gaap_LongDurationInsuranceContractsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_LongDurationInsuranceContractsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Duration Insurance Contracts Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongDurationInsuranceContractsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongDurationInsuranceContractsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongDurationInsuranceContractsDisclosureTextBlock" xlink:to="lab_us-gaap_LongDurationInsuranceContractsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Dividends_019bffd7-5157-71a9-9b01-fa359b043893_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_Dividends" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Shareholder dividends</link:label>
    <link:label id="lab_us-gaap_Dividends_label_en-US" xlink:label="lab_us-gaap_Dividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Dividends" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Dividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Dividends" xlink:to="lab_us-gaap_Dividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_019bffd7-5157-7da0-816d-ffe2dcb8c10f_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract_019c7c09-ac20-7ca9-a317-0609a2a3ef8a_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit), Effective Income Tax Rate Reconciliation, Amount [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_RestrictedStockUnitsInclusiveOfDividendEquivalentUnitsMember_019bffd7-515b-7acf-b17e-00d0cd1b2192_terseLabel_en-US" xlink:label="lab_logan_RestrictedStockUnitsInclusiveOfDividendEquivalentUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">RSUs inclusive of DEUs</link:label>
    <link:label id="lab_logan_RestrictedStockUnitsInclusiveOfDividendEquivalentUnitsMember_label_en-US" xlink:label="lab_logan_RestrictedStockUnitsInclusiveOfDividendEquivalentUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock Units, Inclusive of Dividend Equivalent Units [Member]</link:label>
    <link:label id="lab_logan_RestrictedStockUnitsInclusiveOfDividendEquivalentUnitsMember_documentation_en-US" xlink:label="lab_logan_RestrictedStockUnitsInclusiveOfDividendEquivalentUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Stock Units, Inclusive of Dividend Equivalent Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_RestrictedStockUnitsInclusiveOfDividendEquivalentUnitsMember" xlink:href="logan-20251231.xsd#logan_RestrictedStockUnitsInclusiveOfDividendEquivalentUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_RestrictedStockUnitsInclusiveOfDividendEquivalentUnitsMember" xlink:to="lab_logan_RestrictedStockUnitsInclusiveOfDividendEquivalentUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIncomeTaxRefunds_019cfdbc-2603-732e-8a0c-9176f46324de_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIncomeTaxRefunds" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from income tax refunds</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIncomeTaxRefunds_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIncomeTaxRefunds" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Income Tax Refunds</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIncomeTaxRefunds" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIncomeTaxRefunds"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIncomeTaxRefunds" xlink:to="lab_us-gaap_ProceedsFromIncomeTaxRefunds" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_019bffd7-5159-7780-ae8d-96d68c506250_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:to="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VestingAxis_019bffd7-5158-7755-839c-43f671560b43_terseLabel_en-US" xlink:label="lab_us-gaap_VestingAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting [Axis]</link:label>
    <link:label id="lab_us-gaap_VestingAxis_label_en-US" xlink:label="lab_us-gaap_VestingAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VestingAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VestingAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VestingAxis" xlink:to="lab_us-gaap_VestingAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_019bffd7-5158-7c20-bd45-ce3429e9c1b3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of financial instruments</link:label>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_label_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOfFinancialInstrumentsPolicy"/>
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    <link:label id="lab_us-gaap_GuaranteedInterestContracts_019bffd7-5157-799d-a213-a0d8f88b2aee_terseLabel_en-US" xlink:label="lab_us-gaap_GuaranteedInterestContracts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest sensitive contract liabilities</link:label>
    <link:label id="lab_us-gaap_GuaranteedInterestContracts_label_en-US" xlink:label="lab_us-gaap_GuaranteedInterestContracts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guaranteed Interest Contracts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuaranteedInterestContracts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GuaranteedInterestContracts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuaranteedInterestContracts" xlink:to="lab_us-gaap_GuaranteedInterestContracts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCash_019bffd7-5157-7969-acb0-2b7e44214111_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash</link:label>
    <link:label id="lab_us-gaap_RestrictedCash_label_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCash" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCash" xlink:to="lab_us-gaap_RestrictedCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommercialRealEstatePortfolioSegmentMember_019bffd7-5158-710c-be57-2a4cd23bc0e3_terseLabel_en-US" xlink:label="lab_us-gaap_CommercialRealEstatePortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial real estate mortgage loans</link:label>
    <link:label id="lab_us-gaap_CommercialRealEstatePortfolioSegmentMember_label_en-US" xlink:label="lab_us-gaap_CommercialRealEstatePortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Real Estate Portfolio Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommercialRealEstatePortfolioSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommercialRealEstatePortfolioSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommercialRealEstatePortfolioSegmentMember" xlink:to="lab_us-gaap_CommercialRealEstatePortfolioSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_019bffd7-5157-7866-9120-0250dba91121_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityDomain" xlink:to="lab_dei_EntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_019bffd7-5158-735a-9893-673fbc13b0c5_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by (used in) investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitReinsuranceAssumed_019bffd7-515a-75c7-985a-bbd48f87b2ae_terseLabel_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitReinsuranceAssumed" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance assumed</link:label>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitReinsuranceAssumed_label_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitReinsuranceAssumed" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability For Future Policy Benefit, Reinsurance Assumed</link:label>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitReinsuranceAssumed_documentation_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitReinsuranceAssumed" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Liability For Future Policy Benefit, Reinsurance Assumed</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_LiabilityForFuturePolicyBenefitReinsuranceAssumed" xlink:href="logan-20251231.xsd#logan_LiabilityForFuturePolicyBenefitReinsuranceAssumed"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_LiabilityForFuturePolicyBenefitReinsuranceAssumed" xlink:to="lab_logan_LiabilityForFuturePolicyBenefitReinsuranceAssumed" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSaleOfBusiness_019bffd7-5157-711b-96d7-7a161f4305a1_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain on acquisition</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfBusiness_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Disposition of Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfBusiness" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSaleOfBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnSaleOfBusiness" xlink:to="lab_us-gaap_GainLossOnSaleOfBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaidNet_019bffd7-5158-7048-bd25-4d4025b33cb4_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest paid</link:label>
    <link:label id="lab_us-gaap_InterestPaidNet_label_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidNet" xlink:to="lab_us-gaap_InterestPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_019c46d4-89c1-76c8-8603-a529dcd6515e_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectsOfReinsuranceTableTextBlock_019bffd7-515a-7d14-8786-4b1466c7ddbe_terseLabel_en-US" xlink:label="lab_us-gaap_EffectsOfReinsuranceTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effects of Reinsurance</link:label>
    <link:label id="lab_us-gaap_EffectsOfReinsuranceTableTextBlock_label_en-US" xlink:label="lab_us-gaap_EffectsOfReinsuranceTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effects of Reinsurance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectsOfReinsuranceTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectsOfReinsuranceTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectsOfReinsuranceTableTextBlock" xlink:to="lab_us-gaap_EffectsOfReinsuranceTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_019bffd7-5158-7972-89a8-c380c0233248_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of presentation and Consolidation</link:label>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis of Accounting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_019bffd7-515a-7a33-a0cb-de05a6b9c1b4_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease right of use asset</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_019c7c0d-73ea-7b0d-86ac-5ef1c6426dc2_totalLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income tax expense (benefit)</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperations"/>
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    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostsTableTextBlock_019bffd7-515a-7b34-aa3a-b5474d00be6e_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Deferred Policy Acquisition Costs</link:label>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredPolicyAcquisitionCostsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredPolicyAcquisitionCostsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredPolicyAcquisitionCostsTableTextBlock" xlink:to="lab_us-gaap_DeferredPolicyAcquisitionCostsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSalesAndRepayments_019bffd7-5159-7e9f-87ea-c6b4d7bf8ac5_negatedTerseLabel_en-US" xlink:label="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSalesAndRepayments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Sales and repayments</link:label>
    <link:label id="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSalesAndRepayments_label_en-US" xlink:label="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSalesAndRepayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Sales and Repayments</link:label>
    <link:label id="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSalesAndRepayments_documentation_en-US" xlink:label="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSalesAndRepayments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Sales and Repayments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSalesAndRepayments" xlink:href="logan-20251231.xsd#logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSalesAndRepayments"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract_019bffd7-5158-794d-bcc9-917b353ef896_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Flows from Operating Activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Continuing Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract"/>
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    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_019bffd7-5158-729e-a0b2-00a460fcd1df_terseLabel_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized cost</link:label>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reported Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember"/>
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    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_019bffd7-5158-7522-821d-10d13b83f578_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition-related cost, expense</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Acquisition-Related Cost, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationAcquisitionRelatedCosts"/>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsValuationAllowance_019bffd7-515a-70b6-8461-c216443daa1c_negatedLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Valuation allowance</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsValuationAllowance_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Valuation Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsValuationAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:to="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityAbstract" xlink:to="lab_us-gaap_EquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentNonaccrualStatus_019bffd7-5159-76b5-a2d7-6b27dfaea6f0_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentNonaccrualStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonaccrual loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentNonaccrualStatus_019bffd7-5159-7c8b-8e79-c5b8ecaecdd3_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentNonaccrualStatus" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total nonaccrual loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentNonaccrualStatus_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentNonaccrualStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Nonaccrual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentNonaccrualStatus" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableRecordedInvestmentNonaccrualStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentNonaccrualStatus" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentNonaccrualStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ScheduleOfFinancialAssetsTableTextBlock_019bffd7-5158-793e-b78b-5e0d5b9fa595_terseLabel_en-US" xlink:label="lab_logan_ScheduleOfFinancialAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financial Assets</link:label>
    <link:label id="lab_logan_ScheduleOfFinancialAssetsTableTextBlock_label_en-US" xlink:label="lab_logan_ScheduleOfFinancialAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Financial Assets [Table Text Block]</link:label>
    <link:label id="lab_logan_ScheduleOfFinancialAssetsTableTextBlock_documentation_en-US" xlink:label="lab_logan_ScheduleOfFinancialAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Financial Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ScheduleOfFinancialAssetsTableTextBlock" xlink:href="logan-20251231.xsd#logan_ScheduleOfFinancialAssetsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ScheduleOfFinancialAssetsTableTextBlock" xlink:to="lab_logan_ScheduleOfFinancialAssetsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract_019bffd7-515a-7fa8-b4f1-b240212a7398_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net premiums</link:label>
    <link:label id="lab_us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract_label_en-US" xlink:label="lab_us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Earned, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract" xlink:to="lab_us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_019bffd7-5158-7b54-991c-4f13fc0a2807_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative instruments</link:label>
    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivatives, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativesPolicyTextBlock" xlink:to="lab_us-gaap_DerivativesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_019bffd7-515b-737d-a250-5b773318ebd1_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments</link:label>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTable_019bffd7-5159-75a5-9e87-63e945e69493_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGoodwillTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfGoodwillTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGoodwillTable" xlink:to="lab_us-gaap_ScheduleOfGoodwillTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CurrentFederalTaxExpenseBenefit_019cf498-79f0-73e8-a3b7-fa600ddea7af_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal</link:label>
    <link:label id="lab_us-gaap_CurrentFederalTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Federal Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentFederalTaxExpenseBenefit"/>
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    <link:label id="lab_logan_PolicyholderAccountBalanceMinimumGuaranteedInterestRates_019bffd7-515a-7c5c-aa73-ebddee2f2bfe_terseLabel_en-US" xlink:label="lab_logan_PolicyholderAccountBalanceMinimumGuaranteedInterestRates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum guaranteed interest rates</link:label>
    <link:label id="lab_logan_PolicyholderAccountBalanceMinimumGuaranteedInterestRates_label_en-US" xlink:label="lab_logan_PolicyholderAccountBalanceMinimumGuaranteedInterestRates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance, Minimum Guaranteed Interest Rates</link:label>
    <link:label id="lab_logan_PolicyholderAccountBalanceMinimumGuaranteedInterestRates_documentation_en-US" xlink:label="lab_logan_PolicyholderAccountBalanceMinimumGuaranteedInterestRates" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance, Minimum Guaranteed Interest Rates</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_PolicyholderAccountBalanceMinimumGuaranteedInterestRates" xlink:href="logan-20251231.xsd#logan_PolicyholderAccountBalanceMinimumGuaranteedInterestRates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_PolicyholderAccountBalanceMinimumGuaranteedInterestRates" xlink:to="lab_logan_PolicyholderAccountBalanceMinimumGuaranteedInterestRates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract_019bffd7-5158-7236-a16e-4459d1325c28_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized losses</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Loss Position, Accumulated Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract"/>
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    <link:label id="lab_us-gaap_PolicyholderAccountBalanceWeightedAverageCreditingRate_019bffd7-515a-7c04-96f5-b319a0914237_terseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceWeightedAverageCreditingRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance, Weighted Average Crediting Rate</link:label>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceWeightedAverageCreditingRate_label_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceWeightedAverageCreditingRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance, Weighted Average Crediting Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderAccountBalanceWeightedAverageCreditingRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderAccountBalanceWeightedAverageCreditingRate"/>
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    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_WeightedAverageMember_019bffd7-5159-78a7-8ec9-c26afa720d5e_terseLabel_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average</link:label>
