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  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedTotalLabel"/>
  <link:labelLink xlink:role="http://www.xbrl.org/2003/role/link" xlink:type="extended">
    <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/2026/ecd-2026.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_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/2026/ecd-2026.xsd#ecd_TradingArrAxis"/>
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    <link:label id="lab_srt_MaximumMember_019e4b0b-97b1-78bc-94ae-40acda1370cc_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/2026/elts/srt-2026.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_PortionAtFairValueFairValueDisclosureMember_019e4b0b-9859-72e6-8ea3-ac8859021307_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</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/2026/elts/us-gaap-2026.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_us-gaap_DomesticCountryMember_019e4b0b-97b1-7e1b-9492-ea0a9d94e5a0_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">Income Tax Jurisdiction, Domestic Federal</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">Income Tax Jurisdiction, Domestic Federal [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DomesticCountryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.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_ShortTermDebtTypeAxis_019e4b0b-9859-7787-abff-f2413d238af5_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/2026/elts/us-gaap-2026.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_dei_Security12bTitle_019e4b0b-97b1-7e66-b056-f46ba45bbfbe_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>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventMember_019e4b0b-98ea-79cd-b9ed-f551a8fb4bc5_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/2026/elts/us-gaap-2026.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"/>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_019e4b0b-9859-7b8a-89a0-c9939c5a69f3_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/2026/elts/us-gaap-2026.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:to="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsMember_019e4b0b-9859-7f5c-ac00-5f118037b8bb_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity method</link:label>
    <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/2026/elts/us-gaap-2026.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"/>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearThree_019e4b0b-9859-7670-8578-8ca452f035de_terseLabel_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</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>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearThree" xlink:href="logan-20260630.xsd#logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearThree" xlink:to="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearThree" 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/2026/ecd-2026.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_PolicyholderAccountBalanceTableTextBlock_019e4b0b-9859-72d3-80eb-c7b415669d59_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">Schedule of 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/2026/elts/us-gaap-2026.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_us-gaap_FinancingReceivableNonaccrualNoAllowance_019e4b0b-97b1-75ff-8e10-42dedd4b7693_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/2026/elts/us-gaap-2026.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_us-gaap_FinancialInstrumentAxis_019e4b0b-97b1-78a2-801e-70279611af28_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentAxis" xlink:to="lab_us-gaap_FinancialInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsFairValueDisclosure_019e4b0b-97b1-7235-a559-6627c03544f6_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/2026/elts/us-gaap-2026.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_FinancialLiabilitiesFairValueDisclosureAbstract_019e4b0b-97b1-771b-bfac-e9e1a4b0362a_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/2026/elts/us-gaap-2026.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_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/2026/elts/us-gaap-2026.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_us-gaap_PayableInvestmentPurchase_019e4b0b-9859-7585-9b19-d845a4f15c2a_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/2026/elts/us-gaap-2026.xsd#us-gaap_PayableInvestmentPurchase"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock"/>
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    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitReinsuranceRecoverableAfterAllowance_019e4b0b-9859-7ed5-8c59-43f1758b66b7_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/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForFuturePolicyBenefitReinsuranceRecoverableAfterAllowance"/>
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    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossRealized_019f1239-8ee4-70aa-bf4a-0d2bcc4bb82c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossRealized" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net realized (gains) losses on foreign currency</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossRealized_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossRealized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Realized Gain (Loss), Foreign Currency Transaction, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyTransactionGainLossRealized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignCurrencyTransactionGainLossRealized"/>
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    <link:label id="lab_us-gaap_InterestIncomeInterestEarningAsset_019e4b0b-9859-7e12-90fb-337306e4058b_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/2026/elts/us-gaap-2026.xsd#us-gaap_InterestIncomeInterestEarningAsset"/>
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    <link:label id="lab_us-gaap_ProceedsFromInterestReceived_019e4b0b-96e1-7884-94e5-4edf59b0ded9_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/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromInterestReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromInterestReceived" xlink:to="lab_us-gaap_ProceedsFromInterestReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityExTransitionPeriod_019e4b0b-97b1-7d11-af84-ca56c5664c28_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/2026/dei-2026.xsd#dei_EntityExTransitionPeriod"/>
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    <link:label id="lab_us-gaap_ProceedsFromSaleMaturityAndCollectionsOfInvestments_019e4b0b-97b1-7831-a201-e10bb2a81a8f_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>
    <link:label id="lab_us-gaap_ProceedsFromSaleMaturityAndCollectionsOfInvestments_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleMaturityAndCollectionsOfInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale, Maturity and Collection of Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleMaturityAndCollectionsOfInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleMaturityAndCollectionsOfInvestments"/>
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    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract_019e4b0b-9859-73b3-9f67-0e36e6f5d39e_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/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract"/>
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    <link:label id="lab_logan_OtherGovernmentAndAgencyMember_019e4b0b-96e1-76a5-9057-e71d4f7528cd_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-20260630.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_ReinsurancePayable_019e4b0b-97b1-7dc7-9a87-9441b81b6994_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/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsurancePayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsurancePayable" xlink:to="lab_us-gaap_ReinsurancePayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_019e4b0b-97b1-7c66-9999-05f566bee014_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/2026/elts/us-gaap-2026.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_logan_InvestmentRiskDomain_019e4b0b-97b1-7e89-b578-f937c327220a_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-20260630.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_LiabilityForFuturePolicyBenefitWeightedAverageInterestAccretionRate_019e4b0b-9859-7681-b182-99a046122e51_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/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForFuturePolicyBenefitWeightedAverageInterestAccretionRate"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsMarketableSecurities_019e4b0b-97b1-77db-bbeb-6fd932a2813c_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_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_019e4b0b-97b1-7e98-8951-7d853908934e_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>
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    <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-20260630.xsd#logan_GeneralAdministrativeAndOtherExpensesAdjusted"/>
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    <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/2026/elts/us-gaap-2026.xsd#us-gaap_CurrentIncomeTaxExpenseBenefit"/>
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    <link:label id="lab_us-gaap_USTreasuryAndGovernmentMember_019e4b0b-97b1-7329-a7d9-f598b1ff16c5_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_019e4b0b-97b1-78ee-974f-4d3afe79b921_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/2026/elts/us-gaap-2026.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_srt_ConsolidatedEntitiesAxis_019e4b0b-97b1-7ed7-8113-219747860005_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/2026/elts/srt-2026.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_dei_EntityCommonStockSharesOutstanding_019e4b0b-97b1-7f77-bfa5-fca192b01b98_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/2026/dei-2026.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_logan_TermLoanMember_019e4b0b-9859-7780-8eb7-c119948c6af8_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-20260630.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_ClassOfWarrantOrRightUnissued_019e4b0b-9859-78e7-8052-90ff3296e05a_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/2026/elts/us-gaap-2026.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_logan_RepaymentsOfBorrowingsOfAssetManagementBusiness_019e4b0b-9859-7a87-a861-3542da6681ea_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-20260630.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_AssetBackedSecuritiesMember_019e4b0b-9859-73ee-8653-01d8ec128401_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_019e4b0b-9859-7d8e-9fc1-5b66ce278290_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/2026/elts/us-gaap-2026.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_us-gaap_DeferredTaxLiabilitiesOther_019e4b0b-9859-7abb-98b6-b49cf859639c_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/2026/elts/us-gaap-2026.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_logan_LiabilityForFuturePolicyBenefitExpectedNetPremiumIncreaseDecreaseOfActualVarianceFromExpectedExperience_019e4b0b-97b1-71e1-9ea8-ec296c730ef9_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-20260630.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_FeeIncome_019e4b0b-97b1-7de8-af5c-cb05fb5f28bc_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/2026/elts/us-gaap-2026.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_SeniorDebtObligationsMember_019e4b0b-9859-7d59-8b4c-30a8bd93c6df_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>
    <link:label id="lab_us-gaap_SeniorDebtObligationsMember_label_en-US" xlink:label="lab_us-gaap_SeniorDebtObligationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Debt Obligations [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeniorDebtObligationsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SeniorDebtObligationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeniorDebtObligationsMember" xlink:to="lab_us-gaap_SeniorDebtObligationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_IncentiveFeeIncomeMember_019e4b0b-9859-753d-ab71-60f2206a5d46_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_019e4b0b-9859-79b4-8106-113ee7a7f30e_verboseLabel_en-US" xlink:label="lab_logan_IncentiveFeeIncomeMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" 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-20260630.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_IncomeTaxReconciliationForeignIncomeTaxRateDifferential_019e4b0b-97b1-7005-823b-ae318d76874c_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">Statutory tax rate difference between Canada and the US</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/2026/elts/us-gaap-2026.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_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_019e4b0b-97b1-7b59-94d1-ca758b51b591_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/2026/elts/us-gaap-2026.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_srt_ConsolidatedEntitiesDomain_019e4b0b-97b1-7c44-81ea-4b64239db1f6_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesDomain" xlink:to="lab_srt_ConsolidatedEntitiesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DeferredTaxAssetsDeferredAcquisitionCosts_019e4b0b-9859-70a6-8077-75199ac1ae6a_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-20260630.xsd#logan_DeferredTaxAssetsDeferredAcquisitionCosts"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss_019e4b0b-985a-71ff-8a98-7c72f2c27f8d_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/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss"/>
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    <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>
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    <link:label id="lab_us-gaap_AssetAcquisitionAxis_019e4b0b-97b1-75d8-994b-ace738933bb6_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/2026/elts/us-gaap-2026.xsd#us-gaap_AssetAcquisitionAxis"/>
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    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_019e4b0b-97b1-7c3f-8527-2aaef9209c5e_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 Asset, Excluding Goodwill, after Accumulated Amortization</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019e4b0b-97b1-781f-82ec-9623502321fc_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_019e4b0b-97b1-7a24-bbd7-7cf609d8f75f_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_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/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber"/>
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    <link:label id="lab_us-gaap_ServiceAgreementsMember_019e4b0b-97b1-71dd-aca7-43eabf7d9f23_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServiceAgreementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ServiceAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServiceAgreementsMember" xlink:to="lab_us-gaap_ServiceAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredForeignIncomeTaxExpenseBenefit_019e4b0b-9859-7007-8ddf-93141836d4d8_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/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredForeignIncomeTaxExpenseBenefit"/>
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    <link:label id="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_019e4b0b-96e1-7e91-a421-0c6a1ab4ce76_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net amortization of premiums and accretion of discounts on investments</link:label>
    <link:label id="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_label_en-US" xlink:label="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accretion (Amortization) of Discounts and Premiums, Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:to="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" 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/2026/ecd-2026.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_NumberOfReportableSegments_019e4b0b-9859-7c82-bd2a-2e56c2120a01_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/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfReportableSegments"/>
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    <link:label id="lab_us-gaap_ShortTermDebtTypeDomain_019e4b0b-97b1-760b-ab44-7024514be5f2_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/2026/elts/us-gaap-2026.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_us-gaap_ConcentrationRiskTable_019e4b0b-9859-7842-9be3-b19fb9dadf50_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/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskTable"/>
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    <link:label id="lab_dei_EntityAddressCityOrTown_019e4b0b-97b1-7caa-872b-863854b3efb3_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>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_019e4b0b-97b1-7d74-b70e-1ef3626d7253_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/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod"/>
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    <link:label id="lab_us-gaap_AociLiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeTax_019e4b0b-9859-783c-ba8d-137232418a43_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>
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    <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>
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    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_019e4b0b-9859-7af6-9b8f-221b3cb73b7d_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">Intangible Asset, Finite-Lived, after Accumulated Amortization</link:label>
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    <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>
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    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_019e4b0b-96e1-7457-ae23-044ac1bf31d1_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/2026/elts/us-gaap-2026.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_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <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/2026/ecd-2026.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" 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/2026/ecd-2026.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_GuarantyAssets_019e4b0b-97b1-7cc9-8ec8-9ab07c4aa546_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/2026/elts/us-gaap-2026.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_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_019e4b0b-97b1-732b-9146-88e7c3d497a2_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/2026/elts/us-gaap-2026.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_LiabilityForFuturePolicyBenefitExpectedNetPremiumNetPremiumCollected_019e4b0b-9859-7e20-9716-072139b1dbde_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/2026/elts/us-gaap-2026.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_country_US_019e4b0b-97b1-761d-8d5c-36f46becb8b5_terseLabel_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">United States</link:label>