    <link:label id="lab_srt_WeightedAverageMember_label_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_WeightedAverageMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_WeightedAverageMember"/>
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    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_019bffd7-5158-796b-98c4-598a989c037e_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of intangible assets</link:label>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_label_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Intangible Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfIntangibleAssets"/>
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    <link:label id="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure_019bffd7-5159-7fd5-a05f-99c83d1b8d00_terseLabel_en-US" xlink:label="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage loans</link:label>
    <link:label id="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan, Mortgage, Held-for-Sale, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgagesHeldForSaleFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:to="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxAssetsNet_019bffd7-515a-7d2e-be21-01b1f7f15678_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax assets</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxAssetsNet_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxAssetsNet" xlink:to="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput_019bffd7-5159-7229-8f2e-fb497aaf0edf_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt securities, measurement input</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput"/>
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    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_019bffd7-515a-748c-96fa-071cee3d2613_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accumulated Other Comprehensive Income (Loss)</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accumulated Other Comprehensive Income (Loss) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_SharesIssuedRestrictedStockReleaseShares_019bffd7-5157-7638-a082-f106750297b1_terseLabel_en-US" xlink:label="lab_logan_SharesIssuedRestrictedStockReleaseShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted stock release (in shares)</link:label>
    <link:label id="lab_logan_SharesIssuedRestrictedStockReleaseShares_label_en-US" xlink:label="lab_logan_SharesIssuedRestrictedStockReleaseShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Restricted Stock Release, Shares</link:label>
    <link:label id="lab_logan_SharesIssuedRestrictedStockReleaseShares_documentation_en-US" xlink:label="lab_logan_SharesIssuedRestrictedStockReleaseShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Shares Issued, Restricted Stock Release, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_SharesIssuedRestrictedStockReleaseShares" xlink:href="logan-20251231.xsd#logan_SharesIssuedRestrictedStockReleaseShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_SharesIssuedRestrictedStockReleaseShares" xlink:to="lab_logan_SharesIssuedRestrictedStockReleaseShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_019c7c27-bbba-70a0-97fb-0056baefba89_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of stock, consideration received on transaction</link:label>
    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_label_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Consideration Received on Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleOfStockConsiderationReceivedOnTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:to="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitReinsuranceRecoverableExcludedFromComputation_019bffd7-515a-75d5-9751-27011cefed77_terseLabel_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitReinsuranceRecoverableExcludedFromComputation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable, excluded from computation</link:label>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitReinsuranceRecoverableExcludedFromComputation_label_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitReinsuranceRecoverableExcludedFromComputation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability For Future Policy Benefit, Reinsurance Recoverable, Excluded From Computation</link:label>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitReinsuranceRecoverableExcludedFromComputation_documentation_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitReinsuranceRecoverableExcludedFromComputation" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Liability For Future Policy Benefit, Reinsurance Recoverable, Excluded From Computation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_LiabilityForFuturePolicyBenefitReinsuranceRecoverableExcludedFromComputation" xlink:href="logan-20251231.xsd#logan_LiabilityForFuturePolicyBenefitReinsuranceRecoverableExcludedFromComputation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_LiabilityForFuturePolicyBenefitReinsuranceRecoverableExcludedFromComputation" xlink:to="lab_logan_LiabilityForFuturePolicyBenefitReinsuranceRecoverableExcludedFromComputation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsLiability_019bffd7-5157-7685-9797-290f93c2be90_terseLabel_en-US" xlink:label="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Funds held under reinsurance contracts</link:label>
    <link:label id="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsLiability_019bffd7-515a-796d-a075-187bfa33eed5_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Funds held under reinsurance contracts</link:label>
    <link:label id="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsLiability_label_en-US" xlink:label="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Funds Held under Reinsurance Agreements, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FundsHeldUnderReinsuranceAgreementsLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FundsHeldUnderReinsuranceAgreementsLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FundsHeldUnderReinsuranceAgreementsLiability" xlink:to="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_019bffd7-5159-711a-aab5-b23dce2b3bc8_terseLabel_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility</link:label>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_label_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevolvingCreditFacilityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevolvingCreditFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevolvingCreditFacilityMember" xlink:to="lab_us-gaap_RevolvingCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential_019bffd7-515a-72ec-806a-bc5a7dee7815_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign tax rate differential</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential" xlink:to="lab_us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock_019bffd7-5158-7341-a8c8-aee6e1465739_terseLabel_en-US" xlink:label="lab_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Investments</link:label>
    <link:label id="lab_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock_label_en-US" xlink:label="lab_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, and Equity Securities, FV-NI [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock" xlink:to="lab_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InsuranceSolutionsSegmentConsolidatedVIEsMember_019bffd7-515b-727f-b763-f8b9cc6a79a4_terseLabel_en-US" xlink:label="lab_logan_InsuranceSolutionsSegmentConsolidatedVIEsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance Solutions consolidated VIEs</link:label>
    <link:label id="lab_logan_InsuranceSolutionsSegmentConsolidatedVIEsMember_label_en-US" xlink:label="lab_logan_InsuranceSolutionsSegmentConsolidatedVIEsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance Solutions Segment, Consolidated VIEs [Member]</link:label>
    <link:label id="lab_logan_InsuranceSolutionsSegmentConsolidatedVIEsMember_documentation_en-US" xlink:label="lab_logan_InsuranceSolutionsSegmentConsolidatedVIEsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Insurance Solutions Segment, Consolidated VIEs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InsuranceSolutionsSegmentConsolidatedVIEsMember" xlink:href="logan-20251231.xsd#logan_InsuranceSolutionsSegmentConsolidatedVIEsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InsuranceSolutionsSegmentConsolidatedVIEsMember" xlink:to="lab_logan_InsuranceSolutionsSegmentConsolidatedVIEsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_019bffd7-5157-7acc-a019-44bd6b169d1a_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_019bffd7-5159-7d9e-b5bd-a1596b5a4bb3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value by Liability Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value by Liability Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FinancingCostsPaidAndDeferred_019bffd7-515a-727a-97bd-c91bff8e2765_negatedTerseLabel_en-US" xlink:label="lab_logan_FinancingCostsPaidAndDeferred" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Financing costs paid and deferred</link:label>
    <link:label id="lab_logan_FinancingCostsPaidAndDeferred_label_en-US" xlink:label="lab_logan_FinancingCostsPaidAndDeferred" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Costs Paid and Deferred</link:label>
    <link:label id="lab_logan_FinancingCostsPaidAndDeferred_documentation_en-US" xlink:label="lab_logan_FinancingCostsPaidAndDeferred" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Costs Paid and Deferred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FinancingCostsPaidAndDeferred" xlink:href="logan-20251231.xsd#logan_FinancingCostsPaidAndDeferred"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FinancingCostsPaidAndDeferred" xlink:to="lab_logan_FinancingCostsPaidAndDeferred" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_019c2cbe-0d35-7d0a-ab7e-98e731e87567_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure</link:label>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_label_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Additional402vDisclosureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Additional402vDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ConsolidatedBalanceIncludingVariableInterestEntityMember_019bffd7-5158-7d3c-8c11-2e1fe87507d8_terseLabel_en-US" xlink:label="lab_logan_ConsolidatedBalanceIncludingVariableInterestEntityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Balance Including Variable Interest Entity</link:label>
    <link:label id="lab_logan_ConsolidatedBalanceIncludingVariableInterestEntityMember_label_en-US" xlink:label="lab_logan_ConsolidatedBalanceIncludingVariableInterestEntityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Balance Including Variable Interest Entity [Member]</link:label>
    <link:label id="lab_logan_ConsolidatedBalanceIncludingVariableInterestEntityMember_documentation_en-US" xlink:label="lab_logan_ConsolidatedBalanceIncludingVariableInterestEntityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Consolidated Balance Including Variable Interest Entity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ConsolidatedBalanceIncludingVariableInterestEntityMember" xlink:href="logan-20251231.xsd#logan_ConsolidatedBalanceIncludingVariableInterestEntityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ConsolidatedBalanceIncludingVariableInterestEntityMember" xlink:to="lab_logan_ConsolidatedBalanceIncludingVariableInterestEntityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAccruedInterestWriteoff_019bffd7-5158-71f1-8ccd-77625ce4871c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAccruedInterestWriteoff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total accrued interest receivables written off</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAccruedInterestWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAccruedInterestWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Accrued Interest, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAccruedInterestWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAccruedInterestWriteoff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAccruedInterestWriteoff" xlink:to="lab_us-gaap_FinancingReceivableAccruedInterestWriteoff" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_019c7bd8-793a-7227-b984-b19cbb42da9b_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2031 and thereafter</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_019bffd7-515a-7d7c-88a1-b411a1c2fd9f_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity based compensation</link:label>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:to="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares_019bffd7-5157-7084-a6a2-02ace0ad5006_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Common shares repurchased (shares)</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased and Retired During Period, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRepurchasedAndRetiredDuringPeriodShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares" xlink:to="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseAfterYearFive_019bffd7-515a-7dd5-93e0-f5e2b179890e_terseLabel_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2031 and thereafter</link:label>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseAfterYearFive_label_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense, After Year Five</link:label>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseAfterYearFive_documentation_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense, After Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseAfterYearFive" xlink:href="logan-20251231.xsd#logan_DeferredPolicyAcquisitionCostsAmortizationExpenseAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseAfterYearFive" xlink:to="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceSurrenderAndWithdrawal_019bffd7-515a-780d-8b10-583ae21aa27e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceSurrenderAndWithdrawal" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Surrenders and withdrawals</link:label>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceSurrenderAndWithdrawal_label_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceSurrenderAndWithdrawal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance, Surrender and Withdrawal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderAccountBalanceSurrenderAndWithdrawal" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderAccountBalanceSurrenderAndWithdrawal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyholderAccountBalanceSurrenderAndWithdrawal" xlink:to="lab_us-gaap_PolicyholderAccountBalanceSurrenderAndWithdrawal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffBalanceSheetCreditLossLiability_019bffd7-5158-710f-8999-9843c6ed222b_terseLabel_en-US" xlink:label="lab_us-gaap_OffBalanceSheetCreditLossLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Off balance sheet credit risk</link:label>
    <link:label id="lab_us-gaap_OffBalanceSheetCreditLossLiability_label_en-US" xlink:label="lab_us-gaap_OffBalanceSheetCreditLossLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Off-Balance-Sheet, Credit Loss, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffBalanceSheetCreditLossLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OffBalanceSheetCreditLossLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffBalanceSheetCreditLossLiability" xlink:to="lab_us-gaap_OffBalanceSheetCreditLossLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_019bffd7-5157-7fb8-8f23-338cce76370d_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ASSETS</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityAxis_019bffd7-5159-7a9d-92c4-7a1c64cd5fa1_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityAxis" xlink:to="lab_us-gaap_CreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ReverseAcquisitionOfTURNMember_019bffd7-515a-7ee7-9120-8d634115ae65_terseLabel_en-US" xlink:label="lab_logan_ReverseAcquisitionOfTURNMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reverse Acquisition Of TURN</link:label>
    <link:label id="lab_logan_ReverseAcquisitionOfTURNMember_label_en-US" xlink:label="lab_logan_ReverseAcquisitionOfTURNMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reverse Acquisition Of TURN [Member]</link:label>
    <link:label id="lab_logan_ReverseAcquisitionOfTURNMember_documentation_en-US" xlink:label="lab_logan_ReverseAcquisitionOfTURNMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reverse Acquisition Of TURN</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ReverseAcquisitionOfTURNMember" xlink:href="logan-20251231.xsd#logan_ReverseAcquisitionOfTURNMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ReverseAcquisitionOfTURNMember" xlink:to="lab_logan_ReverseAcquisitionOfTURNMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_terseLabel_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change</link:label>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_label_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_UndrlygSecurityMktPriceChngPct"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:to="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitmentsAxis_019bffd7-515b-7e6a-9d82-2d40656ff358_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Commitments [Axis]</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentsAxis_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentsAxis" xlink:to="lab_us-gaap_OtherCommitmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_019bffd7-5159-7ab7-a40a-4d45ae01f21e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_019bffd7-515b-7c65-a852-2a404dd11015_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forfeitures (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Forfeitures, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_019bffd7-5159-7bb2-93c2-f5cc004e6901_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value measurements</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_019bffd7-5158-74cc-9b78-815df821d124_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Line Items]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems" xlink:to="lab_us-gaap_BusinessAcquisitionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityDomain_019bffd7-5159-7bbd-80e1-08cc7e3edf7e_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityDomain_label_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityDomain" xlink:to="lab_us-gaap_CreditFacilityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityAbstract_019bffd7-5157-7eb0-bc71-e2cb01fe82cf_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EQUITY</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityAbstract" xlink:to="lab_us-gaap_StockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_019bffd7-5158-7a5f-bfb8-ce7deb7c1a24_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting percent</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Rights, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_BusinessCombinationConsiderationTransferredShares_019bffd7-5158-7156-8af7-037fb9f75abb_terseLabel_en-US" xlink:label="lab_logan_BusinessCombinationConsiderationTransferredShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consideration transferred (in shares)</link:label>
    <link:label id="lab_logan_BusinessCombinationConsiderationTransferredShares_label_en-US" xlink:label="lab_logan_BusinessCombinationConsiderationTransferredShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Shares</link:label>
    <link:label id="lab_logan_BusinessCombinationConsiderationTransferredShares_documentation_en-US" xlink:label="lab_logan_BusinessCombinationConsiderationTransferredShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_BusinessCombinationConsiderationTransferredShares" xlink:href="logan-20251231.xsd#logan_BusinessCombinationConsiderationTransferredShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_BusinessCombinationConsiderationTransferredShares" xlink:to="lab_logan_BusinessCombinationConsiderationTransferredShares" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_SurplusNotesMember_019bffd7-5159-7fbf-b8e0-5a7696eaa546_terseLabel_en-US" xlink:label="lab_logan_SurplusNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Surplus Notes</link:label>