    <link:label id="lab_country_US_label_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">UNITED STATES</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_US" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_US"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_US" xlink:to="lab_country_US" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_IncreaseDecreaseFundsHeldUnderReinsuranceAgreementsLiability_019e4b0b-9859-760b-a592-22b787fcdd6f_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-20260630.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_us-gaap_SubsequentEventTypeAxis_019e4b0b-97b1-7aa4-a9df-d6615d3a60b6_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/2026/elts/us-gaap-2026.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_logan_MortgageLoansMember_019e4b0b-9859-7879-92ab-3ca05436b8dd_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-20260630.xsd#logan_MortgageLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_MortgageLoansMember" xlink:to="lab_logan_MortgageLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_019e4b0b-97b1-723a-b4e2-ad2b47e35a50_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/2026/elts/us-gaap-2026.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_us-gaap_DebtInstrumentTable_019e4b0b-9859-7a96-8efd-ceb67f4f9c27_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/2026/elts/us-gaap-2026.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_LiabilityForFuturePolicyBenefitsPaymentForBenefits_019e4b0b-9859-7558-9586-1de657bb50b0_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/2026/elts/us-gaap-2026.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_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent_019e4b0b-97b1-7a3c-b50d-0a5fc2259d92_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/2026/elts/us-gaap-2026.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_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_019e4b0b-9859-7f83-9944-a3cebbb3ffc1_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Income [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable" xlink:to="lab_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_019e4b0b-9859-770b-af61-ecf2b28e1765_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</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">Segment Reporting [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.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_logan_DebentureUnitsMember_019e4b0b-97b1-73ef-9171-8a3fa7680163_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-20260630.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_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_019e4b0b-9859-7f48-bcc1-011cdb1742fe_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesGross_019e4b0b-9859-78d8-ad4b-53db04748cc8_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net reinsurance recoverable</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesGross_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverables, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsuranceRecoverablesGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverablesGross" xlink:to="lab_us-gaap_ReinsuranceRecoverablesGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_019e4b0b-9859-7baf-8382-48817b58470e_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/2026/elts/us-gaap-2026.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_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_019e4b0b-9859-7e3d-9fee-70110d796e52_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/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_019e4b0b-96e1-796e-b74a-e14091f3be96_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/2026/elts/us-gaap-2026.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_dei_DocumentPeriodEndDate_019e4b0b-9859-7ba8-b9b7-762eeb91c009_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/2026/dei-2026.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_DebtInstrumentFaceAmount_019e4b0b-97b1-710e-ae49-a3590f94ff5f_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>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019e4b0b-97b1-7dcc-868d-5d4902cc76b8_netLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Par value</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019e4b0b-97b1-7107-86bc-b48d72594962_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_AbilityAcquisitionSellerNoteMember_019e4b0b-98ea-785a-a304-22f2b500bb6d_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-20260630.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_us-gaap_EarningsPerShareBasicAbstract_019e4b0b-97b1-7df1-99d9-349db9bfefe0_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/2026/elts/us-gaap-2026.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_logan_ServicingFeesExpenses_019e4b0b-96e1-7f26-87dc-657e727484b5_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 (expense)</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-20260630.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_InvestmentsAllOtherInvestmentsAbstract_019e4b0b-96e1-796b-a6d5-63fb2bb906b0_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/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentsAllOtherInvestmentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsAllOtherInvestmentsAbstract" xlink:to="lab_us-gaap_InvestmentsAllOtherInvestmentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_019e4b0b-97b1-73e2-9225-e34b0481c565_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/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTerm" xlink:to="lab_us-gaap_DebtInstrumentTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfOtherSignificantReconcilingItemsFromSegmentsToConsolidatedTextBlock_019e4b0b-97b1-740f-a086-ef4e21bfc5c0_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">Schedule of Segment Reporting, Reconciliation of Other Item by Segment 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 Reporting, Reconciliation of Other Item by Segment 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/2026/elts/us-gaap-2026.xsd#us-gaap_ReconciliationOfOtherSignificantReconcilingItemsFromSegmentsToConsolidatedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReconciliationOfOtherSignificantReconcilingItemsFromSegmentsToConsolidatedTextBlock" xlink:to="lab_us-gaap_ReconciliationOfOtherSignificantReconcilingItemsFromSegmentsToConsolidatedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTextBlock_019e4b0b-97b1-73f6-bbd6-76ee330fafe6_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">Schedule of Segment Reporting, Reconciliation of Revenue by Segment 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">Segment Reporting, Reconciliation of Revenue by Segment 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/2026/elts/us-gaap-2026.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_DebtInstrumentInterestRateEffectivePercentage_019e4b0b-9859-7dbe-8f4a-3e27ff66f1fd_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/2026/elts/us-gaap-2026.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_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_019e4b0b-97b1-7567-aeb0-f16e2e633b80_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/2026/elts/us-gaap-2026.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_GuaranteedInterestContracts_019e4b0b-96e1-7cdc-b542-a61c6d954d5c_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/2026/elts/us-gaap-2026.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_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost_019e4b0b-97b1-793d-9c16-1e9d98f6ce3c_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/2026/elts/us-gaap-2026.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_logan_YearsToCashFlowsMember_019e4b0b-9859-784e-839c-eb9477abab8f_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 exit</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-20260630.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_019e4b0b-9859-753e-9452-d0cd54861379_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-20260630.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_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1_019e4b0b-97b1-766f-8a18-23402a636fbe_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_019e4b0b-97b1-72f2-b9c8-ecfed4fda165_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/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_019e4b0b-97b1-7d4c-8865-ae485537d30f_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>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_019e4b0b-9859-711a-93a7-1f300a81bc07_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/2026/dei-2026.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_srt_ConsolidationItemsDomain_019e4b0b-9859-7fef-8750-fe4c2d73500e_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidationItemsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsDomain" xlink:to="lab_srt_ConsolidationItemsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings_019e4b0b-97b1-7626-95b4-7265e629e6f2_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/2026/elts/us-gaap-2026.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_IncomeTaxReconciliationOtherAdjustments_019e4b0b-97b1-7fa5-a35e-2470c6dbe081_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/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxReconciliationOtherAdjustments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationOtherAdjustments" xlink:to="lab_us-gaap_IncomeTaxReconciliationOtherAdjustments" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_GainLossOnAcquisitionOfBusiness_019e4b0b-97b1-79b3-af05-49dd97e4444c_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-20260630.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_AociLiabilityForFuturePolicyBenefitParentMember_019e4b0b-96e1-73a2-890b-30098693b7d7_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/2026/elts/us-gaap-2026.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_ObligationsMember_019e4b0b-97b1-753c-8d59-cf3eba0349b8_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/2026/elts/us-gaap-2026.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_EarningsPerShareTextBlock_019e4b0b-9859-7bb3-b0da-1008928c645c_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareTextBlock" xlink:to="lab_us-gaap_EarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ProceedsFromTheIssuanceOfDebentureShares_019e4b0b-97b1-721a-914b-676e367a1c9e_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-20260630.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_us-gaap_EarningsPerShareAbstract_019e4b0b-9859-76ae-a9e5-c57362abde2c_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/2026/elts/us-gaap-2026.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_dei_DocumentFiscalPeriodFocus_019e4b0b-97b1-734f-93f6-1a3f2f56e77b_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/2026/dei-2026.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_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/2026/ecd-2026.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_us-gaap_Liabilities_019e4b0b-9859-7771-bf11-a65fe22c8207_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_019e4b0b-9859-765c-8b64-daaeef095bd6_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/2026/elts/us-gaap-2026.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_dei_TradingSymbol_019e4b0b-97b1-7689-a0d2-a49ceb86ec1f_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/2026/dei-2026.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_ChangeDuringPeriodFairValueDisclosureMember_019e4b0b-9859-7ec1-aaa7-5d43e463dd07_terseLabel_en-US" xlink:label="lab_us-gaap_ChangeDuringPeriodFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mark to Fair Value</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ChangeDuringPeriodFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ChangeDuringPeriodFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ChangeDuringPeriodFairValueDisclosureMember" xlink:to="lab_us-gaap_ChangeDuringPeriodFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_019e4b0b-98ea-7da7-9818-a49e0e41c79f_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/2026/elts/us-gaap-2026.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_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomeAmount_019e4b0b-96e1-7387-8f41-63fdc94d7666_terseLabel_en-US" xlink:label="lab_logan_EffectiveIncomeTaxRateReconciliationForeignAccrualPropertyIncomeAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Canadian 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-20260630.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_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss_019e4b0b-9859-7e80-a685-387ea9111f5c_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/2026/elts/us-gaap-2026.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_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/2026/elts/us-gaap-2026.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_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent_019e4b0b-97b1-7897-9359-bad04a6f767f_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/2026/elts/us-gaap-2026.xsd#us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent"/>
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    <link:label id="lab_logan_CreditLossMember_019e4b0b-97b1-7412-ae1b-1f93fe1c524f_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-20260630.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_ConcentrationRiskLineItems_019e4b0b-96e1-7988-b3d9-ddb116487a88_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/2026/elts/us-gaap-2026.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_EarningsPerShareDilutedAbstract_019e4b0b-97b1-7e97-9be9-87604d348611_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/2026/elts/us-gaap-2026.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_ScheduleOfIndefiniteLivedIntangibleAssetsTable_019e4b0b-9859-73b8-9064-c6ef7901a7b7_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/2026/elts/us-gaap-2026.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_logan_MultiFamilyMortgageLoansMember_019e4b0b-9859-7053-b040-3916e6780590_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-20260630.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_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFourAndThereafter_019e4b0b-9859-7117-b7da-ea6f9d8ed96d_terseLabel_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFourAndThereafter" 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_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFourAndThereafter_label_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFourAndThereafter" 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 and Thereafter</link:label>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFourAndThereafter_documentation_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFourAndThereafter" 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 and Thereafter</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFourAndThereafter" xlink:href="logan-20260630.xsd#logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFourAndThereafter"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFourAndThereafter" xlink:to="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFourAndThereafter" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityDomain_019e4b0b-9859-7348-a75e-7f747427672e_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/2026/elts/us-gaap-2026.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_FinancingReceivableRecordedInvestmentNonaccrualStatus_019e4b0b-9859-7bbc-a109-584d5ead06e9_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_019e4b0b-9859-7d80-a519-051c3ac2e61b_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/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableRecordedInvestmentNonaccrualStatus"/>
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    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitRemeasurementGainLoss_019e4b0b-97b1-75a7-a65d-5e02eac2a299_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/2026/elts/us-gaap-2026.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_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign_019e4b0b-9859-7744-b723-e2ff9aa8a956_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign" 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_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Foreign</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassLineItems_019e4b0b-985a-743e-b98a-348a77dcf5bd_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">Intangible Asset, Indefinite-Lived [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">Intangible Asset, Indefinite-Lived [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.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_us-gaap_CommonStockDividendsPerShareCashPaid_019e4b0b-97b1-7d36-8cc9-7d7308c245fb_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareCashPaid_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Cash Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockDividendsPerShareCashPaid"/>
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    <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/2026/ecd-2026.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_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_019e4b0b-9859-71b1-82b5-b77111def581_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/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3_019fad10-daee-77ba-9185-04eb4be12bfe_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Transfer out</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" 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, Transfers out of Level 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Dividends_019e4b0b-96e1-773b-927e-ec46f20db524_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/2026/elts/us-gaap-2026.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_DeferredTaxAssetsOther_019e4b0b-9859-7368-aa87-8c7a04932b5f_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/2026/elts/us-gaap-2026.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_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseOfActualVarianceFromExpectedExperience_019e4b0b-97b1-7610-99e3-7ea36d65a83f_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-20260630.xsd#logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseOfActualVarianceFromExpectedExperience"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseOfActualVarianceFromExpectedExperience" xlink:to="lab_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseOfActualVarianceFromExpectedExperience" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeTextBlock_019e4b0b-9859-7856-9337-3e261267233e_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/2026/elts/us-gaap-2026.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_PaymentsToAcquireInvestmentsOperatingActivities_019e4b0b-9859-746d-8114-e72ec36f4cb5_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-20260630.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_logan_InsuranceSolutionsExpensesAbstract_019e4b0b-97b1-76ce-b6b4-6c771443f615_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-20260630.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_019e4b0b-9859-765f-801b-7efe28766877_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 investment income (loss) on funds withheld</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-20260630.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_LongDurationInsuranceContractsDisclosureTextBlock_019e4b0b-9859-7eda-a7a7-6856ba615128_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_019e4b0b-9859-741d-b856-e4fb9e225b30_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/2026/elts/us-gaap-2026.xsd#us-gaap_LongDurationInsuranceContractsDisclosureTextBlock"/>
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    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019e4b0b-9859-7f2f-9ea3-08c5dcdf2180_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/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
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    <link:label id="lab_us-gaap_DividendAndInterestReceivable_019e4b0b-97b1-7efb-bf59-173759b13671_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/2026/elts/us-gaap-2026.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_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_019e4b0b-9859-70ff-9e04-724e2f08d6c1_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation</link:label>
    <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/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
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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>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgPredtrmndFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgPredtrmndFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgPredtrmndFlag" xlink:to="lab_ecd_AwardTmgPredtrmndFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InvestmentRiskAxis_019e4b0b-9859-7b52-abff-649078fc70dc_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-20260630.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_019e4b0b-9859-78c5-9bf9-acbfabfbc9ff_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_019e4b0b-9859-7482-bad6-c02bcb739a33_verboseLabel_en-US" xlink:label="lab_logan_AdvisoryAndTransactionFeesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Advisory and transaction fees</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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PolicyholderBenefitsAndClaimsIncurredNet"/>
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    <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>
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    <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/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxLiabilitiesAbstract"/>
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    <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/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableforSaleUnrealizedLossPositionAbstract"/>
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    <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/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureBenefitOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange"/>
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    <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>
    <link:label id="lab_logan_DepositsOnInvestmentTypePoliciesAndContracts_documentation_en-US" xlink:label="lab_logan_DepositsOnInvestmentTypePoliciesAndContracts" xlink:role="http://www.xbrl.org/2003/role/documentation" 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_us-gaap_SubordinatedDebtMember_019e4b0b-97b1-70aa-932a-0cb4a0c6cad2_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/2026/elts/us-gaap-2026.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"/>
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    <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/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract"/>
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    <link:label id="lab_us-gaap_NonrelatedPartyMember_019e4b0b-97b1-70df-b5f6-0efd4b11354e_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/2026/elts/us-gaap-2026.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_srt_AffiliatedEntityMember_019e4b0b-9859-77c2-b6d5-1bb90c7c3243_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/2026/elts/srt-2026.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"/>
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    <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-20260630.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_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/2026/ecd-2026.xsd#ecd_AggtPnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:to="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeTable_019e4b0b-97b1-7628-8528-a9d60cb620a9_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/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeTable"/>
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    <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/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable"/>
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    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFour_019e4b0b-97b1-7002-8e5f-1ffe91415069_terseLabel_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearFour" 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_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>
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    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_019fad5d-46a6-728c-b314-3647799b5d98_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized equity-based compensation expense</link:label>
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    <link:label id="lab_us-gaap_SegmentDomain_label_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.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_logan_InterestAndOtherCreditFacilityExpenses_019e4b0b-9859-763b-b84e-68cd692dc412_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_019e4b0b-9859-7027-bd1a-cd4e17ca1d50_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-20260630.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_srt_StatementScenarioAxis_019e4b0b-97b1-77c3-a8aa-08e5175681e4_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/2026/elts/srt-2026.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_ProceedsFromSaleOfInvestmentsOperatingActivities_019e4b0b-9859-728e-8fe6-976f4994d79a_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-20260630.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_NotesReceivableNet_019e4b0b-97b1-7b89-b960-c06be4457272_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/2026/elts/us-gaap-2026.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_us-gaap_DeferredFinanceCostsNet_019e4b0b-97b1-764f-aa97-c43025290662_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transaction costs</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_019e4b0b-97b1-7c2f-b739-9ccb363fddfa_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/2026/elts/us-gaap-2026.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_logan_DebtRepaymentOnMaturityDateAdjustmentAmount_019e4b0b-96e1-7779-93cc-4653ba6dc4be_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-20260630.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_019e4b0b-97b1-7e38-a05d-a2eca8c1203a_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-20260630.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_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_019e4b0b-97b1-78d1-b43b-6abc1cdc6a16_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_logan_DebentureUnitPaidInKindPercentage_019e4b0b-9859-7337-b609-14534ea05328_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-20260630.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_AccountsPayableTradeCurrent_019e4b0b-97b1-7795-a0cb-5b836d972d84_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/2026/elts/us-gaap-2026.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_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/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationAndAssetAcquisitionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:to="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostsAndExpenses_019e4b0b-9859-7074-b9ca-1847598f3cea_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/2026/elts/us-gaap-2026.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_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_019e4b0b-9859-7b9e-a676-2e396ca01bd2_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/2026/elts/us-gaap-2026.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_DebtInstrumentInterestRateStatedPercentage_019e4b0b-98ea-7467-8533-8ec52eff9178_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/2026/elts/us-gaap-2026.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_StockholdersEquity_019e4b0b-97b1-7d5a-9097-5380c9c8862d_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_019e4b0b-97b1-7b3e-850a-6e54253bdb91_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_019e4b0b-97b1-7f69-8008-9febd83c3e98_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/2026/elts/us-gaap-2026.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_us-gaap_WriteOffOfDeferredDebtIssuanceCost_019e4b0b-97b1-72d9-a960-c4354f5c72db_terseLabel_en-US" xlink:label="lab_us-gaap_WriteOffOfDeferredDebtIssuanceCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Write-off of unamortized debt issuance costs</link:label>
    <link:label id="lab_us-gaap_WriteOffOfDeferredDebtIssuanceCost_label_en-US" xlink:label="lab_us-gaap_WriteOffOfDeferredDebtIssuanceCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Debt Issuance Cost, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WriteOffOfDeferredDebtIssuanceCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WriteOffOfDeferredDebtIssuanceCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WriteOffOfDeferredDebtIssuanceCost" xlink:to="lab_us-gaap_WriteOffOfDeferredDebtIssuanceCost" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InternalCreditAssessmentLevelTwoMember_019e4b0b-9859-7bc2-9459-665b6bf833f2_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-20260630.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_us-gaap_AssetsAbstract_019e4b0b-97b1-7d5c-992a-7cb16f7db8a0_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/2026/elts/us-gaap-2026.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_logan_FrontStreetReMember_019e4b0b-9859-7572-964c-98e82be43faa_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_019e4b0b-9859-727c-829b-45f8b8b87f7f_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-20260630.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_ContractualRightsMember_019e4b0b-97b1-7533-99c5-28824d2e04ab_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/2026/elts/us-gaap-2026.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_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_019e4b0b-96e1-7737-a2ae-c5334eb0d2a7_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_019e4b0b-96e1-78c3-942b-5027c742b030_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/2026/elts/us-gaap-2026.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_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_019e4b0b-9859-765c-9934-7fa24d1d3793_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">Corporate loans</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/2026/elts/us-gaap-2026.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_FinancingReceivableCreditQualityIndicatorsTableTextBlock_019e4b0b-97b1-7479-923b-e439b1ca1a04_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/2026/elts/us-gaap-2026.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_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_019e4b0b-97b1-714b-a313-401feb7be034_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/2026/elts/us-gaap-2026.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_logan_SentinelSecurityLifeInsuranceCompanySurplusNotesMember_019e4b0b-97b1-7df1-a75f-4bf830db3341_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-20260630.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_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/2026/ecd-2026.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_us-gaap_PolicyholderAccountBalanceSurrenderAndWithdrawal_019e4b0b-97b1-7587-9577-8c0570a96bac_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/2026/elts/us-gaap-2026.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_logan_UnpaidPrincipalBalance_019e4b0b-9859-7700-ada3-0928c57e579a_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-20260630.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_us-gaap_ProductLiabilityContingencyLineItems_019e4b0b-9859-70e6-bdac-34c3992d723d_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/2026/elts/us-gaap-2026.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_DeferredIncomeTaxExpenseBenefit_019e4b0b-9859-7d25-9153-2056fe977c72_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/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_019e4b0b-97b1-7f02-8380-172bc9e0424e_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">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</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/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InterestSensitiveContractLiabilitiesFairValue_019e4b0b-97b1-7c1f-a5bb-82d5ce7fd4fd_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-20260630.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_CommercialRealEstatePortfolioSegmentMember_019e4b0b-9859-785c-9f0d-3fd8e8f63179_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/2026/elts/us-gaap-2026.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_us-gaap_FinancingReceivablePortfolioSegmentDomain_019e4b0b-97b1-755f-8498-0fc937239afe_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/2026/elts/us-gaap-2026.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_logan_InternalCreditAssessmentLevelOneMember_019e4b0b-97b1-705e-bef7-519aa92a9e32_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-20260630.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_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_019e4b0b-97b1-76bd-a699-a5d20100a6c0_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/2026/elts/us-gaap-2026.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_us-gaap_ScheduleOfGoodwillTextBlock_019e4b0b-97b1-76b5-8b03-89221677d077_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">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/2026/elts/us-gaap-2026.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_us-gaap_GoodwillGross_019e4b0b-97b1-79f4-a8fb-1a2d0dc9312e_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill, gross</link:label>
    <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/2026/elts/us-gaap-2026.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"/>
    <link:label id="lab_dei_EntityCentralIndexKey_019e4b0b-9859-7b88-b593-2e183aaafd68_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/2026/dei-2026.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_PolicyholderAccountBalanceWeightedAverageCreditingRate_019e4b0b-97b1-760c-badd-89ad0a23ce18_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">Weighted-average annual 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/2026/elts/us-gaap-2026.xsd#us-gaap_PolicyholderAccountBalanceWeightedAverageCreditingRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyholderAccountBalanceWeightedAverageCreditingRate" xlink:to="lab_us-gaap_PolicyholderAccountBalanceWeightedAverageCreditingRate" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_UnrealizedGainLossOnPurchaseReceivables_019face3-124b-7f6a-b663-c2a51121e6d1_terseLabel_en-US" xlink:label="lab_logan_UnrealizedGainLossOnPurchaseReceivables" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gain on purchase receivables</link:label>
    <link:label id="lab_logan_UnrealizedGainLossOnPurchaseReceivables_label_en-US" xlink:label="lab_logan_UnrealizedGainLossOnPurchaseReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) On Purchase Receivables</link:label>
    <link:label id="lab_logan_UnrealizedGainLossOnPurchaseReceivables_documentation_en-US" xlink:label="lab_logan_UnrealizedGainLossOnPurchaseReceivables" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) On Purchase Receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_UnrealizedGainLossOnPurchaseReceivables" xlink:href="logan-20260630.xsd#logan_UnrealizedGainLossOnPurchaseReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_UnrealizedGainLossOnPurchaseReceivables" xlink:to="lab_logan_UnrealizedGainLossOnPurchaseReceivables" 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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate_019e4b0b-9859-7b4d-b647-c487d10fc834_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" 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_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" 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, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:to="lab_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipAxis_019e4b0b-9859-7850-8b19-a2cc88a21d04_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/2026/elts/srt-2026.xsd#srt_OwnershipAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipAxis" xlink:to="lab_srt_OwnershipAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_019e4b0b-9859-7019-bc2a-2e204c7de914_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/2026/elts/us-gaap-2026.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_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019e4b0b-97b1-72b1-88b6-372c063a86f3_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/2026/elts/srt-2026.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
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    <link:label id="lab_logan_ExchangeListedNotesMember_019e4b0b-97b1-799e-81ce-c4bf0b00346d_terseLabel_en-US" xlink:label="lab_logan_ExchangeListedNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exchange Listed Notes</link:label>
    <link:label id="lab_logan_ExchangeListedNotesMember_label_en-US" xlink:label="lab_logan_ExchangeListedNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Exchange Listed Notes [Member]</link:label>
    <link:label id="lab_logan_ExchangeListedNotesMember_documentation_en-US" xlink:label="lab_logan_ExchangeListedNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Exchange Listed Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ExchangeListedNotesMember" xlink:href="logan-20260630.xsd#logan_ExchangeListedNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ExchangeListedNotesMember" xlink:to="lab_logan_ExchangeListedNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DesignatedAsHedgingInstrumentMember_019e4b0b-9859-7ba5-b847-f921f489581c_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/2026/elts/us-gaap-2026.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_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock_019e4b0b-97b1-7e53-b4aa-8692dae56de9_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>
    <link:label id="lab_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Components of Income Tax Expense (Benefit) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock"/>
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    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract_019e4b0b-9859-7df2-8438-51bff2e98dee_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/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract"/>
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    <link:label id="lab_us-gaap_EffectsOfReinsuranceTableTextBlock_019e4b0b-9859-73c1-9619-82b590db363f_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">Schedule of 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/2026/elts/us-gaap-2026.xsd#us-gaap_EffectsOfReinsuranceTableTextBlock"/>