    <link:label id="lab_logan_SurplusNotesMember_label_en-US" xlink:label="lab_logan_SurplusNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Surplus Notes [Member]</link:label>
    <link:label id="lab_logan_SurplusNotesMember_documentation_en-US" xlink:label="lab_logan_SurplusNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Surplus Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_SurplusNotesMember" xlink:href="logan-20251231.xsd#logan_SurplusNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_SurplusNotesMember" xlink:to="lab_logan_SurplusNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019bffd7-5158-77db-9d5e-65d8cb65a06c_terseLabel_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_label_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:to="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_019bffd7-5159-7f15-a893-b00cc5bc4345_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalLiabilityLongDurationInsuranceTableTextBlock_019bffd7-515a-72d7-8fd8-efb5307cff17_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalLiabilityLongDurationInsuranceTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional Liability, Long-Duration Insurance</link:label>
    <link:label id="lab_us-gaap_AdditionalLiabilityLongDurationInsuranceTableTextBlock_label_en-US" xlink:label="lab_us-gaap_AdditionalLiabilityLongDurationInsuranceTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Liability, Long-Duration Insurance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalLiabilityLongDurationInsuranceTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalLiabilityLongDurationInsuranceTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalLiabilityLongDurationInsuranceTableTextBlock" xlink:to="lab_us-gaap_AdditionalLiabilityLongDurationInsuranceTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivables30To59DaysPastDueMember_019bffd7-5159-7dd1-bce4-75dfd0489da5_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivables30To59DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans 30-59 days past due</link:label>
    <link:label id="lab_us-gaap_FinancingReceivables30To59DaysPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancingReceivables30To59DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, 30 to 59 Days Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivables30To59DaysPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivables30To59DaysPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivables30To59DaysPastDueMember" xlink:to="lab_us-gaap_FinancingReceivables30To59DaysPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityVoluntaryFilers_019c7b2c-7025-70b6-be61-926e0871f5ab_terseLabel_en-US" xlink:label="lab_dei_EntityVoluntaryFilers" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Voluntary Filers</link:label>
    <link:label id="lab_dei_EntityVoluntaryFilers_label_en-US" xlink:label="lab_dei_EntityVoluntaryFilers" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Voluntary Filers</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityVoluntaryFilers" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityVoluntaryFilers"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityVoluntaryFilers" xlink:to="lab_dei_EntityVoluntaryFilers" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_NetInvestmentIncomeTextBlock_019bffd7-5158-787c-b4ca-89c525247f84_terseLabel_en-US" xlink:label="lab_logan_NetInvestmentIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net investment income</link:label>
    <link:label id="lab_logan_NetInvestmentIncomeTextBlock_label_en-US" xlink:label="lab_logan_NetInvestmentIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Investment Income [Text Block]</link:label>
    <link:label id="lab_logan_NetInvestmentIncomeTextBlock_documentation_en-US" xlink:label="lab_logan_NetInvestmentIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Investment Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_NetInvestmentIncomeTextBlock" xlink:href="logan-20251231.xsd#logan_NetInvestmentIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_NetInvestmentIncomeTextBlock" xlink:to="lab_logan_NetInvestmentIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableNet_019cc426-f0da-7449-90e5-e20347cf9213_negatedLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNet" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Intersegment receivables</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNet_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableNet" xlink:to="lab_us-gaap_AccountsReceivableNet" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_019bffd7-5157-77cd-92db-3b679adf26c4_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IndustrySpecificPoliciesInsuranceCompaniesTextBlock_019bffd7-5158-7497-abfe-1c2459895e20_terseLabel_en-US" xlink:label="lab_us-gaap_IndustrySpecificPoliciesInsuranceCompaniesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance</link:label>
    <link:label id="lab_us-gaap_IndustrySpecificPoliciesInsuranceCompaniesTextBlock_label_en-US" xlink:label="lab_us-gaap_IndustrySpecificPoliciesInsuranceCompaniesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Industry-Specific Policies, Insurance Companies [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndustrySpecificPoliciesInsuranceCompaniesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IndustrySpecificPoliciesInsuranceCompaniesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IndustrySpecificPoliciesInsuranceCompaniesTextBlock" xlink:to="lab_us-gaap_IndustrySpecificPoliciesInsuranceCompaniesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_TransactionWithServicingFeesMember_019bffd7-515b-7c3c-b7a1-d3f131150f42_terseLabel_en-US" xlink:label="lab_logan_TransactionWithServicingFeesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transaction With Servicing Fees</link:label>
    <link:label id="lab_logan_TransactionWithServicingFeesMember_label_en-US" xlink:label="lab_logan_TransactionWithServicingFeesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transaction With Servicing Fees [Member]</link:label>
    <link:label id="lab_logan_TransactionWithServicingFeesMember_documentation_en-US" xlink:label="lab_logan_TransactionWithServicingFeesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Transaction With Servicing Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_TransactionWithServicingFeesMember" xlink:href="logan-20251231.xsd#logan_TransactionWithServicingFeesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_TransactionWithServicingFeesMember" xlink:to="lab_logan_TransactionWithServicingFeesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StateAndLocalTaxJurisdictionOtherMember_019c7c1d-d183-70c2-a1ff-9a3d2df4e7e7_terseLabel_en-US" xlink:label="lab_us-gaap_StateAndLocalTaxJurisdictionOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other States</link:label>
    <link:label id="lab_us-gaap_StateAndLocalTaxJurisdictionOtherMember_label_en-US" xlink:label="lab_us-gaap_StateAndLocalTaxJurisdictionOtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">State and Local Tax Jurisdiction, Other [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StateAndLocalTaxJurisdictionOtherMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StateAndLocalTaxJurisdictionOtherMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StateAndLocalTaxJurisdictionOtherMember" xlink:to="lab_us-gaap_StateAndLocalTaxJurisdictionOtherMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_019bffd7-5159-7f94-bd9a-8c16b0ba0f16_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total financial assets &#8212; Asset Management</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_019bffd7-5159-7ce1-b95f-7ba5b2a6eeb8_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosure" xlink:to="lab_us-gaap_AssetsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses_019bffd7-5158-7b09-bda3-969b4a5a0954_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Credit releases (losses)</link:label>
    <link:label id="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses_label_en-US" xlink:label="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Provision for Loan, Lease, and Other Losses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProvisionForLoanLeaseAndOtherLosses"/>
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    <link:label id="lab_us-gaap_FinancialInstrumentOtherMember_019bffd7-5158-7621-82af-d30c7933a6a6_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentOtherMember_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentOtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument, Other [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentOtherMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentOtherMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentOtherMember" xlink:to="lab_us-gaap_FinancialInstrumentOtherMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfOtherSignificantReconcilingItemsFromSegmentsToConsolidatedTextBlock_019bffd7-515b-70a2-be64-1e7081a3a5fc_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfOtherSignificantReconcilingItemsFromSegmentsToConsolidatedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment, Reconciliation of Other Items from Segments to Consolidated</link:label>
    <link:label id="lab_us-gaap_ReconciliationOfOtherSignificantReconcilingItemsFromSegmentsToConsolidatedTextBlock_label_en-US" xlink:label="lab_us-gaap_ReconciliationOfOtherSignificantReconcilingItemsFromSegmentsToConsolidatedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment, Reconciliation of Other Items from Segments to Consolidated [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfOtherSignificantReconcilingItemsFromSegmentsToConsolidatedTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReconciliationOfOtherSignificantReconcilingItemsFromSegmentsToConsolidatedTextBlock"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions_019bffd7-5158-7a6d-b7d7-ce4a12b56d91_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AFS securities with continuous loss position (security)</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Loss Position, Number of Positions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions"/>
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    <link:label id="lab_us-gaap_NumberOfOperatingSegments_019bffd7-5158-73a8-9b83-9dcc73d880b5_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of operating segments</link:label>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Operating Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfOperatingSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfOperatingSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfOperatingSegments" xlink:to="lab_us-gaap_NumberOfOperatingSegments" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments"/>
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    <link:label id="lab_us-gaap_MaterialReconcilingItemsMember_019bffd7-515b-7b4b-8fb6-641848cf9cfb_terseLabel_en-US" xlink:label="lab_us-gaap_MaterialReconcilingItemsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciling Item</link:label>
    <link:label id="lab_us-gaap_MaterialReconcilingItemsMember_label_en-US" xlink:label="lab_us-gaap_MaterialReconcilingItemsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Reconciling Item, Excluding Corporate Nonsegment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MaterialReconcilingItemsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MaterialReconcilingItemsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MaterialReconcilingItemsMember" xlink:to="lab_us-gaap_MaterialReconcilingItemsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_019bffd7-515b-72bb-a663-1addb58d1058_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Granted (in dollars per share)</link:label>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_019bffd7-5157-7848-ab7c-e610444808dc_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_019bffd7-5159-7188-a720-f4b0ad4aca09_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Finite-Lived Intangible Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Finite-Lived Intangible Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock"/>
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    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDateAxis"/>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_019bffd7-5157-725b-a094-acf86e2237c5_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity based compensation</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Value, Share-Based Payment Arrangement, after Forfeiture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation"/>
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    <link:label id="lab_us-gaap_DeferredForeignIncomeTaxExpenseBenefit_019bffd7-515a-7ba7-bed5-72b47c505687_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredForeignIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign</link:label>
    <link:label id="lab_us-gaap_DeferredForeignIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredForeignIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Foreign Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredForeignIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredForeignIncomeTaxExpenseBenefit"/>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_019bffd7-515a-7f17-802b-f881e097f085_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportingUnits_019bffd7-5158-7e39-a528-dc6b27ab23bc_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportingUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reporting units</link:label>
    <link:label id="lab_us-gaap_NumberOfReportingUnits_label_en-US" xlink:label="lab_us-gaap_NumberOfReportingUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reporting Units</link:label>
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    <link:label id="lab_us-gaap_ReportingUnitAxis_019c77dd-785f-748f-84c0-d4b00a9a605e_terseLabel_en-US" xlink:label="lab_us-gaap_ReportingUnitAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reporting Unit [Axis]</link:label>
    <link:label id="lab_us-gaap_ReportingUnitAxis_label_en-US" xlink:label="lab_us-gaap_ReportingUnitAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reporting Unit [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReportingUnitAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReportingUnitAxis"/>
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    <link:label id="lab_us-gaap_InterestExpenseDebt_label_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Debt</link:label>
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    <link:label id="lab_logan_CommonSharesPurchaseWarrantsMember_019bffd7-5159-7db2-a5d3-32d78a5021b4_terseLabel_en-US" xlink:label="lab_logan_CommonSharesPurchaseWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Shares Purchase Warrants</link:label>
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    <link:label id="lab_logan_CommonSharesPurchaseWarrantsMember_documentation_en-US" xlink:label="lab_logan_CommonSharesPurchaseWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Shares Purchase Warrants</link:label>
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    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
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    <link:label id="lab_us-gaap_LoansHeldForSaleFairValueDisclosure_019bffd7-5159-782e-9ddd-1ee9b3bfe60a_terseLabel_en-US" xlink:label="lab_us-gaap_LoansHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate loans</link:label>
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    <link:label id="lab_logan_InvestmentCommitmentsMember_019bffd7-515b-76ac-aa39-f9063e270ac7_terseLabel_en-US" xlink:label="lab_logan_InvestmentCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Commitments</link:label>
    <link:label id="lab_logan_InvestmentCommitmentsMember_label_en-US" xlink:label="lab_logan_InvestmentCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Commitments [Member]</link:label>
    <link:label id="lab_logan_InvestmentCommitmentsMember_documentation_en-US" xlink:label="lab_logan_InvestmentCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InvestmentCommitmentsMember" xlink:href="logan-20251231.xsd#logan_InvestmentCommitmentsMember"/>
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    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019bffd7-5159-77a1-9bb4-a201a7127241_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total facility</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019bffd7-5159-77c3-9c90-473dc8626b55_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Debt issuance amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Face Amount</link:label>
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    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract"/>
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    <link:label id="lab_srt_ConsolidatedEntityExcludingVariableInterestEntitiesVIEMember_label_en-US" xlink:label="lab_srt_ConsolidatedEntityExcludingVariableInterestEntitiesVIEMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entity, Excluding Consolidated VIE [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntityExcludingVariableInterestEntitiesVIEMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntityExcludingVariableInterestEntitiesVIEMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntityExcludingVariableInterestEntitiesVIEMember" xlink:to="lab_srt_ConsolidatedEntityExcludingVariableInterestEntitiesVIEMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_019bffd7-5159-71bc-bf13-664e01777b41_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common share purchase warrants (in shares)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Number of Securities Called by Warrants or Rights</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:to="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember_019bffd7-515a-7924-8a4c-d9cb582b6921_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized investment gains (losses) on available-for-sale securities</link:label>
    <link:label id="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI, Accumulated Gain (Loss), Debt Securities, Available-for-Sale, Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:to="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyholderFunds_019bffd7-515a-7b78-b2c2-c687882de4de_periodStartLabel_en-US" xlink:label="lab_us-gaap_PolicyholderFunds" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance, beginning of year</link:label>
    <link:label id="lab_us-gaap_PolicyholderFunds_019bffd7-515a-748f-8172-ecb3fe8d9e76_periodEndLabel_en-US" xlink:label="lab_us-gaap_PolicyholderFunds" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance, end of year</link:label>
    <link:label id="lab_us-gaap_PolicyholderFunds_019bffd7-515a-7168-bc18-4d6f58ce5fe4_terseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderFunds" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Policyholder account balance</link:label>
    <link:label id="lab_us-gaap_PolicyholderFunds_label_en-US" xlink:label="lab_us-gaap_PolicyholderFunds" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderFunds" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderFunds"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyholderFunds" xlink:to="lab_us-gaap_PolicyholderFunds" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerSharePolicyTextBlock_019bffd7-5158-7c43-bcd3-621ff423ee4a_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings per share</link:label>