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    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_019e4b0b-98ea-715a-9347-632279f30cb5_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/2026/elts/us-gaap-2026.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_logan_StockIssuedDuringPeriodSharesInvestments_019e4b0b-9859-7b54-90f0-0df68903d16b_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-20260630.xsd#logan_StockIssuedDuringPeriodSharesInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_StockIssuedDuringPeriodSharesInvestments" xlink:to="lab_logan_StockIssuedDuringPeriodSharesInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_RelatedPartyTransactionRenewalTerm_019fd08e-f985-7bc5-9ada-6ba1f24619e5_terseLabel_en-US" xlink:label="lab_logan_RelatedPartyTransactionRenewalTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Renewal term</link:label>
    <link:label id="lab_logan_RelatedPartyTransactionRenewalTerm_label_en-US" xlink:label="lab_logan_RelatedPartyTransactionRenewalTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Renewal Term</link:label>
    <link:label id="lab_logan_RelatedPartyTransactionRenewalTerm_documentation_en-US" xlink:label="lab_logan_RelatedPartyTransactionRenewalTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Renewal Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_RelatedPartyTransactionRenewalTerm" xlink:href="logan-20260630.xsd#logan_RelatedPartyTransactionRenewalTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_RelatedPartyTransactionRenewalTerm" xlink:to="lab_logan_RelatedPartyTransactionRenewalTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDividendsPayableTextBlock_019e4b0b-97b1-7f9f-b850-276465c037ef_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/2026/elts/us-gaap-2026.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_InterestSensitiveLifeMember_019e4b0b-9859-7ba2-9f19-e23732388b3c_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestSensitiveLifeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestSensitiveLifeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestSensitiveLifeMember" xlink:to="lab_us-gaap_InterestSensitiveLifeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_019e4b0b-9859-7d9c-ab56-fd95f41e0cf3_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarningsNet_019e4b0b-9859-7421-8f42-208d6a22bb83_terseLabel_en-US" xlink:label="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarningsNet" 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_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarningsNet_label_en-US" xlink:label="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarningsNet" 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, Net</link:label>
    <link:label id="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarningsNet_documentation_en-US" xlink:label="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarningsNet" 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, Liability, Gain (Loss) Included in Earnings, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarningsNet" xlink:href="logan-20260630.xsd#logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarningsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarningsNet" xlink:to="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarningsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDividends_019e4b0b-9859-718a-bca7-72f7514da632_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/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfDividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDividends" xlink:to="lab_us-gaap_PaymentsOfDividends" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FinancingReceivableNonaccrualWithAnAllowance_019e4b0b-9859-70af-b4a6-947b2633fdb5_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>
    <link:label id="lab_logan_FinancingReceivableNonaccrualWithAnAllowance_label_en-US" xlink:label="lab_logan_FinancingReceivableNonaccrualWithAnAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Nonaccrual, With an Allowance</link:label>
    <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-20260630.xsd#logan_FinancingReceivableNonaccrualWithAnAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FinancingReceivableNonaccrualWithAnAllowance" xlink:to="lab_logan_FinancingReceivableNonaccrualWithAnAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_019e4b0b-97b1-79a7-8756-50f168db1595_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">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</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/2026/elts/us-gaap-2026.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_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_019fad5d-46a6-7fda-b51c-eda2a1ffc83d_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average term</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_AdministrationAndServicingFeeExpense_019e4b0b-9859-7ea6-8781-e0236b8a7ee7_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-20260630.xsd#logan_AdministrationAndServicingFeeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_AdministrationAndServicingFeeExpense" xlink:to="lab_logan_AdministrationAndServicingFeeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_019e4b0b-97b1-7760-b0b8-af59606165d2_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase price determination of hypothetical Legacy Mount Logan shares issued to TURN shareholders</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Equity Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable"/>
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    <link:label id="lab_us-gaap_StatementLineItems_019e4b0b-97b1-70d3-9884-ee7e8e93e337_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_019e4b0b-97b1-70c0-9b56-5c69400ab126_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_019e4b0b-97b1-79a7-a355-21b65aadddae_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_019e4b0b-97b1-79cf-aa75-b34d495f5a82_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/2026/elts/us-gaap-2026.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_logan_OtherTransactionsWithBCPAOrAffiliatesMember_019e4b0b-9859-79b7-918a-dc3caaa62e08_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>
    <link:loc xlink:type="locator" xlink:label="loc_logan_OtherTransactionsWithBCPAOrAffiliatesMember" xlink:href="logan-20260630.xsd#logan_OtherTransactionsWithBCPAOrAffiliatesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_OtherTransactionsWithBCPAOrAffiliatesMember" xlink:to="lab_logan_OtherTransactionsWithBCPAOrAffiliatesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationsAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationsAbstract" xlink:to="lab_us-gaap_BusinessCombinationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseOperating_019e4b0b-97b1-76c0-a74d-769380c5e075_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_019e4b0b-97b1-7e39-a54e-b1cda8e002d7_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/2026/elts/us-gaap-2026.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_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_019e4b0b-9859-7bc9-80f7-949902118e04_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/2026/elts/us-gaap-2026.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_InternalCreditAssessmentDomain_019e4b0b-9859-7fad-a212-11f879a55b94_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/2026/elts/us-gaap-2026.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_VariableInterestEntityNotPrimaryBeneficiaryMember_019e4b0b-96e1-79be-a3e7-6205bc165e0f_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/2026/elts/us-gaap-2026.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_logan_ManagementFeesMember_019e4b0b-97b1-75ae-8f08-519b2789c57f_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_019e4b0b-97b1-7e8c-a46d-99bf25fb1594_verboseLabel_en-US" xlink:label="lab_logan_ManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" 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-20260630.xsd#logan_ManagementFeesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ManagementFeesMember" xlink:to="lab_logan_ManagementFeesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleListNotDisclosedFlag_019e4b0b-97b1-7142-b6aa-0b24ed51247d_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>
    <link:label id="lab_logan_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleListNotDisclosedFlag_label_en-US" xlink:label="lab_logan_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleListNotDisclosedFlag" 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 Statement Of Income Extensible List Not Disclosed Flag</link:label>
    <link:label id="lab_logan_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleListNotDisclosedFlag_documentation_en-US" xlink:label="lab_logan_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleListNotDisclosedFlag" xlink:role="http://www.xbrl.org/2003/role/documentation" 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>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleListNotDisclosedFlag" xlink:href="logan-20260630.xsd#logan_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleListNotDisclosedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleListNotDisclosedFlag" xlink:to="lab_logan_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleListNotDisclosedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract_019e4b0b-9859-7f89-b29e-db673e5ecea3_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/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_AMBestNotRatedMember_019e4b0b-9859-77e6-a47d-e790ec19181a_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>
    <link:loc xlink:type="locator" xlink:label="loc_logan_AMBestNotRatedMember" xlink:href="logan-20260630.xsd#logan_AMBestNotRatedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_AMBestNotRatedMember" xlink:to="lab_logan_AMBestNotRatedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitActivityTable_019e4b0b-97b1-7b16-b9df-50f9c3c66721_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/2026/elts/us-gaap-2026.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_us-gaap_OperatingSegmentsMember_019e4b0b-9859-7d68-b92e-ceb2fecf52cc_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/2026/elts/us-gaap-2026.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_logan_OtherGeographicalAreasMember_019e4b0b-9859-7bd3-85f4-17c32a1a53a1_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-20260630.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_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_019e4b0b-9859-78e0-a1ae-286273aebb4a_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/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_019e4b0b-9859-74d7-bb25-24478a9dd540_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/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities"/>
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    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_019e4b0b-96e1-75be-a6dc-6cd37de5584d_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/2026/elts/us-gaap-2026.xsd#us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock"/>
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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>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoMember" xlink:to="lab_ecd_PeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProductLiabilityContingencyTable_019e4b0b-97b1-7932-87f7-1abc8237b2e3_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/2026/elts/us-gaap-2026.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_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_019e4b0b-97b1-7b47-ba31-073d28a4cf2d_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/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtLongtermAndShorttermCombinedAmount_019e4b0b-9859-793e-abdb-de9737dc129c_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/2026/elts/us-gaap-2026.xsd#us-gaap_DebtLongtermAndShorttermCombinedAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtLongtermAndShorttermCombinedAmount" xlink:to="lab_us-gaap_DebtLongtermAndShorttermCombinedAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ClassOfWarrantOrRightPeriodNotExercisableFromIssuance_019e4b0b-97b1-7555-b7b0-338c5bb51cbc_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-20260630.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_019e4b0b-9859-7703-ae42-dea39a458dbf_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-20260630.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_019e4b0b-97b1-72cc-9804-fd5de24421f7_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-20260630.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_ReinsurerConcentrationRiskMember_019e4b0b-97b1-78c2-9848-408dc63ab66a_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/2026/elts/us-gaap-2026.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_CededCreditRiskReinsurerDomain_019e4b0b-9859-7705-ac96-420bead04911_terseLabel_en-US" xlink:label="lab_us-gaap_CededCreditRiskReinsurerDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurer, Name [Domain]</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskReinsurerDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CededCreditRiskReinsurerDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CededCreditRiskReinsurerDomain" xlink:to="lab_us-gaap_CededCreditRiskReinsurerDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Goodwill_019e4b0b-97b1-75ab-8335-31ce64e95886_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_019e4b0b-97b1-775d-ae62-3bdcaaca0f2c_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_019e4b0b-97b1-76bb-963a-991144790f2d_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/2026/elts/us-gaap-2026.xsd#us-gaap_Goodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Goodwill" xlink:to="lab_us-gaap_Goodwill" xlink:type="arc" order="1"/>
    <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/2026/ecd-2026.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_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions_019e4b0b-9859-799b-b33b-45b22d01dea9_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/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CreditRatingAMBestAxis_019e4b0b-97b1-77ac-9fd7-d0e6b1ec08e4_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/2026/elts/srt-2026.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_DeferredTaxLiabilitiesDeferredExpenseReservesAndAccruals_019e4b0b-97b1-7b2e-a0cb-53fc84b610a9_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/2026/elts/us-gaap-2026.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_LiabilityForFuturePolicyBenefitActivityLineItems_019e4b0b-9859-7e11-8232-e01343abade9_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/2026/elts/us-gaap-2026.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_us-gaap_RetainedEarningsMember_019e4b0b-97b1-76e5-92bb-07ca511e2e36_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/2026/elts/us-gaap-2026.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_DeferredProfitSharingMember_019e4b0b-9859-7161-8904-1c4e2befe930_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredProfitSharingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Profit Sharing</link:label>
    <link:label id="lab_us-gaap_DeferredProfitSharingMember_label_en-US" xlink:label="lab_us-gaap_DeferredProfitSharingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Profit Sharing [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredProfitSharingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredProfitSharingMember"/>
    <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"/>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_019e4b0b-9859-7faa-b9ed-fd2c2041d9f8_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/2026/elts/us-gaap-2026.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_logan_ValuationTechniqueEquityValueMember_019facfc-b7dc-7dbe-9bef-34998c6105f7_terseLabel_en-US" xlink:label="lab_logan_ValuationTechniqueEquityValueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity value</link:label>
    <link:label id="lab_logan_ValuationTechniqueEquityValueMember_label_en-US" xlink:label="lab_logan_ValuationTechniqueEquityValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Equity Value [Member]</link:label>
    <link:label id="lab_logan_ValuationTechniqueEquityValueMember_documentation_en-US" xlink:label="lab_logan_ValuationTechniqueEquityValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Valuation Technique, Equity Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ValuationTechniqueEquityValueMember" xlink:href="logan-20260630.xsd#logan_ValuationTechniqueEquityValueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ValuationTechniqueEquityValueMember" xlink:to="lab_logan_ValuationTechniqueEquityValueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019e4b0b-9859-7f85-bac3-d7df66086e5d_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_019e4b0b-9859-7b09-a010-b619212054e2_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_019e4b0b-9859-7ec6-8ead-6ae40352868e_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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"/>
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    <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/2026/elts/us-gaap-2026.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_FairValueByBalanceSheetGroupingTextBlock_019e4b0b-9859-7f4c-9ab5-c466865a364e_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/2026/elts/us-gaap-2026.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_CorporateDebtSecuritiesMember_019e4b0b-9859-7fd5-a28b-6d5223facc5b_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_019e4b0b-9859-7175-a980-7469c543de57_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/2026/elts/us-gaap-2026.xsd#us-gaap_CorporateDebtSecuritiesMember"/>
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    <link:label id="lab_us-gaap_EarningsPerShareDiluted_019e4b0b-9859-7a34-abe7-247dda647f03_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to common shareholders - Diluted (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_019e4b0b-9859-7340-965e-210c1f684652_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/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InternalCreditAssessmentAxis_019e4b0b-97b1-7d5d-817b-0fcd302d4a0e_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/2026/elts/us-gaap-2026.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_ProvisionForLoanLossesExpensed_019e4b0b-97b1-72b4-9573-dafb49c58e17_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>
    <link:label id="lab_us-gaap_ProvisionForLoanLossesExpensed_label_en-US" xlink:label="lab_us-gaap_ProvisionForLoanLossesExpensed" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Loss, Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProvisionForLoanLossesExpensed" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.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_UnrealizedGainLossOnInvestments_019e4b0b-9859-76cb-8f86-3aad3b48c8c8_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net change in unrealized (gains) losses on investments</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_019e4b0b-9859-7172-a281-7c500697fe23_netLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Net unrealized gains (losses)</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_019e4b0b-9859-7158-99f9-7bb97a0e6efb_terseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gain/(loss) on investments</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_019e4b0b-9859-7b0a-8e5f-912f51df2f07_verboseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized gains (losses) from investment activities</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) on Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossOnInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrealizedGainLossOnInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrealizedGainLossOnInvestments" xlink:to="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_019e4b0b-97b1-7200-8653-021b275cc793_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">Intangible Asset, Finite-Lived, Amortization Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfIntangibleAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:to="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredOfferingCosts_019e4b0b-9859-7cf6-8ce6-7fc49333b835_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/2026/elts/us-gaap-2026.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_srt_OwnershipDomain_019e4b0b-97b1-7c59-b1eb-efd96d6a5ee5_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/2026/elts/srt-2026.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_us-gaap_FinanceReceivablesMember_019fcdad-dbe4-75ba-8623-fa64f4a472b1_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable</link:label>
    <link:label id="lab_us-gaap_FinanceReceivablesMember_label_en-US" xlink:label="lab_us-gaap_FinanceReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceReceivablesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceReceivablesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceReceivablesMember" xlink:to="lab_us-gaap_FinanceReceivablesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CededCreditRiskAxis_019e4b0b-9859-7ada-aee8-547a6a76edaf_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/2026/elts/us-gaap-2026.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_us-gaap_CededCreditRiskLineItems_019e4b0b-97b1-755b-938b-97cd47487715_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/2026/elts/us-gaap-2026.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_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/2026/elts/us-gaap-2026.xsd#us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract"/>
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    <link:label id="lab_logan_OtherInvestedAssetsFairValue_019e4b0b-97b1-754b-9544-6f01329d8146_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-20260630.xsd#logan_OtherInvestedAssetsFairValue"/>
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    <link:label id="lab_srt_ConsolidatedEntityExcludingVariableInterestEntitiesVIEMember_019e4b0b-96e1-7a50-9875-b06e00288955_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntityExcludingVariableInterestEntitiesVIEMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entity, Excluding Consolidated VIE</link:label>
    <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/2026/elts/srt-2026.xsd#srt_ConsolidatedEntityExcludingVariableInterestEntitiesVIEMember"/>
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    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract_019e4b0b-97b1-7e48-a402-879e156fd038_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/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract"/>
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    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLosses_019e4b0b-9859-719d-af8b-da3651fe5d6e_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_019e4b0b-985a-76fc-904c-b30be5dd787f_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/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableAllowanceForCreditLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAllowanceForCreditLosses" xlink:to="lab_us-gaap_FinancingReceivableAllowanceForCreditLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:to="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceNetAmountAtRisk_019e4b0b-97b1-72d7-8aa7-d284488789a0_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/2026/elts/us-gaap-2026.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_IntangibleAssetsGrossExcludingGoodwill_019e4b0b-97b1-76c5-bcfb-d1d939b4d42b_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 Asset, Excluding Goodwill, before Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.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_logan_NicholModcoFundsMember_019e4b0b-97b1-74b3-9c9d-eff7a2a9c0aa_terseLabel_en-US" xlink:label="lab_logan_NicholModcoFundsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nichol Modco Funds Withheld</link:label>
    <link:label id="lab_logan_NicholModcoFundsMember_label_en-US" xlink:label="lab_logan_NicholModcoFundsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nichol Modco Funds [Member]</link:label>
    <link:label id="lab_logan_NicholModcoFundsMember_documentation_en-US" xlink:label="lab_logan_NicholModcoFundsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Nichol Modco Funds</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_NicholModcoFundsMember" xlink:href="logan-20260630.xsd#logan_NicholModcoFundsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_NicholModcoFundsMember" xlink:to="lab_logan_NicholModcoFundsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ScheduleOfDeferredAcquisitionCostFutureAmortizationExpenseTableTextBlock_019e4b0b-97b1-73f7-88d1-8fa0490d3065_terseLabel_en-US" xlink:label="lab_logan_ScheduleOfDeferredAcquisitionCostFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Deferred Acquisition Cost Future Amortization Expense</link:label>
    <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-20260630.xsd#logan_ScheduleOfDeferredAcquisitionCostFutureAmortizationExpenseTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ScheduleOfDeferredAcquisitionCostFutureAmortizationExpenseTableTextBlock" xlink:to="lab_logan_ScheduleOfDeferredAcquisitionCostFutureAmortizationExpenseTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrentAndNoncurrent_019e4b0b-9859-7777-bc71-9ed21b37f4e7_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other accrued expenses</link:label>
    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAccruedLiabilitiesCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAccruedLiabilitiesCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAccruedLiabilitiesCurrentAndNoncurrent" xlink:to="lab_us-gaap_OtherAccruedLiabilitiesCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumUndiscountedBeforeReinsurance_019e4b0b-97b1-76f4-8117-a8212a7a2dc2_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/2026/elts/us-gaap-2026.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_logan_ValuationTechniqueVolatilityMember_019e4b0b-9859-7888-9322-098924f4e9df_terseLabel_en-US" xlink:label="lab_logan_ValuationTechniqueVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Technique, Volatility</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ValuationTechniqueVolatilityMember" xlink:href="logan-20260630.xsd#logan_ValuationTechniqueVolatilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ValuationTechniqueVolatilityMember" xlink:to="lab_logan_ValuationTechniqueVolatilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_019e4b0b-97b1-71da-904b-d17a81cc470f_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/2026/elts/us-gaap-2026.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_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract_019e4b0b-97b1-7a62-ba62-07d07cf4460c_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/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignCountryMember_019e4b0b-9859-76ab-863f-29d11df91eb9_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCountryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction, Foreign</link:label>
    <link:label id="lab_us-gaap_ForeignCountryMember_label_en-US" xlink:label="lab_us-gaap_ForeignCountryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction, Foreign [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCountryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignCountryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignCountryMember" xlink:to="lab_us-gaap_ForeignCountryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_019e4b0b-9859-7177-bb3d-c4a2e254c23b_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 income (expense)</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/2026/elts/us-gaap-2026.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_logan_InvestedAssetsMeasurementInputs_019e4b0b-97b1-732a-89e7-c38a3527c1b2_terseLabel_en-US" xlink:label="lab_logan_InvestedAssetsMeasurementInputs" 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_InvestedAssetsMeasurementInputs_label_en-US" xlink:label="lab_logan_InvestedAssetsMeasurementInputs" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Invested Assets, Measurement Inputs</link:label>
    <link:label id="lab_logan_InvestedAssetsMeasurementInputs_documentation_en-US" xlink:label="lab_logan_InvestedAssetsMeasurementInputs" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Invested Assets, Measurement Inputs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InvestedAssetsMeasurementInputs" xlink:href="logan-20260630.xsd#logan_InvestedAssetsMeasurementInputs"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InvestedAssetsMeasurementInputs" xlink:to="lab_logan_InvestedAssetsMeasurementInputs" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WarrantsAndRightsOutstanding_019e4b0b-9859-74b9-8cb0-1cf45f075c89_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WarrantsAndRightsOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WarrantsAndRightsOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WarrantsAndRightsOutstanding" xlink:to="lab_us-gaap_WarrantsAndRightsOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeDividend_019e4b0b-97b1-78b7-9400-7eb1d4059ca6_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/2026/elts/us-gaap-2026.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_logan_ArrangementWarrantsMember_019e4b0b-9859-79d8-9bd6-c9f6fd9c8205_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-20260630.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_RelatedPartyTransactionDomain_019e4b0b-9859-7887-9110-2df5e0634a13_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/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain" xlink:to="lab_us-gaap_RelatedPartyTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_019e4b0b-9859-7098-b159-0e96d119a479_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/2026/elts/us-gaap-2026.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_ForeignGovernmentDebtSecuritiesMember_019e4b0b-97b1-7aa7-806b-7de4f91bac2f_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignGovernmentDebtSecuritiesMember" 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_us-gaap_ForeignGovernmentDebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_ForeignGovernmentDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Security, Government, Non-US [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignGovernmentDebtSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignGovernmentDebtSecuritiesMember"/>
    <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"/>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesMember_019e4b0b-9859-7c4c-aa7a-6d4d9d62eb80_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_019e4b0b-9859-7c0b-a82f-80b197925153_verboseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" 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/2026/elts/us-gaap-2026.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_logan_SingleLargestInvestmentMember_019e4b0b-9859-7741-9ca8-b6d02e09c667_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-20260630.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_AdministrativeFeesExpense_019e4b0b-97b1-77d3-b54e-becefb1a403b_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/2026/elts/us-gaap-2026.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_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_019e4b0b-97b1-7106-b7ad-4352fc6fdd97_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/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ClassOfWarrantOrRightExercisablePeriod_019e4b0b-9859-7819-97a3-fb03b99eea79_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-20260630.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_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_019e4b0b-9859-766f-b66f-bcd956af65f7_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/2026/elts/us-gaap-2026.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_us-gaap_CommonStockSharesIssued_019e4b0b-97b1-79b9-8cb2-3431c74d1fba_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/2026/elts/us-gaap-2026.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_logan_RepaymentsOfBorrowingsOfInsuranceBusiness_019facca-2fc6-750a-9aac-c04f13fd9486_negatedTerseLabel_en-US" xlink:label="lab_logan_RepaymentsOfBorrowingsOfInsuranceBusiness" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repayments of borrowings of insurance business</link:label>
    <link:label id="lab_logan_RepaymentsOfBorrowingsOfInsuranceBusiness_label_en-US" xlink:label="lab_logan_RepaymentsOfBorrowingsOfInsuranceBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments Of Borrowings Of Insurance Business</link:label>
    <link:label id="lab_logan_RepaymentsOfBorrowingsOfInsuranceBusiness_documentation_en-US" xlink:label="lab_logan_RepaymentsOfBorrowingsOfInsuranceBusiness" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Repayments Of Borrowings Of Insurance Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_RepaymentsOfBorrowingsOfInsuranceBusiness" xlink:href="logan-20260630.xsd#logan_RepaymentsOfBorrowingsOfInsuranceBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_RepaymentsOfBorrowingsOfInsuranceBusiness" xlink:to="lab_logan_RepaymentsOfBorrowingsOfInsuranceBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019e4b0b-9859-76b2-a5a7-2890f7c40a09_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_019e4b0b-9859-7f0f-be81-3a649c7319b4_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_019e4b0b-9859-70c3-977b-a60f785666c9_netLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Total financial assets</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/2026/elts/us-gaap-2026.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_logan_MLCSCMember_019e4b0b-97b1-7cfc-8de5-9db95b4e3805_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-20260630.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_srt_RestatementAdjustmentMember_019fc6ab-a7b1-7959-8d01-8ea2e833eeab_terseLabel_en-US" xlink:label="lab_srt_RestatementAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revision of Prior Period, Adjustment</link:label>
    <link:label id="lab_srt_RestatementAdjustmentMember_label_en-US" xlink:label="lab_srt_RestatementAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revision of Prior Period, Adjustment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RestatementAdjustmentMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RestatementAdjustmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RestatementAdjustmentMember" xlink:to="lab_srt_RestatementAdjustmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_019e4b0b-97b1-7d47-a7ef-8a08d0cec027_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/2026/elts/us-gaap-2026.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_logan_TURNMember_019e4b0b-9859-7a92-a574-1fd97e7d4f54_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-20260630.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_019e4b0b-9859-7b78-b6cb-609d31641c92_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-20260630.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_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss_019e4b0b-97b1-7c28-9ff7-5881e144c776_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">12 months or more</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" 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, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_CapitalaAcquisitionMember_019e4b0b-9859-7bbe-a4a9-fdeb796f57be_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-20260630.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_srt_ProductsAndServicesDomain_019e4b0b-9859-71f8-b16a-2f2c3c91081c_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/2026/elts/srt-2026.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_ClassOfStockLineItems_019e4b0b-97b1-799d-a21c-35625608d728_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/2026/elts/us-gaap-2026.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_us-gaap_DisaggregationOfRevenueTable_019e4b0b-9859-7e1f-a1ff-9c38e425374a_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/2026/elts/us-gaap-2026.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_VariableInterestEntityLineItems_019e4b0b-9859-71c5-8d19-773c152e31fd_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_LiabilityForFuturePolicyBenefitAfterReinsuranceAbstract_019e4b0b-9859-75a4-9d44-b753d81d5fea_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/2026/elts/us-gaap-2026.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_us-gaap_ReinsuranceRecoverablesAbstract_019e4b0b-97b1-757e-8992-75201b9c2eee_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/2026/elts/us-gaap-2026.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_logan_RevenuesAdjusted_019e4b0b-97b1-78c2-b5b5-8c3407a803f6_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-20260630.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_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearOne_019e4b0b-97b1-799f-9229-8228e470f47f_terseLabel_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearOne" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearOne_label_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearOne" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense, Year One</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearOne" xlink:href="logan-20260630.xsd#logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearOne"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearOne" xlink:to="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearOne" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <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/2026/ecd-2026.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_OtherCommitmentsAxis_019e4b0b-97b1-7691-8891-bb8da9ba8aa3_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/2026/elts/us-gaap-2026.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_logan_ModcoInvestmentsWithNicholInternationalReinsuranceS.A.CLtdMember_019e4b0b-96e1-7904-98dd-8462357181b6_terseLabel_en-US" xlink:label="lab_logan_ModcoInvestmentsWithNicholInternationalReinsuranceS.A.CLtdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Modco investments with Nichol International Reinsurance (S.A.C), Ltd</link:label>
    <link:label id="lab_logan_ModcoInvestmentsWithNicholInternationalReinsuranceS.A.CLtdMember_label_en-US" xlink:label="lab_logan_ModcoInvestmentsWithNicholInternationalReinsuranceS.A.CLtdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Modco investments with Nichol International Reinsurance (S.A.C), Ltd [Member]</link:label>