    <link:label id="lab_us-gaap_EarningsPerSharePolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerSharePolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerSharePolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerSharePolicyTextBlock" xlink:to="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRecognitionPolicyTextBlock_019bffd7-5158-7a53-871f-31b90894cfa2_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_RevenueRecognitionPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueRecognitionPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:to="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember_019bffd7-5158-7a94-a7d5-14d5cdd17102_terseLabel_en-US" xlink:label="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. state, territories and municipalities</link:label>
    <link:label id="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember_019c4c24-7100-7561-b140-265945b3a013_verboseLabel_en-US" xlink:label="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">U.S. state, territories and municipalities</link:label>
    <link:label id="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember_label_en-US" xlink:label="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US States and Political Subdivisions Debt Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USStatesAndPoliticalSubdivisionsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_USStatesAndPoliticalSubdivisionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USStatesAndPoliticalSubdivisionsMember" xlink:to="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract_019bffd7-5158-7ede-810e-aff56deb2916_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, Allocated and Single Maturity Date, Fair Value [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_019bffd7-5158-7e8f-94da-3b09bc59a5b5_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquired net liability</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubordinatedDebtMember_019bffd7-5159-771e-af3f-761f950f6428_terseLabel_en-US" xlink:label="lab_us-gaap_SubordinatedDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subordinated Debt</link:label>
    <link:label id="lab_us-gaap_SubordinatedDebtMember_label_en-US" xlink:label="lab_us-gaap_SubordinatedDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subordinated Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubordinatedDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubordinatedDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubordinatedDebtMember" xlink:to="lab_us-gaap_SubordinatedDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_019bffd7-5159-7fa0-985d-48cdc577d3ad_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablesPeriodPastDueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:to="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllExecutiveCategoriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllExecutiveCategoriesMember" xlink:to="lab_ecd_AllExecutiveCategoriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_019bffd7-515a-76e7-a913-20b31d66bd82_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Deferred Tax Assets and Liabilities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Deferred Tax Assets and Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_019bffd7-5157-77ff-8572-82489df49d67_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of deferred acquisition costs</link:label>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_019c4b64-e84f-7a5f-823c-5d3acad09453_verboseLabel_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Amortization of deferred acquisition costs</link:label>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_019bffd7-515a-7111-8483-08dc6e127191_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Amortization</link:label>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_label_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:to="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_019bffd7-5157-7a68-9787-f009dd65b802_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitsDirect_019bffd7-515a-7ac2-843f-2454509cd5a8_terseLabel_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitsDirect" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Direct</link:label>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitsDirect_label_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitsDirect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability For Future Policy Benefits, Direct</link:label>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitsDirect_documentation_en-US" xlink:label="lab_logan_LiabilityForFuturePolicyBenefitsDirect" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Liability For Future Policy Benefits, Direct</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_LiabilityForFuturePolicyBenefitsDirect" xlink:href="logan-20251231.xsd#logan_LiabilityForFuturePolicyBenefitsDirect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_LiabilityForFuturePolicyBenefitsDirect" xlink:to="lab_logan_LiabilityForFuturePolicyBenefitsDirect" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumsEarnedNet_019bffd7-5157-7a28-b1a3-b1c9f10381b0_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsEarnedNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net premiums</link:label>
    <link:label id="lab_us-gaap_PremiumsEarnedNet_019bffd7-515a-7412-97ae-d4f70aca7a4d_totalLabel_en-US" xlink:label="lab_us-gaap_PremiumsEarnedNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total net premiums</link:label>
    <link:label id="lab_us-gaap_PremiumsEarnedNet_label_en-US" xlink:label="lab_us-gaap_PremiumsEarnedNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Earned, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsEarnedNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PremiumsEarnedNet"/>
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    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_019bffd7-5159-7bcf-8711-42517f228b56_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_019bffd7-5157-76ca-9097-22c79384c66d_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearTwo_019bffd7-515a-74d3-a330-1ceae665e63c_terseLabel_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearTwo_label_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense, Year Two</link:label>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearTwo_documentation_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearTwo" xlink:href="logan-20251231.xsd#logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearTwo" xlink:to="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract_019bffd7-5158-754b-95a9-4acf8459a747_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (decrease) in operating liabilities:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Operating Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ProductChargeRevenue_019bffd7-5157-78c6-b219-1468233fc46f_terseLabel_en-US" xlink:label="lab_logan_ProductChargeRevenue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product charges</link:label>
    <link:label id="lab_logan_ProductChargeRevenue_label_en-US" xlink:label="lab_logan_ProductChargeRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product Charge Revenue</link:label>
    <link:label id="lab_logan_ProductChargeRevenue_documentation_en-US" xlink:label="lab_logan_ProductChargeRevenue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Product Charge Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ProductChargeRevenue" xlink:href="logan-20251231.xsd#logan_ProductChargeRevenue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ProductChargeRevenue" xlink:to="lab_logan_ProductChargeRevenue" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DebentureUnitsIssued_019bffd7-5159-77b1-b2f6-fa8a7b15babd_terseLabel_en-US" xlink:label="lab_logan_DebentureUnitsIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debenture units, issued (in shares)</link:label>
    <link:label id="lab_logan_DebentureUnitsIssued_label_en-US" xlink:label="lab_logan_DebentureUnitsIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debenture Units, Issued</link:label>
    <link:label id="lab_logan_DebentureUnitsIssued_documentation_en-US" xlink:label="lab_logan_DebentureUnitsIssued" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debenture Units, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DebentureUnitsIssued" xlink:href="logan-20251231.xsd#logan_DebentureUnitsIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DebentureUnitsIssued" xlink:to="lab_logan_DebentureUnitsIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember_019bffd7-5159-7786-bb89-4052a64edeb2_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NAV</link:label>
    <link:label id="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember_label_en-US" xlink:label="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measured at Net Asset Value Per Share [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember" xlink:to="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_019bffd7-5157-75b4-acd0-719f9274cc4e_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Axis]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAxis" xlink:to="lab_us-gaap_BusinessAcquisitionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DividendEquivalentUnitsMember_019bffd7-515a-7fac-bf60-dd42e4046291_terseLabel_en-US" xlink:label="lab_logan_DividendEquivalentUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DEUs</link:label>
    <link:label id="lab_logan_DividendEquivalentUnitsMember_label_en-US" xlink:label="lab_logan_DividendEquivalentUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividend Equivalent Units [Member]</link:label>
    <link:label id="lab_logan_DividendEquivalentUnitsMember_documentation_en-US" xlink:label="lab_logan_DividendEquivalentUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Dividend Equivalent Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DividendEquivalentUnitsMember" xlink:href="logan-20251231.xsd#logan_DividendEquivalentUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DividendEquivalentUnitsMember" xlink:to="lab_logan_DividendEquivalentUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FormerLegacyMLCMember_019bffd7-5158-732b-ad1a-38db74a14340_terseLabel_en-US" xlink:label="lab_logan_FormerLegacyMLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Former Legacy MLC</link:label>
    <link:label id="lab_logan_FormerLegacyMLCMember_label_en-US" xlink:label="lab_logan_FormerLegacyMLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Former Legacy MLC [Member]</link:label>
    <link:label id="lab_logan_FormerLegacyMLCMember_documentation_en-US" xlink:label="lab_logan_FormerLegacyMLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Former Legacy MLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FormerLegacyMLCMember" xlink:href="logan-20251231.xsd#logan_FormerLegacyMLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FormerLegacyMLCMember" xlink:to="lab_logan_FormerLegacyMLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeTextBlock_019bffd7-5158-7e38-bc7c-4a678034452e_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Investment Income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeTextBlock" xlink:to="lab_us-gaap_InvestmentIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ProceedsFromBorrowingsOfInsuranceBusiness_019bffd7-5158-73a6-a40e-8d4b0501f1a6_terseLabel_en-US" xlink:label="lab_logan_ProceedsFromBorrowingsOfInsuranceBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from borrowings of insurance business</link:label>
    <link:label id="lab_logan_ProceedsFromBorrowingsOfInsuranceBusiness_label_en-US" xlink:label="lab_logan_ProceedsFromBorrowingsOfInsuranceBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Borrowings Of Insurance Business</link:label>
    <link:label id="lab_logan_ProceedsFromBorrowingsOfInsuranceBusiness_documentation_en-US" xlink:label="lab_logan_ProceedsFromBorrowingsOfInsuranceBusiness" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Borrowings Of Insurance Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ProceedsFromBorrowingsOfInsuranceBusiness" xlink:href="logan-20251231.xsd#logan_ProceedsFromBorrowingsOfInsuranceBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ProceedsFromBorrowingsOfInsuranceBusiness" xlink:to="lab_logan_ProceedsFromBorrowingsOfInsuranceBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskLineItems_019bffd7-515b-78be-861b-2f8e8c8d4656_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk [Line Items]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskLineItems_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskLineItems" xlink:to="lab_us-gaap_ConcentrationRiskLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet_019bffd7-515a-705e-9a7a-55e0d93cda9e_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net deferred tax assets</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsLiabilitiesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:to="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceEffectOnClaimsAndBenefitsIncurredAmountCeded_019bffd7-515a-7f0a-9e0f-85f1b3b611b7_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceEffectOnClaimsAndBenefitsIncurredAmountCeded" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance ceded, net of provision for credit losses</link:label>
    <link:label id="lab_us-gaap_ReinsuranceEffectOnClaimsAndBenefitsIncurredAmountCeded_label_en-US" xlink:label="lab_us-gaap_ReinsuranceEffectOnClaimsAndBenefitsIncurredAmountCeded" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Benefits and Claims Incurred, Ceded</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceEffectOnClaimsAndBenefitsIncurredAmountCeded" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceEffectOnClaimsAndBenefitsIncurredAmountCeded"/>
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    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_019bffd7-5159-7917-9c2a-643457ddb08b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:to="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_label_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoActuallyPaidCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoActuallyPaidCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoActuallyPaidCompAmt" xlink:to="lab_ecd_PeoActuallyPaidCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue_019bffd7-5158-743d-afe1-d35d3c476f8b_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InsuranceRegulationCapitalConservationBufferTotalRiskBasedCapitalActual_019bffd7-515b-7fd4-8335-02f1ea2de580_terseLabel_en-US" xlink:label="lab_logan_InsuranceRegulationCapitalConservationBufferTotalRiskBasedCapitalActual" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance regulation, capital conservation buffer, total risk-based capital, actual</link:label>
    <link:label id="lab_logan_InsuranceRegulationCapitalConservationBufferTotalRiskBasedCapitalActual_label_en-US" xlink:label="lab_logan_InsuranceRegulationCapitalConservationBufferTotalRiskBasedCapitalActual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance Regulation, Capital Conservation Buffer, Total Risk-Based Capital, Actual</link:label>
    <link:label id="lab_logan_InsuranceRegulationCapitalConservationBufferTotalRiskBasedCapitalActual_documentation_en-US" xlink:label="lab_logan_InsuranceRegulationCapitalConservationBufferTotalRiskBasedCapitalActual" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Insurance Regulation, Capital Conservation Buffer, Total Risk-Based Capital, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InsuranceRegulationCapitalConservationBufferTotalRiskBasedCapitalActual" xlink:href="logan-20251231.xsd#logan_InsuranceRegulationCapitalConservationBufferTotalRiskBasedCapitalActual"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InsuranceRegulationCapitalConservationBufferTotalRiskBasedCapitalActual" xlink:to="lab_logan_InsuranceRegulationCapitalConservationBufferTotalRiskBasedCapitalActual" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDilutedAbstract_019bffd7-515b-7bbc-b0fc-a57ee205999c_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted earnings per share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDilutedAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDilutedAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareDilutedAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDilutedAbstract" xlink:to="lab_us-gaap_EarningsPerShareDilutedAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember_019bffd7-5159-7b54-883c-99686cf656b8_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans 60-89 days past due</link:label>
    <link:label id="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, 60 to 89 Days Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivables60To89DaysPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivables60To89DaysPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivables60To89DaysPastDueMember" xlink:to="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerAbstract_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingDesignationAxis_019bffd7-5159-7982-b471-51082ee12125_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingDesignationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Designation [Axis]</link:label>
    <link:label id="lab_us-gaap_HedgingDesignationAxis_label_en-US" xlink:label="lab_us-gaap_HedgingDesignationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Designation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HedgingDesignationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingDesignationAxis" xlink:to="lab_us-gaap_HedgingDesignationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFairValue_019bffd7-5159-71c8-9748-34827748eaa7_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt obligations</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFairValue_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFairValue" xlink:to="lab_us-gaap_DebtInstrumentFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StatementScenarioAxis_019bffd7-5158-7fdc-a2fd-7f66947c40a3_terseLabel_en-US" xlink:label="lab_srt_StatementScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario [Axis]</link:label>
    <link:label id="lab_srt_StatementScenarioAxis_label_en-US" xlink:label="lab_srt_StatementScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementScenarioAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementScenarioAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StatementScenarioAxis" xlink:to="lab_srt_StatementScenarioAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FeeRelatedCompensation_019bffd7-515b-77bc-a3ac-997053f28d70_negatedTerseLabel_en-US" xlink:label="lab_logan_FeeRelatedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Fee-related compensation</link:label>
    <link:label id="lab_logan_FeeRelatedCompensation_label_en-US" xlink:label="lab_logan_FeeRelatedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fee-Related Compensation</link:label>
    <link:label id="lab_logan_FeeRelatedCompensation_documentation_en-US" xlink:label="lab_logan_FeeRelatedCompensation" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fee-Related Compensation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FeeRelatedCompensation" xlink:href="logan-20251231.xsd#logan_FeeRelatedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FeeRelatedCompensation" xlink:to="lab_logan_FeeRelatedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_OtherThanFairValueAbstractAbstract_019bffd7-5159-7cc4-8405-289ab344712f_terseLabel_en-US" xlink:label="lab_logan_OtherThanFairValueAbstractAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value</link:label>
    <link:label id="lab_logan_OtherThanFairValueAbstractAbstract_label_en-US" xlink:label="lab_logan_OtherThanFairValueAbstractAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Than Fair Value Abstract [Abstract]</link:label>
    <link:label id="lab_logan_OtherThanFairValueAbstractAbstract_documentation_en-US" xlink:label="lab_logan_OtherThanFairValueAbstractAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Than Fair Value Abstract</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_OtherThanFairValueAbstractAbstract" xlink:href="logan-20251231.xsd#logan_OtherThanFairValueAbstractAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_OtherThanFairValueAbstractAbstract" xlink:to="lab_logan_OtherThanFairValueAbstractAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_019bffd7-5159-70d3-a327-6d73f4231b17_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_label_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeContractTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeContractTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeContractTypeDomain" xlink:to="lab_us-gaap_DerivativeContractTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FinancialAssets_019bffd7-5158-732e-9a45-bc176c5b69ae_terseLabel_en-US" xlink:label="lab_logan_FinancialAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Assets</link:label>
    <link:label id="lab_logan_FinancialAssets_label_en-US" xlink:label="lab_logan_FinancialAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Assets</link:label>
    <link:label id="lab_logan_FinancialAssets_documentation_en-US" xlink:label="lab_logan_FinancialAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financial Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FinancialAssets" xlink:href="logan-20251231.xsd#logan_FinancialAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FinancialAssets" xlink:to="lab_logan_FinancialAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_019bffd7-5159-7043-a163-d8ed6a61aa15_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_OtherAssetsAndOtherLiabilitiesLineItems_019bffd7-515a-7d11-b04c-58447fb918d6_terseLabel_en-US" xlink:label="lab_logan_OtherAssetsAndOtherLiabilitiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Assets and Other Liabilities [Line Items]</link:label>
    <link:label id="lab_logan_OtherAssetsAndOtherLiabilitiesLineItems_label_en-US" xlink:label="lab_logan_OtherAssetsAndOtherLiabilitiesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets and Other Liabilities [Line Items]</link:label>
    <link:label id="lab_logan_OtherAssetsAndOtherLiabilitiesLineItems_documentation_en-US" xlink:label="lab_logan_OtherAssetsAndOtherLiabilitiesLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Assets and Other Liabilities [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_OtherAssetsAndOtherLiabilitiesLineItems" xlink:href="logan-20251231.xsd#logan_OtherAssetsAndOtherLiabilitiesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_OtherAssetsAndOtherLiabilitiesLineItems" xlink:to="lab_logan_OtherAssetsAndOtherLiabilitiesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ProbabilityWeightedExpectedReturnMethodMember_019bffd7-5159-74ac-a789-9eb72b730b67_terseLabel_en-US" xlink:label="lab_logan_ProbabilityWeightedExpectedReturnMethodMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Probability-Weighted Expected Return Method</link:label>
    <link:label id="lab_logan_ProbabilityWeightedExpectedReturnMethodMember_label_en-US" xlink:label="lab_logan_ProbabilityWeightedExpectedReturnMethodMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Probability-Weighted Expected Return Method [Member]</link:label>
    <link:label id="lab_logan_ProbabilityWeightedExpectedReturnMethodMember_documentation_en-US" xlink:label="lab_logan_ProbabilityWeightedExpectedReturnMethodMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Probability-Weighted Expected Return Method</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ProbabilityWeightedExpectedReturnMethodMember" xlink:href="logan-20251231.xsd#logan_ProbabilityWeightedExpectedReturnMethodMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ProbabilityWeightedExpectedReturnMethodMember" xlink:to="lab_logan_ProbabilityWeightedExpectedReturnMethodMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:to="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_LineOfCreditIncreaseDecreaseInBorrowingCapacity_019bffd7-5159-7299-bb4d-d1a5d452d5d9_terseLabel_en-US" xlink:label="lab_logan_LineOfCreditIncreaseDecreaseInBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit facility increase in borrowing capacity</link:label>
    <link:label id="lab_logan_LineOfCreditIncreaseDecreaseInBorrowingCapacity_label_en-US" xlink:label="lab_logan_LineOfCreditIncreaseDecreaseInBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit, Increase (Decrease) In Borrowing Capacity</link:label>
    <link:label id="lab_logan_LineOfCreditIncreaseDecreaseInBorrowingCapacity_documentation_en-US" xlink:label="lab_logan_LineOfCreditIncreaseDecreaseInBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line of Credit, Increase (Decrease) In Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_LineOfCreditIncreaseDecreaseInBorrowingCapacity" xlink:href="logan-20251231.xsd#logan_LineOfCreditIncreaseDecreaseInBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_LineOfCreditIncreaseDecreaseInBorrowingCapacity" xlink:to="lab_logan_LineOfCreditIncreaseDecreaseInBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_CollateralizedAsset_019bffd7-5158-76c3-b36b-2785a44d2bd9_terseLabel_en-US" xlink:label="lab_logan_CollateralizedAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateralized asset</link:label>
    <link:label id="lab_logan_CollateralizedAsset_label_en-US" xlink:label="lab_logan_CollateralizedAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateralized Asset</link:label>
    <link:label id="lab_logan_CollateralizedAsset_documentation_en-US" xlink:label="lab_logan_CollateralizedAsset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collateralized Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_CollateralizedAsset" xlink:href="logan-20251231.xsd#logan_CollateralizedAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_CollateralizedAsset" xlink:to="lab_logan_CollateralizedAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_TenderOfferMember_019c7c2d-20ec-72b3-8fca-808f28a276c6_terseLabel_en-US" xlink:label="lab_logan_TenderOfferMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tender Offer</link:label>
    <link:label id="lab_logan_TenderOfferMember_label_en-US" xlink:label="lab_logan_TenderOfferMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tender Offer [Member]</link:label>
    <link:label id="lab_logan_TenderOfferMember_documentation_en-US" xlink:label="lab_logan_TenderOfferMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tender Offer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_TenderOfferMember" xlink:href="logan-20251231.xsd#logan_TenderOfferMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_TenderOfferMember" xlink:to="lab_logan_TenderOfferMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum_019bffd7-515a-7fe0-a9be-e96a77295f60_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent of common shares issuable</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Percentage of Outstanding Stock Maximum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableNonaccrualNoAllowance_019bffd7-5159-7cc3-b9c2-a020277854b1_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableNonaccrualNoAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonaccrual loans with no allowance</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableNonaccrualNoAllowance_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableNonaccrualNoAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Nonaccrual, No Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableNonaccrualNoAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableNonaccrualNoAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableNonaccrualNoAllowance" xlink:to="lab_us-gaap_FinancingReceivableNonaccrualNoAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFive_019c7be1-fcfa-73a4-88f0-3d7742309865_terseLabel_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFive_label_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense, Year Five</link:label>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFive_documentation_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFive" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFive" xlink:href="logan-20251231.xsd#logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFive" xlink:to="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFour_019bffd7-5158-7248-8ad8-8ccbf206a482_terseLabel_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFour_label_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss Maturity, Year Four</link:label>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFour_documentation_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss Maturity, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFour" xlink:href="logan-20251231.xsd#logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFour" xlink:to="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract_019bffd7-5158-7e64-9fde-cf8fcfc9a38e_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost or amortized cost</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, Allocated and Single Maturity Date, Amortized Cost [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYear_019bffd7-5159-7352-b3e3-cdf18b96cc2d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated, More than Five Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitActivityTable_019bffd7-515a-7a27-b52c-b07dd05035b5_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitActivityTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit Activity [Table]</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitActivityTable_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitActivityTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit Activity [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitActivityTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitActivityTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitActivityTable" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitActivityTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StatementGeographicalAxis_019bffd7-515a-7498-a176-e192fa7b0dd3_terseLabel_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:label id="lab_srt_StatementGeographicalAxis_label_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementGeographicalAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementGeographicalAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StatementGeographicalAxis" xlink:to="lab_srt_StatementGeographicalAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossAmount_019bffd7-515a-7664-b4f6-b239883003a5_terseLabel_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">No benefit recorded on current-year NOL (domestication)</link:label>
    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossAmount_label_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Net Operating Loss, Amount</link:label>
    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossAmount_documentation_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Net Operating Loss, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossAmount" xlink:href="logan-20251231.xsd#logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossAmount" xlink:to="lab_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ReinsuranceRecoverablesExcludingFundsHeldUnderReinsuranceContracts_019bffd7-515a-7343-abe7-766f95774ad4_terseLabel_en-US" xlink:label="lab_logan_ReinsuranceRecoverablesExcludingFundsHeldUnderReinsuranceContracts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable</link:label>
    <link:label id="lab_logan_ReinsuranceRecoverablesExcludingFundsHeldUnderReinsuranceContracts_label_en-US" xlink:label="lab_logan_ReinsuranceRecoverablesExcludingFundsHeldUnderReinsuranceContracts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverables, Excluding Funds Held Under Reinsurance Contracts</link:label>
    <link:label id="lab_logan_ReinsuranceRecoverablesExcludingFundsHeldUnderReinsuranceContracts_documentation_en-US" xlink:label="lab_logan_ReinsuranceRecoverablesExcludingFundsHeldUnderReinsuranceContracts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverables, Excluding Funds Held Under Reinsurance Contracts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ReinsuranceRecoverablesExcludingFundsHeldUnderReinsuranceContracts" xlink:href="logan-20251231.xsd#logan_ReinsuranceRecoverablesExcludingFundsHeldUnderReinsuranceContracts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ReinsuranceRecoverablesExcludingFundsHeldUnderReinsuranceContracts" xlink:to="lab_logan_ReinsuranceRecoverablesExcludingFundsHeldUnderReinsuranceContracts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosureAssetAndLiabilityNotMeasuredAtFairValueLineItems_019bffd7-5159-7d13-b2a3-288bcf7007d1_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureAssetAndLiabilityNotMeasuredAtFairValueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Disclosure, Asset and Liability, Not Measured at Fair Value [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosureAssetAndLiabilityNotMeasuredAtFairValueLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureAssetAndLiabilityNotMeasuredAtFairValueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosure, Asset and Liability, Not Measured at Fair Value [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureAssetAndLiabilityNotMeasuredAtFairValueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosureAssetAndLiabilityNotMeasuredAtFairValueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosureAssetAndLiabilityNotMeasuredAtFairValueLineItems" xlink:to="lab_us-gaap_FairValueDisclosureAssetAndLiabilityNotMeasuredAtFairValueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_019bffd7-515b-7a09-8cc9-dee3b61041b5_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:to="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeOperating_019c47fa-fba0-778f-9953-3f49916e8121_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income - bank interest</link:label>
    <link:label id="lab_us-gaap_InterestIncomeOperating_label_en-US" xlink:label="lab_us-gaap_InterestIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeOperating" xlink:to="lab_us-gaap_InterestIncomeOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_019c2cbe-7e08-7631-a7ff-34c08a04923a_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
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    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationPartnershipDifferencesPercent_019c8fb4-0ed3-7d9b-ae87-2d0d42bca5f8_terseLabel_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationPartnershipDifferencesPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Partnership differences</link:label>
    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationPartnershipDifferencesPercent_label_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationPartnershipDifferencesPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Partnership Differences, Percent</link:label>
    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationPartnershipDifferencesPercent_documentation_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationPartnershipDifferencesPercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Partnership Differences, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_EffectiveIncomeTaxRateReconciliationPartnershipDifferencesPercent" xlink:href="logan-20251231.xsd#logan_EffectiveIncomeTaxRateReconciliationPartnershipDifferencesPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_EffectiveIncomeTaxRateReconciliationPartnershipDifferencesPercent" xlink:to="lab_logan_EffectiveIncomeTaxRateReconciliationPartnershipDifferencesPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitWeightedAverageInterestAccretionRate_019bffd7-515a-78c3-869a-eadbc7d12fe0_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitWeightedAverageInterestAccretionRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average interest rate at original rate</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitWeightedAverageInterestAccretionRate_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitWeightedAverageInterestAccretionRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Weighted-Average Interest Accretion Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitWeightedAverageInterestAccretionRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitWeightedAverageInterestAccretionRate"/>
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    <link:label id="lab_logan_VistaLifeAndCasualtyReinsuranceCoMember_019bffd7-515a-75a0-aad2-f03d10bc5e48_terseLabel_en-US" xlink:label="lab_logan_VistaLifeAndCasualtyReinsuranceCoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vista Life and Casualty Reinsurance Co</link:label>
    <link:label id="lab_logan_VistaLifeAndCasualtyReinsuranceCoMember_019c4c0b-bce1-76d6-bce5-22c2df712f5d_verboseLabel_en-US" xlink:label="lab_logan_VistaLifeAndCasualtyReinsuranceCoMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Vista Life and Casualty Reinsurance Co</link:label>
    <link:label id="lab_logan_VistaLifeAndCasualtyReinsuranceCoMember_label_en-US" xlink:label="lab_logan_VistaLifeAndCasualtyReinsuranceCoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vista Life And Casualty Reinsurance Co [Member]</link:label>
    <link:label id="lab_logan_VistaLifeAndCasualtyReinsuranceCoMember_documentation_en-US" xlink:label="lab_logan_VistaLifeAndCasualtyReinsuranceCoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Vista Life And Casualty Reinsurance Co</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_VistaLifeAndCasualtyReinsuranceCoMember" xlink:href="logan-20251231.xsd#logan_VistaLifeAndCasualtyReinsuranceCoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_VistaLifeAndCasualtyReinsuranceCoMember" xlink:to="lab_logan_VistaLifeAndCasualtyReinsuranceCoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidInsurance_019bffd7-515a-7cb7-833c-022e67552e8b_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidInsurance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid insurance</link:label>
    <link:label id="lab_us-gaap_PrepaidInsurance_label_en-US" xlink:label="lab_us-gaap_PrepaidInsurance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Insurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidInsurance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrepaidInsurance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidInsurance" xlink:to="lab_us-gaap_PrepaidInsurance" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CreditRatingAMBestDomain_019bffd7-515b-7451-9e8e-cdfbf41dfade_terseLabel_en-US" xlink:label="lab_srt_CreditRatingAMBestDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Rating, AM Best [Domain]</link:label>
    <link:label id="lab_srt_CreditRatingAMBestDomain_label_en-US" xlink:label="lab_srt_CreditRatingAMBestDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Rating, AM Best [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CreditRatingAMBestDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CreditRatingAMBestDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CreditRatingAMBestDomain" xlink:to="lab_srt_CreditRatingAMBestDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReportingUnitPercentageOfFairValueInExcessOfCarryingAmount_019c7b9f-90c9-7d10-93dc-62e9a7eec3ac_terseLabel_en-US" xlink:label="lab_us-gaap_ReportingUnitPercentageOfFairValueInExcessOfCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reporting unit exceeded its respective carrying value percentage</link:label>