    <link:label id="lab_logan_ModcoInvestmentsWithNicholInternationalReinsuranceS.A.CLtdMember_documentation_en-US" xlink:label="lab_logan_ModcoInvestmentsWithNicholInternationalReinsuranceS.A.CLtdMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Modco investments with Nichol International Reinsurance (S.A.C), Ltd</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ModcoInvestmentsWithNicholInternationalReinsuranceS.A.CLtdMember" xlink:href="logan-20260630.xsd#logan_ModcoInvestmentsWithNicholInternationalReinsuranceS.A.CLtdMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ModcoInvestmentsWithNicholInternationalReinsuranceS.A.CLtdMember" xlink:to="lab_logan_ModcoInvestmentsWithNicholInternationalReinsuranceS.A.CLtdMember" xlink:type="arc" order="1"/>
    <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/2026/elts/us-gaap-2026.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_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_019e4b0b-97b1-7723-9ec7-d2bd6332ded1_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_019e4b0b-97b1-7f41-b840-90ea682ef141_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 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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_logan_LaborAndRelatedExpenseAdjusted_019e4b0b-9859-7768-8131-4aa62d242599_negatedTerseLabel_en-US" xlink:label="lab_logan_LaborAndRelatedExpenseAdjusted" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Compensation and benefits</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_logan_LaborAndRelatedExpenseAdjusted" xlink:href="logan-20260630.xsd#logan_LaborAndRelatedExpenseAdjusted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_LaborAndRelatedExpenseAdjusted" xlink:to="lab_logan_LaborAndRelatedExpenseAdjusted" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_AdministrativeExpensesMember_019fcdcc-b03e-7614-9939-3d3b41933c0f_terseLabel_en-US" xlink:label="lab_logan_AdministrativeExpensesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administrative Expenses</link:label>
    <link:label id="lab_logan_AdministrativeExpensesMember_label_en-US" xlink:label="lab_logan_AdministrativeExpensesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Administrative Expenses [Member]</link:label>
    <link:label id="lab_logan_AdministrativeExpensesMember_documentation_en-US" xlink:label="lab_logan_AdministrativeExpensesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Administrative Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_AdministrativeExpensesMember" xlink:href="logan-20260630.xsd#logan_AdministrativeExpensesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_AdministrativeExpensesMember" xlink:to="lab_logan_AdministrativeExpensesMember" xlink:type="arc" order="1"/>
    <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>
    <link:label id="lab_ecd_AwardGrantDateFairValue_label_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardGrantDateFairValue" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardGrantDateFairValue" xlink:to="lab_ecd_AwardGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock_019e4b0b-97b1-76e2-930a-b38b43c03c03_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Debt Securities, Available-for-Sale, Unrealized Loss Position, Fair Value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Loss Position, Fair Value [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTable_019e4b0b-97b1-78d9-83bd-32d3e9f697eb_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/2026/elts/us-gaap-2026.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_OtherInsuranceProductLineMember_019e4b0b-97b1-749c-a443-93e145735c98_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.xsd#ecd_PvpTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTableTextBlock" xlink:to="lab_ecd_PvpTableTextBlock" 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/2026/ecd-2026.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_logan_InvestmentAndOtherIncomeLossNet_019e4b0b-96e1-79b6-bf39-34346f67fd4f_totalLabel_en-US" xlink:label="lab_logan_InvestmentAndOtherIncomeLossNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total investment and other income (loss)</link:label>
    <link:label id="lab_logan_InvestmentAndOtherIncomeLossNet_label_en-US" xlink:label="lab_logan_InvestmentAndOtherIncomeLossNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment And Other Income (Loss), Net</link:label>
    <link:label id="lab_logan_InvestmentAndOtherIncomeLossNet_documentation_en-US" xlink:label="lab_logan_InvestmentAndOtherIncomeLossNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment And Other Income (Loss), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InvestmentAndOtherIncomeLossNet" xlink:href="logan-20260630.xsd#logan_InvestmentAndOtherIncomeLossNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InvestmentAndOtherIncomeLossNet" xlink:to="lab_logan_InvestmentAndOtherIncomeLossNet" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FinancingReceivableCollateralDependentLoans_019e4b0b-9859-74d4-ae4b-083f35a9b96c_terseLabel_en-US" xlink:label="lab_logan_FinancingReceivableCollateralDependentLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Loans</link:label>
    <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-20260630.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_ConsolidationItemsAxis_019e4b0b-96e1-701e-8f9c-260b92017e66_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/2026/elts/srt-2026.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_dei_EntityAddressPostalZipCode_019e4b0b-97b1-7dbc-8cb1-ab7572a5731d_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/2026/dei-2026.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_dei_EntityRegistrantName_019e4b0b-9859-7627-a9e4-d7effa10ace2_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/2026/dei-2026.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_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss_019e4b0b-9859-718c-aac9-fd06d213b9c0_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>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" 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, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesAllowance_019e4b0b-9859-7874-b0ff-4e71507a2c1b_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/2026/elts/us-gaap-2026.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_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:to="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceLiabilitiesAbstract_019e4b0b-9859-7ccc-822a-b14a72e21ce2_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/2026/elts/us-gaap-2026.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_FiniteLivedIntangibleAssetsGross_019e4b0b-97b1-78d6-aff3-c4f9b19cdeb7_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">Intangible Asset, Finite-Lived, before Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.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_logan_FinancingReceivableCreditLossExpenseReversalNet_019e4b0b-98ea-7c12-847a-d078ca160384_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-20260630.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_us-gaap_Revenues_019e4b0b-97b1-7bf4-b42c-a1b60bd7a940_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_019e4b0b-97b1-7e98-88b4-5888918a7ac8_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/2026/elts/us-gaap-2026.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_logan_ScheduleOfCollateralDependentLoansTableTextBlock_019e4b0b-97b1-7ad9-b45b-935b64cc8395_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-20260630.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_us-gaap_IncomeLossFromEquityMethodInvestments_019e4b0b-98ea-7ed9-87f0-d49c99cc3c1e_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_019e4b0b-98ea-7a16-975e-3a94e7e066d5_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_019e4b0b-98ea-7d71-a872-27033f334819_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" 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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_srt_CreditRatingAMBestDomain_019e4b0b-9859-766b-8570-30d8abc901ab_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/2026/elts/srt-2026.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_logan_ProbabilityWeightedExpectedReturnMethodDependentProbabilitiesMember_019e4b0b-9859-70c5-a619-ecefaead9fd5_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</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-20260630.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_logan_CorporateLoansMember_019e4b0b-97b1-7737-ab34-01c55e9df056_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-20260630.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_logan_ReinsuranceRecoverableNetCreditExposure_019e4b0b-97b1-7a25-9bfb-a110c87be7fe_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-20260630.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_IncreaseDecreaseInOperatingLiabilitiesAbstract_019e4b0b-98ea-7daf-bef8-b29f557aa0de_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/2026/elts/us-gaap-2026.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_us-gaap_GoodwillRollForward_019e4b0b-97b1-7188-9b4b-11e63d1504e2_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/2026/elts/us-gaap-2026.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_FiniteLivedIntangibleAssetsMajorClassNameDomain_019e4b0b-9859-7b3b-9187-3e8ab95be898_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">Intangible Asset, Finite-Lived, Class [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">Intangible Asset, Finite-Lived, Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MovementAnalysisOfDeferredPolicyAcquisitionCostsRollForward_019e4b0b-97b1-7e4e-b2a4-169359ea25db_terseLabel_en-US" xlink:label="lab_us-gaap_MovementAnalysisOfDeferredPolicyAcquisitionCostsRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Movement Analysis of Deferred Policy Acquisition Costs [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_MovementAnalysisOfDeferredPolicyAcquisitionCostsRollForward_label_en-US" xlink:label="lab_us-gaap_MovementAnalysisOfDeferredPolicyAcquisitionCostsRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Movement Analysis of Deferred Policy Acquisition Costs [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MovementAnalysisOfDeferredPolicyAcquisitionCostsRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.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"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019e4b0b-97b1-7e00-bd1d-ff55392c244a_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/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_019e4b0b-97b1-7e00-876d-c3bb23ef2722_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/2026/elts/us-gaap-2026.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_MeasurementInputRevenueMultipleMember_019e4b0b-9859-7591-b7bd-dd2173c9a93c_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">Equity and 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/2026/elts/us-gaap-2026.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_FairValueInputsLevel3Member_019e4b0b-97b1-7365-af2c-f7be912204f3_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/2026/elts/us-gaap-2026.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_LiabilityForFuturePolicyBenefitActivityTableTextBlock_019e4b0b-97b1-741e-a6d4-675bd89f5c74_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">Schedule of 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/2026/elts/us-gaap-2026.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_logan_InternalCreditAssessmentLevelThreeMember_019e4b0b-9859-7b8e-ab7d-24b5ee2c3d3c_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>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InternalCreditAssessmentLevelThreeMember" xlink:href="logan-20260630.xsd#logan_InternalCreditAssessmentLevelThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InternalCreditAssessmentLevelThreeMember" xlink:to="lab_logan_InternalCreditAssessmentLevelThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_019e4b0b-9859-75bf-9df7-f11402e37567_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">2027</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StatementGeographicalAxis_019e4b0b-9859-7cda-99ae-cf082f40b286_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/2026/elts/srt-2026.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_us-gaap_RestrictedCash_019e4b0b-97b1-7e7b-8d16-b3acb7838103_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/2026/elts/us-gaap-2026.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_FairValueMeasuredAtNetAssetValuePerShareMember_019e4b0b-97b1-7348-9986-624fc01d0dd6_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/2026/elts/us-gaap-2026.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_LiabilityForFuturePolicyBenefitExpectedNetPremiumInterestIncome_019e4b0b-9859-7dc5-a4ea-1f284b966450_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/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumInterestIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumInterestIncome" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumInterestIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ProceedsFromBorrowingsOfAssetManagementBusiness_019e4b0b-9859-7df7-a2f5-f529452d737b_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>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ProceedsFromBorrowingsOfAssetManagementBusiness" xlink:href="logan-20260630.xsd#logan_ProceedsFromBorrowingsOfAssetManagementBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ProceedsFromBorrowingsOfAssetManagementBusiness" xlink:to="lab_logan_ProceedsFromBorrowingsOfAssetManagementBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssets_019e4b0b-96e1-72ea-b6d9-20abdac11c4d_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_019e4b0b-96e1-7384-8ab1-fae31b430817_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" 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_us-gaap_OtherAssets_019e4b0b-96e1-7800-8f39-624dab76275c_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/2026/elts/us-gaap-2026.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_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityRemainderOfTheYear_019e4b0b-9859-7f79-8971-ba3654028dfb_terseLabel_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityRemainderOfTheYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remainder of 2026</link:label>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityRemainderOfTheYear_label_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityRemainderOfTheYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss Maturity, Remainder of The Year</link:label>
    <link:label id="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityRemainderOfTheYear_documentation_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityRemainderOfTheYear" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss Maturity, Remainder of The Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityRemainderOfTheYear" xlink:href="logan-20260630.xsd#logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityRemainderOfTheYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityRemainderOfTheYear" xlink:to="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityRemainderOfTheYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivables30To59DaysPastDueMember_019e4b0b-9859-7c07-9bda-2ace6bdb65a1_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/2026/elts/us-gaap-2026.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_LegalEntityAxis_019e4b0b-97b1-7894-b12e-96fe79d5f8fa_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/2026/dei-2026.xsd#dei_LegalEntityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseDebt_019e4b0b-9859-78b4-b92c-f78735e45441_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt interest expense</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseDebt" xlink:to="lab_us-gaap_InterestExpenseDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodFairValue_019e4b0b-97b1-796c-a5f8-1475fdd490fb_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>
    <link:label id="lab_logan_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodFairValue_documentation_en-US" xlink:label="lab_logan_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" 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>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodFairValue" xlink:href="logan-20260630.xsd#logan_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodFairValue" xlink:to="lab_logan_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_019e4b0b-96e1-788d-8aef-168d4260c9c6_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByLiabilityClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:to="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_First10YearsMember_019e4b0b-9859-7353-8c9e-0b4457305ac5_terseLabel_en-US" xlink:label="lab_logan_First10YearsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">First 10 Years</link:label>
    <link:label id="lab_logan_First10YearsMember_label_en-US" xlink:label="lab_logan_First10YearsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">First 10 Years [Member]</link:label>