    <link:label id="lab_us-gaap_ReportingUnitPercentageOfFairValueInExcessOfCarryingAmount_label_en-US" xlink:label="lab_us-gaap_ReportingUnitPercentageOfFairValueInExcessOfCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reporting Unit, Percentage of Fair Value in Excess of Carrying Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReportingUnitPercentageOfFairValueInExcessOfCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReportingUnitPercentageOfFairValueInExcessOfCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReportingUnitPercentageOfFairValueInExcessOfCarryingAmount" xlink:to="lab_us-gaap_ReportingUnitPercentageOfFairValueInExcessOfCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_BelowInvestmentGradeMember_019bffd7-5158-7962-9dfc-b3bae6f2763d_terseLabel_en-US" xlink:label="lab_logan_BelowInvestmentGradeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Below Investment Grade</link:label>
    <link:label id="lab_logan_BelowInvestmentGradeMember_label_en-US" xlink:label="lab_logan_BelowInvestmentGradeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Below Investment Grade [Member]</link:label>
    <link:label id="lab_logan_BelowInvestmentGradeMember_documentation_en-US" xlink:label="lab_logan_BelowInvestmentGradeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Below Investment Grade</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_BelowInvestmentGradeMember" xlink:href="logan-20251231.xsd#logan_BelowInvestmentGradeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_BelowInvestmentGradeMember" xlink:to="lab_logan_BelowInvestmentGradeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsNet_019bffd7-5159-7027-b41f-5a5246f8e5f1_terseLabel_en-US" xlink:label="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net realized gain (loss)</link:label>
    <link:label id="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsNet_label_en-US" xlink:label="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Gain (Loss) Included in Earnings, Net</link:label>
    <link:label id="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsNet_documentation_en-US" xlink:label="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Gain (Loss) Included in Earnings, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsNet" xlink:href="logan-20251231.xsd#logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsNet" xlink:to="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_019bffd7-5157-7e5c-9ac6-0d2ebb2cf1fd_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings per share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_019bffd7-515b-71c8-95c5-134ec0e45709_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiary, ownership percentage</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:to="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_OtherInvestedAssetsMember_019bffd7-5158-7bd6-9658-fe95823d763f_terseLabel_en-US" xlink:label="lab_logan_OtherInvestedAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other invested assets</link:label>
    <link:label id="lab_logan_OtherInvestedAssetsMember_019c4c24-f779-7322-ad46-567607bb254f_verboseLabel_en-US" xlink:label="lab_logan_OtherInvestedAssetsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other invested assets</link:label>
    <link:label id="lab_logan_OtherInvestedAssetsMember_label_en-US" xlink:label="lab_logan_OtherInvestedAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Invested Assets [Member]</link:label>
    <link:label id="lab_logan_OtherInvestedAssetsMember_documentation_en-US" xlink:label="lab_logan_OtherInvestedAssetsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Invested Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_OtherInvestedAssetsMember" xlink:href="logan-20251231.xsd#logan_OtherInvestedAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_OtherInvestedAssetsMember" xlink:to="lab_logan_OtherInvestedAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_AmortizationAndImpairmentOfIntangibleAssets_019bffd7-5157-7715-b6d7-e4cf9f4e54a4_terseLabel_en-US" xlink:label="lab_logan_AmortizationAndImpairmentOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization and impairment of intangible assets</link:label>
    <link:label id="lab_logan_AmortizationAndImpairmentOfIntangibleAssets_019cadd0-4fcc-7518-8299-e24c67e0c7eb_negatedLabel_en-US" xlink:label="lab_logan_AmortizationAndImpairmentOfIntangibleAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Amortization and impairment of intangible assets</link:label>
    <link:label id="lab_logan_AmortizationAndImpairmentOfIntangibleAssets_label_en-US" xlink:label="lab_logan_AmortizationAndImpairmentOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization and Impairment of Intangible Assets</link:label>
    <link:label id="lab_logan_AmortizationAndImpairmentOfIntangibleAssets_documentation_en-US" xlink:label="lab_logan_AmortizationAndImpairmentOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amortization and Impairment of Intangible Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_AmortizationAndImpairmentOfIntangibleAssets" xlink:href="logan-20251231.xsd#logan_AmortizationAndImpairmentOfIntangibleAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_AmortizationAndImpairmentOfIntangibleAssets" xlink:to="lab_logan_AmortizationAndImpairmentOfIntangibleAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_019bffd7-515b-7f0f-b2e5-bbab552abb0c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share</link:label>
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    <link:label id="lab_logan_KeyManagementPersonnelEquityCompensationPercentage_019bffd7-515b-7baa-b76d-61de020a2e15_terseLabel_en-US" xlink:label="lab_logan_KeyManagementPersonnelEquityCompensationPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity-based compensation percentage</link:label>
    <link:label id="lab_logan_KeyManagementPersonnelEquityCompensationPercentage_label_en-US" xlink:label="lab_logan_KeyManagementPersonnelEquityCompensationPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Key Management Personnel, Equity Compensation, Percentage</link:label>
    <link:label id="lab_logan_KeyManagementPersonnelEquityCompensationPercentage_documentation_en-US" xlink:label="lab_logan_KeyManagementPersonnelEquityCompensationPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Key Management Personnel, Equity Compensation, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_KeyManagementPersonnelEquityCompensationPercentage" xlink:href="logan-20251231.xsd#logan_KeyManagementPersonnelEquityCompensationPercentage"/>
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    <link:label id="lab_us-gaap_ShortTermDebtTypeAxis_019bffd7-5158-7f62-a528-e502e2de7eea_terseLabel_en-US" xlink:label="lab_us-gaap_ShortTermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ShortTermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_ShortTermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortTermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermDebtTypeAxis" xlink:to="lab_us-gaap_ShortTermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdministrativeFeesExpense_019bffd7-515b-79e3-89dc-d0c749691c78_terseLabel_en-US" xlink:label="lab_us-gaap_AdministrativeFeesExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administrative fees</link:label>
    <link:label id="lab_us-gaap_AdministrativeFeesExpense_label_en-US" xlink:label="lab_us-gaap_AdministrativeFeesExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Administrative Fees Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdministrativeFeesExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdministrativeFeesExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdministrativeFeesExpense" xlink:to="lab_us-gaap_AdministrativeFeesExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_MedicoInsuranceCompanyMember_019bffd7-515a-7d5a-b73f-4a5790d67f3a_terseLabel_en-US" xlink:label="lab_logan_MedicoInsuranceCompanyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Medico Insurance Company</link:label>
    <link:label id="lab_logan_MedicoInsuranceCompanyMember_019c4c0b-7b0e-74ad-b9ff-f822e5f36663_verboseLabel_en-US" xlink:label="lab_logan_MedicoInsuranceCompanyMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Medico Insurance Company</link:label>
    <link:label id="lab_logan_MedicoInsuranceCompanyMember_label_en-US" xlink:label="lab_logan_MedicoInsuranceCompanyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Medico Insurance Company [Member]</link:label>
    <link:label id="lab_logan_MedicoInsuranceCompanyMember_documentation_en-US" xlink:label="lab_logan_MedicoInsuranceCompanyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Medico Insurance Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_MedicoInsuranceCompanyMember" xlink:href="logan-20251231.xsd#logan_MedicoInsuranceCompanyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_MedicoInsuranceCompanyMember" xlink:to="lab_logan_MedicoInsuranceCompanyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_MultiYearGuaranteedAnnuitiesMember_019c77de-bbc5-7ccd-851f-0d071bf1571d_terseLabel_en-US" xlink:label="lab_logan_MultiYearGuaranteedAnnuitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multi Year Guaranteed Annuities</link:label>
    <link:label id="lab_logan_MultiYearGuaranteedAnnuitiesMember_label_en-US" xlink:label="lab_logan_MultiYearGuaranteedAnnuitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Multi Year Guaranteed Annuities [Member]</link:label>
    <link:label id="lab_logan_MultiYearGuaranteedAnnuitiesMember_documentation_en-US" xlink:label="lab_logan_MultiYearGuaranteedAnnuitiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Multi Year Guaranteed Annuities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_MultiYearGuaranteedAnnuitiesMember" xlink:href="logan-20251231.xsd#logan_MultiYearGuaranteedAnnuitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_MultiYearGuaranteedAnnuitiesMember" xlink:to="lab_logan_MultiYearGuaranteedAnnuitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredOfferingCosts_019bffd7-515a-7629-8967-d32d0da3d689_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredOfferingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred offering costs</link:label>
    <link:label id="lab_us-gaap_DeferredOfferingCosts_label_en-US" xlink:label="lab_us-gaap_DeferredOfferingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Offering Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredOfferingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredOfferingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredOfferingCosts" xlink:to="lab_us-gaap_DeferredOfferingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_019bffd7-5159-7eab-8c89-050793137c8c_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScenarioPlanMember_019bffd7-5158-77d6-849d-d626207b5e60_terseLabel_en-US" xlink:label="lab_us-gaap_ScenarioPlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario, Plan</link:label>
    <link:label id="lab_us-gaap_ScenarioPlanMember_label_en-US" xlink:label="lab_us-gaap_ScenarioPlanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario, Plan [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScenarioPlanMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScenarioPlanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScenarioPlanMember" xlink:to="lab_us-gaap_ScenarioPlanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ScheduleOfAccruedInterestWriteOffTableTextBlock_019bffd7-5158-7f1e-b71f-82255d6986f9_terseLabel_en-US" xlink:label="lab_logan_ScheduleOfAccruedInterestWriteOffTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule Of Accrued Interest Write-off</link:label>
    <link:label id="lab_logan_ScheduleOfAccruedInterestWriteOffTableTextBlock_label_en-US" xlink:label="lab_logan_ScheduleOfAccruedInterestWriteOffTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Accrued Interest Write-off [Table Text Block]</link:label>
    <link:label id="lab_logan_ScheduleOfAccruedInterestWriteOffTableTextBlock_documentation_en-US" xlink:label="lab_logan_ScheduleOfAccruedInterestWriteOffTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule Of Accrued Interest Write-off</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ScheduleOfAccruedInterestWriteOffTableTextBlock" xlink:href="logan-20251231.xsd#logan_ScheduleOfAccruedInterestWriteOffTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ScheduleOfAccruedInterestWriteOffTableTextBlock" xlink:to="lab_logan_ScheduleOfAccruedInterestWriteOffTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross_019bffd7-5159-7e84-ad31-9fbdc8d20d23_terseLabel_en-US" xlink:label="lab_logan_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross carrying amount</link:label>
    <link:label id="lab_logan_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross_label_en-US" xlink:label="lab_logan_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets (Excluding Goodwill), Gross</link:label>
    <link:label id="lab_logan_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross_documentation_en-US" xlink:label="lab_logan_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets (Excluding Goodwill), Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross" xlink:href="logan-20251231.xsd#logan_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross" xlink:to="lab_logan_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CreditRatingAMBestAxis_019bffd7-515b-7407-9655-464b86abd554_terseLabel_en-US" xlink:label="lab_srt_CreditRatingAMBestAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Rating, AM Best [Axis]</link:label>
    <link:label id="lab_srt_CreditRatingAMBestAxis_label_en-US" xlink:label="lab_srt_CreditRatingAMBestAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Rating, AM Best [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CreditRatingAMBestAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CreditRatingAMBestAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CreditRatingAMBestAxis" xlink:to="lab_srt_CreditRatingAMBestAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_019bffd7-515a-73fa-b903-bb4ceff278ae_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_019cf499-5012-7507-9c85-a6c0dd91adaa_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State</link:label>
    <link:label id="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred State and Local Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYear_019bffd7-5159-7a9f-ad2c-73ebc63c752c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year three</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Year Three, Originated, Two Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceTextBlock_019bffd7-515a-7470-ac2e-d2e50e4578b4_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance</link:label>
    <link:label id="lab_us-gaap_ReinsuranceTextBlock_label_en-US" xlink:label="lab_us-gaap_ReinsuranceTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceTextBlock" xlink:to="lab_us-gaap_ReinsuranceTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_019bffd7-5157-7c91-8ebd-4dac437452e0_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019bffd7-5157-7e6a-ab86-ab508d8c50a0_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019c4bc1-5073-762b-89e4-5a9f81f3eb4c_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTable_019bffd7-515b-732b-bf65-30c96af3e1b7_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTable_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTable" xlink:to="lab_us-gaap_SubsequentEventTable" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_Second10YearsMember_019bffd7-515b-7094-8034-ac5855f4ddb5_terseLabel_en-US" xlink:label="lab_logan_Second10YearsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Second 10 Years</link:label>
    <link:label id="lab_logan_Second10YearsMember_label_en-US" xlink:label="lab_logan_Second10YearsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Second 10 Years [Member]</link:label>
    <link:label id="lab_logan_Second10YearsMember_documentation_en-US" xlink:label="lab_logan_Second10YearsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Second 10 Years</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_Second10YearsMember" xlink:href="logan-20251231.xsd#logan_Second10YearsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_Second10YearsMember" xlink:to="lab_logan_Second10YearsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_GA_019c7c1d-d183-7efb-9b32-b31d8d14b6e2_terseLabel_en-US" xlink:label="lab_stpr_GA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Georgia</link:label>
    <link:label id="lab_stpr_GA_label_en-US" xlink:label="lab_stpr_GA" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">GEORGIA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_GA" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_GA"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_GA" xlink:to="lab_stpr_GA" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_019bffd7-515a-7bc7-bdb6-7ac765fb73fb_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Effective Income Tax Rate</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Effective Income Tax Rate Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_019bffd7-5158-7dcf-83e4-6d1b7ea0394d_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting period</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefits_019bffd7-5157-753b-b0f4-a694e515282d_verboseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefits" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Future policy benefits</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefits_019bffd7-515a-7c77-8679-c3b3440eef0f_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Direct</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefits_019bffd7-515a-7be2-9f62-d10ffe839ca4_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefits" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total future policy benefits</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefits_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, before Reinsurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefits" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefits" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments_019c7c0b-a191-7d58-8cf3-6cb71469e0df_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Other Adjustments, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_019bffd7-515b-7cd7-b07b-bc8f53352955_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems" xlink:to="lab_us-gaap_SegmentReportingInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_019bffd7-515a-7e32-a5b6-793cbbe68af2_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesAuthorized" xlink:to="lab_us-gaap_PreferredStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ShareBasedPaymentArrangementEquityInstrumentsOtherThanOptionsExchangeToCommonShare_019bffd7-515a-70ea-ae28-69454adb88a8_terseLabel_en-US" xlink:label="lab_logan_ShareBasedPaymentArrangementEquityInstrumentsOtherThanOptionsExchangeToCommonShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exchange to common shares (in shares)</link:label>
    <link:label id="lab_logan_ShareBasedPaymentArrangementEquityInstrumentsOtherThanOptionsExchangeToCommonShare_label_en-US" xlink:label="lab_logan_ShareBasedPaymentArrangementEquityInstrumentsOtherThanOptionsExchangeToCommonShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Equity Instruments Other Than Options, Exchange To Common Share</link:label>
    <link:label id="lab_logan_ShareBasedPaymentArrangementEquityInstrumentsOtherThanOptionsExchangeToCommonShare_documentation_en-US" xlink:label="lab_logan_ShareBasedPaymentArrangementEquityInstrumentsOtherThanOptionsExchangeToCommonShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Equity Instruments Other Than Options, Exchange To Common Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ShareBasedPaymentArrangementEquityInstrumentsOtherThanOptionsExchangeToCommonShare" xlink:href="logan-20251231.xsd#logan_ShareBasedPaymentArrangementEquityInstrumentsOtherThanOptionsExchangeToCommonShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ShareBasedPaymentArrangementEquityInstrumentsOtherThanOptionsExchangeToCommonShare" xlink:to="lab_logan_ShareBasedPaymentArrangementEquityInstrumentsOtherThanOptionsExchangeToCommonShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_019bffd7-5158-7c4f-986b-1a121eabf62a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repurchase of common shares</link:label>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Repurchase of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForRepurchaseOfCommonStock"/>
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    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
    <link:label id="lab_ecd_TrdArrAdoptionDate_label_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Adoption Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrAdoptionDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrAdoptionDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrAdoptionDate" xlink:to="lab_ecd_TrdArrAdoptionDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharesIssuedPricePerShare_019c4675-30a2-7d0b-9de3-03bbf82110e9_terseLabel_en-US" xlink:label="lab_us-gaap_SharesIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares issued, price per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_SharesIssuedPricePerShare_label_en-US" xlink:label="lab_us-gaap_SharesIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesIssuedPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharesIssuedPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharesIssuedPricePerShare" xlink:to="lab_us-gaap_SharesIssuedPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumNetPremiumCollected_019bffd7-515a-7bad-9fb9-1e28a1e6fd17_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumNetPremiumCollected" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net premiums collected</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumNetPremiumCollected_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumNetPremiumCollected" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Net Premium, Net Premium Collected</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumNetPremiumCollected" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumNetPremiumCollected"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumNetPremiumCollected" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumNetPremiumCollected" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_AssetManagementRevenueAbstract_019bffd7-5157-7bd5-9ead-aeeb0014229c_terseLabel_en-US" xlink:label="lab_logan_AssetManagementRevenueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Management</link:label>
    <link:label id="lab_logan_AssetManagementRevenueAbstract_label_en-US" xlink:label="lab_logan_AssetManagementRevenueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Management, Revenue [Abstract]</link:label>
    <link:label id="lab_logan_AssetManagementRevenueAbstract_documentation_en-US" xlink:label="lab_logan_AssetManagementRevenueAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Management, Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_AssetManagementRevenueAbstract" xlink:href="logan-20251231.xsd#logan_AssetManagementRevenueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_AssetManagementRevenueAbstract" xlink:to="lab_logan_AssetManagementRevenueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract_019bffd7-5158-72e5-a9f3-6e35f9257c5e_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Continuing Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditMember_019bffd7-5158-73c1-81bc-8f15803c1b2c_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit</link:label>
    <link:label id="lab_us-gaap_LineOfCreditMember_label_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditMember" xlink:to="lab_us-gaap_LineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchasesSalesIssuancesSettlements_019c9fea-19e8-7cfd-8659-f1d72be9bdfe_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchasesSalesIssuancesSettlements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sales and repayments</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchasesSalesIssuancesSettlements_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchasesSalesIssuancesSettlements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Purchases, (Sales), Issuances, (Settlements)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchasesSalesIssuancesSettlements" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchasesSalesIssuancesSettlements"/>
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    <link:label id="lab_us-gaap_CompensationRelatedCostsPolicyTextBlock_019bffd7-5158-7d70-ada7-efd559493ed4_terseLabel_en-US" xlink:label="lab_us-gaap_CompensationRelatedCostsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation and benefits</link:label>
    <link:label id="lab_us-gaap_CompensationRelatedCostsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_CompensationRelatedCostsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Related Costs, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CompensationRelatedCostsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CompensationRelatedCostsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CompensationRelatedCostsPolicyTextBlock" xlink:to="lab_us-gaap_CompensationRelatedCostsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_019bffd7-5157-7a9d-b0f3-b698c6e9382b_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retained earnings (accumulated deficit)</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
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    <link:label id="lab_logan_WarrantsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_logan_WarrantsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants, Policy [Policy Text Block]</link:label>
    <link:label id="lab_logan_WarrantsPolicyPolicyTextBlock_documentation_en-US" xlink:label="lab_logan_WarrantsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrants, Policy</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_WarrantsPolicyPolicyTextBlock" xlink:to="lab_logan_WarrantsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFive_019c467f-2205-7754-b455-cc249297a298_terseLabel_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
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    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFive_documentation_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFive" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss, Maturity Year Five</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFive" xlink:to="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_019bffd7-515a-7f55-a884-29e299f0dea3_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gains (losses) on hedging instruments</link:label>
    <link:label id="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Gain (Loss), Net, Cash Flow Hedge, Parent [Member]</link:label>
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    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_019bffd7-515b-749a-bd6c-677e8d60d7c8_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeDomain" xlink:to="lab_us-gaap_SubsequentEventTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract_019bffd7-5159-720a-b9b1-2594129e70fa_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets &#8212; definite life</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ImpairmentOfIntangibleAssetsFinitelived_019bffd7-5158-7168-9f7a-5d098e069efe_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOfIntangibleAssetsFinitelived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment of intangible assets</link:label>
    <link:label id="lab_us-gaap_ImpairmentOfIntangibleAssetsFinitelived_label_en-US" xlink:label="lab_us-gaap_ImpairmentOfIntangibleAssetsFinitelived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment of Intangible Assets, Finite-Lived</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairmentOfIntangibleAssetsFinitelived" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ImpairmentOfIntangibleAssetsFinitelived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ImpairmentOfIntangibleAssetsFinitelived" xlink:to="lab_us-gaap_ImpairmentOfIntangibleAssetsFinitelived" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeDividend_019bffd7-5157-73b6-bf28-7a692872e464_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeDividend" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeDividend_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeDividend" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Dividend</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeDividend" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeDividend"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeDividend" xlink:to="lab_us-gaap_InvestmentIncomeDividend" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesOther_019bffd7-515a-709e-8f6b-d47f97471a91_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesOther_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesOther" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_019bffd7-5157-7b4b-9898-dd65dc7ea362_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsMarketableSecurities_019bffd7-5158-7312-adbf-1716ee1b748c_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsMarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquired net investment</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsMarketableSecurities_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsMarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Investment in Debt and Equity Securities, Current</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock_019bffd7-5158-7f6e-90cc-0ed0e7780046_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Hypothetical Number of Shares</link:label>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_019bffd7-515a-7a47-88b4-4354678f0961_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total deferred tax</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
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    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_019bffd7-5158-73d9-9a36-5ddbf0ad881e_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net income (loss) to net cash used in operating activities:</link:label>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense_019c8fd3-271e-79ab-bb8d-6548d5522f35_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nondeductible Differences</link:label>
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    <link:label id="lab_logan_DebtCovenantAmendmentFeeAsAPercentageOfOutstandingPrincipal_documentation_en-US" xlink:label="lab_logan_DebtCovenantAmendmentFeeAsAPercentageOfOutstandingPrincipal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Covenant, Amendment Fee As a Percentage Of Outstanding Principal</link:label>
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    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
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    <link:label id="lab_stpr_MA_019c7c1d-d183-7671-b1e9-8b58a99e5c77_terseLabel_en-US" xlink:label="lab_stpr_MA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Massachusetts</link:label>
    <link:label id="lab_stpr_MA_label_en-US" xlink:label="lab_stpr_MA" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MASSACHUSETTS</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_MA" xlink:to="lab_stpr_MA" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllAdjToCompMember_terseLabel_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation</link:label>
    <link:label id="lab_ecd_AllAdjToCompMember_label_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllAdjToCompMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllAdjToCompMember" xlink:to="lab_ecd_AllAdjToCompMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_SaleOfStockPricePerShare_019c7c30-1efe-7db8-8cd0-139dc7ff126e_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of stock, price per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_SaleOfStockPricePerShare_label_en-US" xlink:label="lab_us-gaap_SaleOfStockPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleOfStockPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockPricePerShare" xlink:to="lab_us-gaap_SaleOfStockPricePerShare" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MovementAnalysisOfDeferredPolicyAcquisitionCostsRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MovementAnalysisOfDeferredPolicyAcquisitionCostsRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MovementAnalysisOfDeferredPolicyAcquisitionCostsRollForward" xlink:to="lab_us-gaap_MovementAnalysisOfDeferredPolicyAcquisitionCostsRollForward" xlink:type="arc" order="1"/>
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    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrTerminationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrTerminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrTerminationDate" xlink:to="lab_ecd_TrdArrTerminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitOriginalDiscountRateBeforeCashFlowAndReinsurance_019bffd7-515a-7eed-9ee2-2e19bda64359_periodStartLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitOriginalDiscountRateBeforeCashFlowAndReinsurance" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance at locked-in discount rate</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitOriginalDiscountRateBeforeCashFlowAndReinsurance_019bffd7-515a-7c7b-a7a7-49b5bd0daef2_periodEndLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitOriginalDiscountRateBeforeCashFlowAndReinsurance" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance at locked-in discount rate</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitOriginalDiscountRateBeforeCashFlowAndReinsurance_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitOriginalDiscountRateBeforeCashFlowAndReinsurance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Future Policy Benefit, Original Discount Rate, before Cash Flow and Reinsurance</link:label>
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    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTrdPoliciesProcAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:to="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyTransactionGainLossRealized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ForeignCurrencyTransactionGainLossRealized"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheThreeMember_019bffd7-5158-7a02-be30-066a7f6515f0_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tranche Three</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheThreeMember_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Tranche Three [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationAwardTrancheThreeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationAwardTrancheThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationAwardTrancheThreeMember" xlink:to="lab_us-gaap_ShareBasedCompensationAwardTrancheThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019bffd7-5157-7124-83d4-e8cb8b978b46_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average shares outstanding &#8211; Basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019c4638-c0a0-7550-84ae-8b5d802bffd0_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average number of common shares outstanding &#8211; basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
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    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwillAbstract_019bffd7-5159-7a36-a441-52199a629379_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwillAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets &#8212; indefinite life</link:label>
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    <link:label id="lab_us-gaap_WarrantsAndRightsOutstanding_019bffd7-5157-7082-829c-fad8c5f8fc6c_terseLabel_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants</link:label>
    <link:label id="lab_us-gaap_WarrantsAndRightsOutstanding_label_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants and Rights Outstanding</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_019bffd7-515b-732a-a11a-0798adcd9598_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Earnings Per Share, Basic and Diluted</link:label>
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    <link:label id="lab_logan_InvestmentConcentrationRiskMember_documentation_en-US" xlink:label="lab_logan_InvestmentConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Concentration Risk</link:label>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_019bffd7-515a-735a-a999-0c88922e5380_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionDomain"/>
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    <link:label id="lab_us-gaap_SubsequentEventsAbstract_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsAbstract" xlink:to="lab_us-gaap_SubsequentEventsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingAbstract" xlink:to="lab_us-gaap_SegmentReportingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_AssetManagementSegmentMember_019bffd7-5157-7f4a-bf4f-a473f147db9f_terseLabel_en-US" xlink:label="lab_logan_AssetManagementSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Management</link:label>
    <link:label id="lab_logan_AssetManagementSegmentMember_019c4b5b-a03b-7dd1-88f5-f10770dea0e4_verboseLabel_en-US" xlink:label="lab_logan_AssetManagementSegmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Asset Management</link:label>
    <link:label id="lab_logan_AssetManagementSegmentMember_label_en-US" xlink:label="lab_logan_AssetManagementSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Management Segment [Member]</link:label>
    <link:label id="lab_logan_AssetManagementSegmentMember_documentation_en-US" xlink:label="lab_logan_AssetManagementSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Management Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_AssetManagementSegmentMember" xlink:href="logan-20251231.xsd#logan_AssetManagementSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_AssetManagementSegmentMember" xlink:to="lab_logan_AssetManagementSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScenarioUnspecifiedDomain_019bffd7-5158-7e53-bc0c-afd860cf8d4b_terseLabel_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:label id="lab_srt_ScenarioUnspecifiedDomain_label_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioUnspecifiedDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScenarioUnspecifiedDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScenarioUnspecifiedDomain" xlink:to="lab_srt_ScenarioUnspecifiedDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostsAndExpensesAbstract_019bffd7-5157-72d3-a8da-db34fed8f563_terseLabel_en-US" xlink:label="lab_us-gaap_CostsAndExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EXPENSES</link:label>
    <link:label id="lab_us-gaap_CostsAndExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_CostsAndExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Costs and Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostsAndExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostsAndExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostsAndExpensesAbstract" xlink:to="lab_us-gaap_CostsAndExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProductLiabilityContingencyLineItems_019bffd7-515b-7b1e-beb0-d0799ba57b38_terseLabel_en-US" xlink:label="lab_us-gaap_ProductLiabilityContingencyLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product Liability Contingency [Line Items]</link:label>