    <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-20260630.xsd#logan_First10YearsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_First10YearsMember" xlink:to="lab_logan_First10YearsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdministrativeFeePayable_019e4b0b-9859-7feb-ac2b-1eaec04ca85a_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/2026/elts/us-gaap-2026.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_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019fdc0f-7e2a-7561-8b61-ff8c48c30d38_terseLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019e4b0b-9859-7937-bcd1-c138f5673602_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_019e4b0b-9859-7c41-a911-5d3f80f267e6_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/2026/elts/us-gaap-2026.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_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-20260630.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_EffectsOfReinsuranceTable_019e4b0b-9859-79f3-b9a3-cb792cefb245_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_FinancingReceivableAllowanceForCreditLossesRollForward_019e4b0b-9859-7a30-a18e-87b14ac06108_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/2026/elts/us-gaap-2026.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_ReportingUnitDomain_019e4b0b-97b1-7164-b2b4-d3c510adfe89_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/2026/elts/us-gaap-2026.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_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_019e4b0b-9859-7c76-a0b2-a9811defe73d_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">2028</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">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.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_InterestCreditedToPolicyholdersAccountBalances_019e4b0b-96e1-7941-b5fa-1c7b4f70e549_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/2026/elts/us-gaap-2026.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_srt_EquityMethodInvesteeNameDomain_019e4b0b-97b1-7be4-90fb-f9eaec58cbab_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/2026/elts/srt-2026.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_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_019e4b0b-985a-7d42-8a49-81315f6f3431_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">Remainder of 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/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_019e4b0b-97b1-7ccc-bb24-847bd6e66874_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/2026/elts/us-gaap-2026.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_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_019e4b0b-96e1-7c4a-96f3-9404cd5d8405_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/2026/elts/us-gaap-2026.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_logan_LegacyMountLoganShareholdersMember_019e4b0b-9859-76ea-ac79-f04b67748974_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-20260630.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_PaymentsForRepurchaseOfCommonStock_019e4b0b-96e1-708c-a8f3-1931c28bbfb6_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/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForRepurchaseOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:to="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_019e4b0b-9859-7ece-a93b-5aaa67cb6f62_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/2026/elts/srt-2026.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_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable_019e4b0b-9859-7777-959c-f3ba24ad2be3_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/2026/elts/us-gaap-2026.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_logan_LongTermCareInsuranceMember_019e4b0b-97b1-7a24-921b-09a86b5cc1fe_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-20260630.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_AwardTypeAxis_019e4b0b-97b1-7eb5-a85a-6c95071497a4_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/2026/elts/us-gaap-2026.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_LiabilityForFuturePolicyBenefitExpectedNetPremiumRollForward_019e4b0b-97b1-7c2a-9738-b746e4610a24_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_us-gaap_RetainedEarningsAccumulatedDeficit_019e4b0b-9859-79d3-999f-2688e56a2932_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/2026/elts/us-gaap-2026.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_srt_ProductOrServiceAxis_019e4b0b-9859-7b3a-91db-f64e549da166_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/2026/elts/srt-2026.xsd#srt_ProductOrServiceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductOrServiceAxis" xlink:to="lab_srt_ProductOrServiceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent_019e4b0b-97b1-707b-ba5c-f4600f53701a_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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent"/>
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    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_019e4b0b-97b1-7c9d-8ae1-8ab616e5a860_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities_019e4b0b-97b1-7e1a-b2ff-085b114cdab9_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_019e4b0b-97b1-7844-80fd-1eabd86f2179_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_019e4b0b-97b1-73a1-9ecc-f513cc080252_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_019e4b0b-97b1-7571-abd5-c5f827ec3744_netLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Corporate loans</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/2026/elts/us-gaap-2026.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_us-gaap_IncreaseDecreaseInOtherAccountsPayable_019e4b0b-9859-7ee9-ab47-88a3e164a3ed_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>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherAccountsPayable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherAccountsPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Accounts Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherAccountsPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherAccountsPayable"/>
    <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_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_019e4b0b-97b1-7b02-b47f-4406836471d0_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/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod"/>
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    <link:label id="lab_us-gaap_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossOci_019e4b0b-9859-7800-9744-a427dff9d64c_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/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossOci"/>
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    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_019e4b0b-9859-705e-9df3-2e369581763e_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/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis"/>
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    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_019e4b0b-97b1-7d18-a40a-c8cb7abac1ef_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/2026/elts/us-gaap-2026.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_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitPeriodIncreaseDecrease_019e4b0b-9859-7ced-810a-151ce2511db3_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/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitPeriodIncreaseDecrease"/>
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    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_019e4b0b-9859-7d5c-8db5-1ebbcc4724bc_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/2026/elts/us-gaap-2026.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_DeferredPolicyAcquisitionCostsTextBlock1_019e4b0b-9859-7aed-bad0-5e98a96f5343_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/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredPolicyAcquisitionCostsTextBlock1"/>
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    <link:label id="lab_us-gaap_RealizedInvestmentGainsLosses_019e4b0b-9859-7ab5-a893-c17abad97bd9_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>
    <link:label id="lab_us-gaap_RealizedInvestmentGainsLosses_019e4b0b-9859-7036-ae8e-eb8b202f05e4_verboseLabel_en-US" xlink:label="lab_us-gaap_RealizedInvestmentGainsLosses" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net realized gains (losses)</link:label>
    <link:label id="lab_us-gaap_RealizedInvestmentGainsLosses_019e4b0b-9859-7be9-bb96-0941518f9093_terseLabel_en-US" xlink:label="lab_us-gaap_RealizedInvestmentGainsLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized gain/(loss) on investments</link:label>
    <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_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/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeStockOptionMember"/>
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    <link:label id="lab_us-gaap_CededCreditRiskTable_019e4b0b-9859-72fc-8a7b-3359180a7057_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/2026/elts/us-gaap-2026.xsd#us-gaap_CededCreditRiskTable"/>
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    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseAfterYearFour_019e4b0b-97b1-7f67-bee4-044efca06cdc_terseLabel_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2031 and thereafter</link:label>
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    <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>
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    <link:label id="lab_us-gaap_RelatedPartyDomain_019e4b0b-9859-7374-9aa7-201f0853201e_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>
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    <link:label id="lab_us-gaap_AdditionalPaidInCapital_019e4b0b-9859-7319-9629-c881f16eefb0_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/2026/elts/us-gaap-2026.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_us-gaap_IncreaseDecreaseInReinsuranceRecoverable_019e4b0b-9859-7cd3-8ac3-072309e66de3_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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInReinsuranceRecoverable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInReinsuranceRecoverable"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionEquityInterestIssuedOrIssuableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionEquityInterestIssuedOrIssuableTextBlock"/>
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    <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/2026/elts/us-gaap-2026.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_PortionAtOtherThanFairValueFairValueDisclosureMember_019e4b0b-97b1-7d9f-8e05-ea7d6a31187c_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_019e4b0b-97b1-7f8b-97f9-be27fba63a9e_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/2026/elts/us-gaap-2026.xsd#us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_PromissoryNoteMember_019e4b0b-9859-733e-a862-aecd5e025a2f_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-20260630.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_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/2026/ecd-2026.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_logan_MLCUSHoldingsCreditFacilityMember_019e4b0b-97b1-752f-b124-8f4ad9d87f6a_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-20260630.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_logan_DebtInstrumentInterestRatePayablePeriodDomain_019e4b0b-97b1-7a2e-8dd2-28d07e5e0f01_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-20260630.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_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/2026/ecd-2026.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_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/2026/ecd-2026.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_us-gaap_PrepaidTaxes_019e4b0b-97b1-73fc-8ecf-bbce3e85f4ea_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/2026/elts/us-gaap-2026.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_InterestPaidNet_019e4b0b-9859-7313-ab01-92d4a273fdb4_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/2026/elts/us-gaap-2026.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_us-gaap_HedgingDesignationAxis_019e4b0b-9859-7c87-a799-db9b5a608429_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/2026/elts/us-gaap-2026.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_FinancingReceivables60To89DaysPastDueMember_019e4b0b-9859-7f12-8bb4-7e823bd18b7a_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/2026/elts/us-gaap-2026.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_CreditFacilityAxis_019e4b0b-97b1-7020-8697-d7bae47c2e41_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/2026/elts/us-gaap-2026.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_us-gaap_AssetsFairValueDisclosure_019e4b0b-96e1-7019-8754-e72406861ec1_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_019e4b0b-96e1-7be1-94c3-cd1eb162137e_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_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/2026/ecd-2026.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_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange_019e4b0b-97b1-752d-8b7f-f7b7c4fd6ba2_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjusted balance</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange" 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 Reinsurance, after Cash Flow Change</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumOriginalDiscountRateBeforeReinsuranceAfterCashFlowChange" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_019e4b0b-9859-7060-860f-9858b4ec3520_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_019e4b0b-97b1-7179-8e77-dc547683e2cf_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/2026/elts/us-gaap-2026.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_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitRollForward_019e4b0b-9859-7be8-80ea-30402bd15ec5_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/2026/elts/us-gaap-2026.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_logan_InternalCreditAssessmentLevelFiveMember_019e4b0b-97b1-77e8-86d0-98cbe2ce72eb_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-20260630.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_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic_019e4b0b-97b1-7e36-b233-c61ec7aabdec_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/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_019e4b0b-97b1-7c6e-be48-076b14720fcf_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis_019e4b0b-9859-7ac8-a85f-9b1b6aa64214_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">Intangible Asset, Indefinite-Lived, Class [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">Intangible Asset, Indefinite-Lived, Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" xlink:to="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_019e4b0b-96e1-733c-8e46-1a9e458f2895_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_019e4b0b-96e1-79bf-a42f-648b295d96c3_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">Impairment losses</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/2026/elts/us-gaap-2026.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_InterestReceivable_019e4b0b-97b1-7b14-83c4-78ad47a2dae8_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/2026/elts/us-gaap-2026.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"/>
    <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>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndName" xlink:to="lab_ecd_TrdArrIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_AssetManagementExpenseAbstract_019e4b0b-97b1-76fe-bc73-00b022a393e1_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-20260630.xsd#logan_AssetManagementExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_AssetManagementExpenseAbstract" xlink:to="lab_logan_AssetManagementExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019e4b0b-9859-7aa7-9d80-24789017256f_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleListNotDisclosedFlag_019e4b0b-9859-79de-a189-b28b45f48c79_terseLabel_en-US" xlink:label="lab_logan_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleListNotDisclosedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Recurring Basis Unobservable Input Reconciliation Liability Gain Loss Statement Of Income Extensible List Not Disclosed Flag</link:label>
    <link:label id="lab_logan_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleListNotDisclosedFlag_label_en-US" xlink:label="lab_logan_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleListNotDisclosedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Recurring Basis Unobservable Input Reconciliation Liability Gain Loss Statement Of Income Extensible List Not Disclosed Flag</link:label>
    <link:label id="lab_logan_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleListNotDisclosedFlag_documentation_en-US" xlink:label="lab_logan_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleListNotDisclosedFlag" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Recurring Basis Unobservable Input Reconciliation Liability Gain Loss Statement Of Income Extensible List Not Disclosed Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleListNotDisclosedFlag" xlink:href="logan-20260630.xsd#logan_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleListNotDisclosedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleListNotDisclosedFlag" xlink:to="lab_logan_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleListNotDisclosedFlag" 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/2026/ecd-2026.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_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_019e4b0b-9859-78ec-b4b5-90ab17945935_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/2026/elts/us-gaap-2026.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_EquitySecuritiesFvNiMeasurementInput_019e4b0b-9859-757c-aabe-ebbfa1291a42_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/2026/elts/us-gaap-2026.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_logan_MarketApproachMember_019e4b0b-9859-70ee-866a-ba2ded851706_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-20260630.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_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_019e4b0b-9859-74bf-aa63-40b9eb7a8cfe_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/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ValuationTechniqueYearsToExerciseMember_019e4b0b-9859-7256-ad17-1db18116e4d2_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-20260630.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_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/2026/ecd-2026.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_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/2026/ecd-2026.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_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019e4b0b-96e1-7db8-babe-f1e514e49112_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net increase (decrease) in cash, cash equivalents and restricted cash, and cash and cash equivalents of consolidated VIEs</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" 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, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <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_DeferredTaxAssetsNet_019e4b0b-97b1-752d-aa24-07e945df6c9a_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/2026/elts/us-gaap-2026.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_us-gaap_DeferredTaxAssetsGross_019e4b0b-97b1-71f0-8989-c02ccff6e5fd_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/2026/elts/us-gaap-2026.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_NetIncomeLoss_019e4b0b-97b1-7517-9090-d7d02bb97767_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_019e4b0b-97b1-7201-8d70-8429faec46c4_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_019e4b0b-97b1-73ac-bab4-a65a98e73463_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/2026/elts/us-gaap-2026.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_LongtermDebtTypeAxis_019e4b0b-97b1-73e6-afc4-941fbbc16a5a_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_us-gaap_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYear_019e4b0b-97b1-78cd-ab4c-01ee5b9f2b11_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight_019e4b0b-9859-773e-a696-163ddb6a40e8_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>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" 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 Each Warrant or Right</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:to="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_019e4b0b-97b1-74ce-b424-277758925184_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/2026/elts/us-gaap-2026.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_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearThree_019e4b0b-9859-70be-82f9-2b24527217f3_terseLabel_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</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-20260630.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_logan_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitIncreaseDecreaseFromCashFlowChange_019e4b0b-9859-777d-b2f6-760b9219e6ae_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-20260630.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_logan_IncomeFromProfitSharingAgreement_019e4b0b-97b1-7fff-bbdb-061637d4da43_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-20260630.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_019e4b0b-97b1-7f14-b644-71d352078fa0_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-20260630.xsd#logan_FeeIncomeAdjusted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FeeIncomeAdjusted" xlink:to="lab_logan_FeeIncomeAdjusted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery_019e4b0b-9859-7670-8e62-4e8cbe0dbb05_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/2026/elts/us-gaap-2026.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_logan_ValuationTechniqueRecentTransactionsMember_019e4b0b-97b1-7d1c-8cb2-79ffac913d5c_terseLabel_en-US" xlink:label="lab_logan_ValuationTechniqueRecentTransactionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recent transaction</link:label>