    <link:label id="lab_us-gaap_ProductLiabilityContingencyLineItems_label_en-US" xlink:label="lab_us-gaap_ProductLiabilityContingencyLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product Liability Contingency [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProductLiabilityContingencyLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProductLiabilityContingencyLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProductLiabilityContingencyLineItems" xlink:to="lab_us-gaap_ProductLiabilityContingencyLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumDiscountedBeforeReinsurance_019bffd7-515a-7940-8486-2edb9d42f82b_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumDiscountedBeforeReinsurance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected future gross premiums, Discounted</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumDiscountedBeforeReinsurance_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumDiscountedBeforeReinsurance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Future Gross Premium, Discounted, before Reinsurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumDiscountedBeforeReinsurance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumDiscountedBeforeReinsurance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumDiscountedBeforeReinsurance" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumDiscountedBeforeReinsurance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent_019bffd7-515a-7983-abe0-9b740d4089a3_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: reclassification adjustments for gains (losses) realized</link:label>
    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent_label_en-US" xlink:label="lab_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification from AOCI, Current Period, before Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent"/>
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    <link:label id="lab_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTable_019bffd7-5159-728f-b35c-0a6a6733b9a4_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Disclosure of Asset and Liability Not Measured at Fair Value [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTable_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosure of Asset and Liability Not Measured at Fair Value [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTable" xlink:to="lab_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTable" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag_019cb996-5a34-7208-8280-017053baf4a9_terseLabel_en-US" xlink:label="lab_logan_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Recurring Basis Unobservable Input Reconciliation Asset Gain Loss Statement Of Other Comprehensive Income Extensible List Not Disclosed Flag</link:label>
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    <link:label id="lab_logan_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag_documentation_en-US" xlink:label="lab_logan_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Recurring Basis Unobservable Input Reconciliation Asset Gain Loss Statement Of Other Comprehensive Income Extensible List Not Disclosed Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag" xlink:href="logan-20251231.xsd#logan_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag" xlink:to="lab_logan_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019bffd7-515a-7578-8055-66c1a7120e5d_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_019bffd7-5157-7274-968a-c82522139aa9_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_019bffd7-5157-7582-bf2c-315a69a07345_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesAxis" xlink:to="lab_srt_ConsolidatedEntitiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_MN_019c7c1d-d183-77a2-ac12-7aa2435b010d_terseLabel_en-US" xlink:label="lab_stpr_MN" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minnesota</link:label>
    <link:label id="lab_stpr_MN_label_en-US" xlink:label="lab_stpr_MN" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MINNESOTA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_MN" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_MN"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_MN" xlink:to="lab_stpr_MN" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitRemeasurementGainLoss_019bffd7-5157-7b00-845d-7e106cc61361_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitRemeasurementGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remeasurement gain on policy liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitRemeasurementGainLoss_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitRemeasurementGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Remeasurement Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitRemeasurementGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitRemeasurementGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitRemeasurementGainLoss" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitRemeasurementGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UseOfEstimates_019bffd7-5158-7c73-9276-4581bfe18135_verboseLabel_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Use of estimates</link:label>
    <link:label id="lab_us-gaap_UseOfEstimates_label_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UseOfEstimates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UseOfEstimates" xlink:to="lab_us-gaap_UseOfEstimates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDividends_019bffd7-515a-77b1-9cf7-50afe0596dcc_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividends" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shareholder dividends</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDividends_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDividends" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDividends"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1_019bffd7-5157-70ce-adb7-506466a4e310_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax expense (benefit) related to other comprehensive income (loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1_019bffd7-515a-7149-9668-74296224898a_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Less: Income tax expense (benefit)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1"/>
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    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurements, Recurring and Nonrecurring [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock"/>
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    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsTextBlock" xlink:to="lab_us-gaap_SubsequentEventsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTradingArrLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingArrLineItems" xlink:to="lab_ecd_InsiderTradingArrLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableforsaleAmortizedCostAbstract_019bffd7-5159-7a02-9de9-21d49e3303fb_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableforsaleAmortizedCostAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableforsaleAmortizedCostAbstract_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableforsaleAmortizedCostAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableforsaleAmortizedCostAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableforsaleAmortizedCostAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableforsaleAmortizedCostAbstract" xlink:to="lab_us-gaap_DebtSecuritiesAvailableforsaleAmortizedCostAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_CEOAndCoPresidentsMember_019bffd7-515b-7042-9c41-8809614c8feb_terseLabel_en-US" xlink:label="lab_logan_CEOAndCoPresidentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CEO And Co-Presidents</link:label>
    <link:label id="lab_logan_CEOAndCoPresidentsMember_label_en-US" xlink:label="lab_logan_CEOAndCoPresidentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CEO And Co-Presidents [Member]</link:label>
    <link:label id="lab_logan_CEOAndCoPresidentsMember_documentation_en-US" xlink:label="lab_logan_CEOAndCoPresidentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">CEO And Co-Presidents</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_CEOAndCoPresidentsMember" xlink:href="logan-20251231.xsd#logan_CEOAndCoPresidentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_CEOAndCoPresidentsMember" xlink:to="lab_logan_CEOAndCoPresidentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingRollForward_019bffd7-515a-74ef-afbd-7086b197b244_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingRollForward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Non-Option Equity Instruments, Outstanding [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingRollForward" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInReinsuranceRecoverable_019bffd7-5158-7fbc-8679-2d54440c6617_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInReinsuranceRecoverable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInReinsuranceRecoverable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInReinsuranceRecoverable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Reinsurance Recoverable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInReinsuranceRecoverable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInReinsuranceRecoverable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInReinsuranceRecoverable" xlink:to="lab_us-gaap_IncreaseDecreaseInReinsuranceRecoverable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialAssetNotPastDueMember_019bffd7-5159-7382-9a79-c7e2ed691d91_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current loans</link:label>
    <link:label id="lab_us-gaap_FinancialAssetNotPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Not Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialAssetNotPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialAssetNotPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialAssetNotPastDueMember" xlink:to="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesMember_019bffd7-5158-70c8-8876-5bf716ee5eda_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity securities</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesMember_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesMember" xlink:to="lab_us-gaap_EquitySecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationPriorYearIncomeTaxes_019c8fbc-d0f0-7e26-8fba-dbcd00adb44d_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationPriorYearIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred True Up</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationPriorYearIncomeTaxes_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationPriorYearIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Prior Year Income Taxes, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationPriorYearIncomeTaxes" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationPriorYearIncomeTaxes"/>
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    <link:label id="lab_us-gaap_Liabilities_019bffd7-5157-75b9-a4f5-1310f06128d5_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_019bffd7-5159-7e80-986e-cc5631c40975_terseLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total financial liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_019bffd7-515b-79ca-b4cc-7e363dd97622_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:to="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnAdjsPrrSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:to="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MtrlTermsOfTrdArrTextBlock"/>
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    <link:label id="lab_logan_NumberOfReinsurers_019bffd7-515a-7b94-8831-3a13fc1d1dff_terseLabel_en-US" xlink:label="lab_logan_NumberOfReinsurers" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reinsurers</link:label>
    <link:label id="lab_logan_NumberOfReinsurers_label_en-US" xlink:label="lab_logan_NumberOfReinsurers" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Reinsurers</link:label>
    <link:label id="lab_logan_NumberOfReinsurers_documentation_en-US" xlink:label="lab_logan_NumberOfReinsurers" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Reinsurers</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_NumberOfReinsurers" xlink:href="logan-20251231.xsd#logan_NumberOfReinsurers"/>
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    <link:label id="lab_logan_TransactionCosts_label_en-US" xlink:label="lab_logan_TransactionCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transaction Costs</link:label>
    <link:label id="lab_logan_TransactionCosts_documentation_en-US" xlink:label="lab_logan_TransactionCosts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Transaction Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_TransactionCosts" xlink:href="logan-20251231.xsd#logan_TransactionCosts"/>
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    <link:label id="lab_us-gaap_AssetBackedSecuritiesMember_019bffd7-5158-79e6-bf84-2490e8d2f72e_terseLabel_en-US" xlink:label="lab_us-gaap_AssetBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset and mortgage-backed securities</link:label>
    <link:label id="lab_us-gaap_AssetBackedSecuritiesMember_019c4c24-d277-79e9-b4f6-dd2d5245a83a_verboseLabel_en-US" xlink:label="lab_us-gaap_AssetBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Asset and mortgage-backed securities</link:label>
    <link:label id="lab_us-gaap_AssetBackedSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_AssetBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset-Backed Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetBackedSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetBackedSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetBackedSecuritiesMember" xlink:to="lab_us-gaap_AssetBackedSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsAxis_019bffd7-515b-78c0-a46f-c6421a460d8c_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:label id="lab_srt_ConsolidationItemsAxis_label_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsAxis" xlink:to="lab_srt_ConsolidationItemsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_LongTermCareMember_019c77df-3912-7c83-a9e5-99a0ef9d4fa7_terseLabel_en-US" xlink:label="lab_logan_LongTermCareMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Care</link:label>
    <link:label id="lab_logan_LongTermCareMember_label_en-US" xlink:label="lab_logan_LongTermCareMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Care [Member]</link:label>
    <link:label id="lab_logan_LongTermCareMember_documentation_en-US" xlink:label="lab_logan_LongTermCareMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Care</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_LongTermCareMember" xlink:href="logan-20251231.xsd#logan_LongTermCareMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_LongTermCareMember" xlink:to="lab_logan_LongTermCareMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceTableTextBlock_019bffd7-515a-7eab-85d1-c15d00b29091_terseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance</link:label>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceTableTextBlock_label_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderAccountBalanceTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderAccountBalanceTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyholderAccountBalanceTableTextBlock" xlink:to="lab_us-gaap_PolicyholderAccountBalanceTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CounterpartyNameAxis_019bffd7-5158-7592-8120-a0c68b71cc3d_terseLabel_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:label id="lab_srt_CounterpartyNameAxis_label_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CounterpartyNameAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CounterpartyNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CounterpartyNameAxis" xlink:to="lab_srt_CounterpartyNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock_019bffd7-515a-74fb-bf31-7f54440369d6_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Restricted Stock Unit, Activity</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Restricted Stock Unit, Activity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock"/>
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    <link:label id="lab_us-gaap_GrossInvestmentIncomeOperating_019bffd7-5158-75c8-b5f0-7963b2473216_terseLabel_en-US" xlink:label="lab_us-gaap_GrossInvestmentIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment income</link:label>
    <link:label id="lab_us-gaap_GrossInvestmentIncomeOperating_label_en-US" xlink:label="lab_us-gaap_GrossInvestmentIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gross Investment Income, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GrossInvestmentIncomeOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GrossInvestmentIncomeOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GrossInvestmentIncomeOperating" xlink:to="lab_us-gaap_GrossInvestmentIncomeOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities_019bffd7-5158-772e-a7c8-019efa721a73_verboseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair value</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities_019bffd7-5158-7a0e-8e67-b7a2c0c9b37d_totalLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Debt securities</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities_019bffd7-5159-74a0-9389-82052298c946_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt securities:</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_019c2cb8-d305-73d7-aff3-f2af48de22fb_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonNeosMember_terseLabel_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-NEOs</link:label>
    <link:label id="lab_ecd_NonNeosMember_label_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-NEOs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonNeosMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonNeosMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonNeosMember" xlink:to="lab_ecd_NonNeosMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CorporateDebtSecuritiesMember_019bffd7-5158-7c8a-8723-9d71a45b7763_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate</link:label>
    <link:label id="lab_us-gaap_CorporateDebtSecuritiesMember_019c4c24-9a40-7a75-8268-0e607d751c92_verboseLabel_en-US" xlink:label="lab_us-gaap_CorporateDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Corporate</link:label>
    <link:label id="lab_us-gaap_CorporateDebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_CorporateDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Corporate Debt Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateDebtSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CorporateDebtSecuritiesMember"/>
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    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossPercent_019c7c0b-a191-7170-b4a5-e5e60a4ad841_terseLabel_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">No benefit recorded on current-year NOL (domestication)</link:label>
    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossPercent_label_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Net Operating Loss, Percent</link:label>
    <link:label id="lab_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossPercent_documentation_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossPercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Net Operating Loss, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossPercent" xlink:href="logan-20251231.xsd#logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossPercent" xlink:to="lab_logan_EffectiveIncomeTaxRateReconciliationNetOperatingLossPercent" xlink:type="arc" order="1"/>
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