    <link:label id="lab_logan_ValuationTechniqueRecentTransactionsMember_label_en-US" xlink:label="lab_logan_ValuationTechniqueRecentTransactionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Recent Transactions [Member]</link:label>
    <link:label id="lab_logan_ValuationTechniqueRecentTransactionsMember_documentation_en-US" xlink:label="lab_logan_ValuationTechniqueRecentTransactionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Valuation Technique, Recent Transactions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ValuationTechniqueRecentTransactionsMember" xlink:href="logan-20260630.xsd#logan_ValuationTechniqueRecentTransactionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ValuationTechniqueRecentTransactionsMember" xlink:to="lab_logan_ValuationTechniqueRecentTransactionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfOtherAssetsTableTextBlock_019e4b0b-9859-719b-adc0-cad326597765_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/2026/elts/us-gaap-2026.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_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet_019e4b0b-9859-7ff0-858c-80fa9249799c_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet" xlink:to="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenuesAbstract_019e4b0b-9859-7f9c-be68-cd505510a563_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/2026/elts/us-gaap-2026.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_us-gaap_FairValueOptionChangesInFairValueGainLoss1_019e4b0b-9859-737a-87ce-f414d197d881_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/2026/elts/us-gaap-2026.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_us-gaap_FairValueLiabilityRecurringBasisStillHeldUnrealizedGainLossOci_019e4b0b-9859-7a75-abfa-cc231846e057_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilityRecurringBasisStillHeldUnrealizedGainLossOci" 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_FairValueLiabilityRecurringBasisStillHeldUnrealizedGainLossOci_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilityRecurringBasisStillHeldUnrealizedGainLossOci" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liability, Recurring Basis, Still Held, Unrealized Gain (Loss), OCI</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilityRecurringBasisStillHeldUnrealizedGainLossOci" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueLiabilityRecurringBasisStillHeldUnrealizedGainLossOci"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilityRecurringBasisStillHeldUnrealizedGainLossOci" xlink:to="lab_us-gaap_FairValueLiabilityRecurringBasisStillHeldUnrealizedGainLossOci" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:to="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ClassOfWarrantOrRightNumberOfWarrantsIssuedForEachUnit_019e4b0b-97b1-73ba-992d-04d1a61c597b_terseLabel_en-US" xlink:label="lab_logan_ClassOfWarrantOrRightNumberOfWarrantsIssuedForEachUnit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants issued per unit (in shares)</link:label>
    <link:label id="lab_logan_ClassOfWarrantOrRightNumberOfWarrantsIssuedForEachUnit_label_en-US" xlink:label="lab_logan_ClassOfWarrantOrRightNumberOfWarrantsIssuedForEachUnit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Number Of Warrants Issued For Each Unit</link:label>
    <link:label id="lab_logan_ClassOfWarrantOrRightNumberOfWarrantsIssuedForEachUnit_documentation_en-US" xlink:label="lab_logan_ClassOfWarrantOrRightNumberOfWarrantsIssuedForEachUnit" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Number Of Warrants Issued For Each Unit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ClassOfWarrantOrRightNumberOfWarrantsIssuedForEachUnit" xlink:href="logan-20260630.xsd#logan_ClassOfWarrantOrRightNumberOfWarrantsIssuedForEachUnit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ClassOfWarrantOrRightNumberOfWarrantsIssuedForEachUnit" xlink:to="lab_logan_ClassOfWarrantOrRightNumberOfWarrantsIssuedForEachUnit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OciLiabilityForFuturePolicyBenefitGainLossAfterReclassificationAdjustmentBeforeTaxParent_019e4b0b-97b1-745d-a9ee-5d67a6d41361_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 and reinsurance recoverable 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/2026/elts/us-gaap-2026.xsd#us-gaap_OciLiabilityForFuturePolicyBenefitGainLossAfterReclassificationAdjustmentBeforeTaxParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OciLiabilityForFuturePolicyBenefitGainLossAfterReclassificationAdjustmentBeforeTaxParent" xlink:to="lab_us-gaap_OciLiabilityForFuturePolicyBenefitGainLossAfterReclassificationAdjustmentBeforeTaxParent" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_019e4b0b-97b1-7c28-91f5-cead5840cc00_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceLineItems_019e4b0b-97b1-741a-b0f4-cf1275bb76e5_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/2026/elts/us-gaap-2026.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_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationBeforeTaxParent_019e4b0b-9859-7b2d-bb92-0d16d4700975_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_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/2026/elts/us-gaap-2026.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_CededPremiumsEarned_019e4b0b-96e1-7f59-a22c-b1505a239815_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/2026/elts/us-gaap-2026.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_logan_OptionPricingModelMember_019f1493-4c31-781a-9e4c-5f66bce761bf_verboseLabel_en-US" xlink:label="lab_logan_OptionPricingModelMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Option pricing model</link:label>
    <link:label id="lab_logan_OptionPricingModelMember_label_en-US" xlink:label="lab_logan_OptionPricingModelMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Option Pricing Model [Member]</link:label>
    <link:label id="lab_logan_OptionPricingModelMember_documentation_en-US" xlink:label="lab_logan_OptionPricingModelMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Option Pricing Model</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_OptionPricingModelMember" xlink:href="logan-20260630.xsd#logan_OptionPricingModelMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_OptionPricingModelMember" xlink:to="lab_logan_OptionPricingModelMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_019e4b0b-96e1-7ec1-9f5f-4c140eb1c59b_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/2026/dei-2026.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_BusinessCombinationAcquisitionRelatedCosts_019e4b0b-9859-760b-9f92-2aa2318c80ef_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/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationAcquisitionRelatedCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:to="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DebentureWarrantsMember_019e4b0b-9859-770a-b5c9-d9e38b18c66c_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_019e4b0b-9859-7a8b-9154-2eb103d25263_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-20260630.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_CommonStockValue_019e4b0b-97b1-7cf2-a228-4ae756853d0b_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/2026/elts/us-gaap-2026.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_RelatedPartyTransactionDueToAffiliatesPayable_019e4b0b-97b1-7654-88ba-7d610d3f1b26_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-20260630.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_ScheduleOfDebtInstrumentsTextBlock_019e4b0b-9859-7cc7-bfb9-d9cd9c0e5e3f_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>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDebtInstrumentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability_019e4b0b-9859-7c27-8f72-d537f57bfd23_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/2026/elts/us-gaap-2026.xsd#us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability" xlink:to="lab_us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability" xlink:type="arc" order="1"/>
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    <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-20260630.xsd#logan_InsuranceSolutionsRevenueAbstract"/>
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    <link:label id="lab_us-gaap_LineOfCreditMember_019e4b0b-985a-78bc-9c63-cf165cd0fb39_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/2026/elts/us-gaap-2026.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"/>
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    <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/2026/ecd-2026.xsd#ecd_RestatementDeterminationDate"/>
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    <link:label id="lab_logan_NetInvestmentIncomeAndRealizedGainLossNet_019fdc27-a027-7060-9047-fa64aaad4d77_totalLabel_en-US" xlink:label="lab_logan_NetInvestmentIncomeAndRealizedGainLossNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total revenues</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-20260630.xsd#logan_NetInvestmentIncomeAndRealizedGainLossNet"/>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance_019e4b0b-97b1-7c5b-b06c-0f48c9105d9a_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">Change in valuation allowances&#8203;</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/2026/elts/us-gaap-2026.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_ClassOfWarrantOrRightDomain_019e4b0b-9859-7145-b640-96a978b5522c_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/2026/elts/us-gaap-2026.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_logan_MedcoInsuranceCompanyMember_019e4b0b-9859-7c6e-abea-ca73835ac957_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-20260630.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_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_019e4b0b-9859-72f3-8234-8f077a6831c9_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/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock"/>
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    <link:label id="lab_us-gaap_AociLiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeTax_019e4b0b-97b1-792a-88ba-665d96b2633d_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/2026/elts/us-gaap-2026.xsd#us-gaap_AociLiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeTax"/>
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    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwillAbstract_019e4b0b-985a-7995-9457-1a50241ada87_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>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwillAbstract_label_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwillAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Excluding Goodwill, Indefinite-Lived [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwillAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwillAbstract"/>
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    <link:label id="lab_dei_AmendmentFlag_019e4b0b-985a-7a12-9787-81f5039d4808_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AmendmentFlag"/>
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    <link:label id="lab_us-gaap_GoodwillLineItems_019e4b0b-9859-78ba-b84e-f6431bb9be15_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/2026/elts/us-gaap-2026.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_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems_019e4b0b-97b1-7cb1-8014-32b8ddf8daf7_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems" 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_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>
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    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract_019e4b0b-97b1-77d3-af76-8c5d66288752_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/2026/elts/us-gaap-2026.xsd#us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract"/>
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    <link:label id="lab_us-gaap_NetInvestmentIncome_019e4b0b-97b1-799b-b894-4f691ffe0d33_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/2026/elts/us-gaap-2026.xsd#us-gaap_NetInvestmentIncome"/>
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    <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>
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    <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/2026/elts/us-gaap-2026.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_DebtSecuritiesAvailableForSaleTableTextBlock_019e4b0b-97b1-7086-b5a9-19a1f33b253f_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/2026/elts/us-gaap-2026.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_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitOriginalDiscountRateBeforeCashFlowAndReinsurance_019e4b0b-9859-7bc2-9bfa-f12972dc80d2_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_019e4b0b-9859-722c-87f2-4595ea7aaf1d_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitOriginalDiscountRateBeforeCashFlowAndReinsurance" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitOriginalDiscountRateBeforeCashFlowAndReinsurance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitOriginalDiscountRateBeforeCashFlowAndReinsurance" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitOriginalDiscountRateBeforeCashFlowAndReinsurance" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DeferredTaxAssetsUnrealizedLossesOnRemeasurementOfInvestments_019e4b0b-9859-7e70-96d7-c4c75e1b3a89_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-20260630.xsd#logan_DeferredTaxAssetsUnrealizedLossesOnRemeasurementOfInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DeferredTaxAssetsUnrealizedLossesOnRemeasurementOfInvestments" xlink:to="lab_logan_DeferredTaxAssetsUnrealizedLossesOnRemeasurementOfInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationDeductionsDividends_019e4b0b-97b1-7be1-9653-814985e56e79_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/2026/elts/us-gaap-2026.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_logan_OtherAssetsAndOtherLiabilitiesTable_019e4b0b-96e1-7a72-90cb-5fc02b07c2d9_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-20260630.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_019e4b0b-9859-78c0-a8c9-a5626c1630f8_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-20260630.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_logan_ProbabilityWeightedExpectedReturnMethodYearsToCashFlowsMember_019e4b0b-97b1-7bca-b631-14a9cd26d46c_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</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-20260630.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_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss_019e4b0b-97b1-736a-9e42-4798907acfe3_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/2026/elts/us-gaap-2026.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_InterestSensitiveContractBenefitExpense_019e4b0b-97b1-75c7-9f87-fe1f47d54496_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-20260630.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_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/2026/ecd-2026.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3_019e4b0b-97b1-7bcb-8a06-654d2f4b0fba_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>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" 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 Transfers Into Level 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3"/>
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    <link:label id="lab_dei_EntityAddressStateOrProvince_019e4b0b-97b1-77d9-981d-5851acfe4c35_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/2026/dei-2026.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_LicensingAgreementsMember_019e4b0b-96e1-7165-b388-88509ea641c2_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/2026/elts/us-gaap-2026.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_logan_MergersMember_019e4b0b-9859-7d37-9cc1-6abfb000df39_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-20260630.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_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/2026/ecd-2026.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_AssetsFairValueDisclosureAbstract_019e4b0b-97b1-7ef9-88b7-969a047a5695_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/2026/elts/us-gaap-2026.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_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_019e4b0b-9859-7eac-bb36-7112cc4136fa_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_019e4b0b-97b1-71e4-9ff2-24c1538441d5_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/2026/elts/us-gaap-2026.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_WeightedAverageNumberOfSharesOutstandingBasic_019e4b0b-9859-7583-887e-6450104fb807_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_019e4b0b-9859-7988-a5ea-df60f45879ee_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 (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/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_AtlanticCoastLifeInsuranceCompanySurplusNotesMember_019e4b0b-97b1-768c-b339-826dc7170b9d_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-20260630.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_GoodwillImpairedAccumulatedImpairmentLoss_019e4b0b-97b1-7dfe-a1fd-3a0224699d06_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</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/2026/elts/us-gaap-2026.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_logan_PortmanLoganMember_019e4b0b-97b1-77ba-8048-b5d40b6ac050_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-20260630.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_DirectPremiumsEarned_019e4b0b-9859-777d-b2d5-bbb46cded496_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/2026/elts/us-gaap-2026.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_us-gaap_IncreaseDecreaseInDeferredPolicyAcquisitionCosts_019e4b0b-97b1-7efe-ba32-92d1e29ac52b_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/2026/elts/us-gaap-2026.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_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_019e4b0b-9859-750f-bb67-9e24273fd122_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>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" 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 5 Through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRetentionPolicyReinsuredRiskPercentage_019e4b0b-97b1-7c37-83a6-665df7b0ea3e_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/2026/elts/us-gaap-2026.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_DebtObligationMember_019e4b0b-9859-7f3c-9b8e-55d150c6f799_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-20260630.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_logan_InsurancePolicyBenefitsAndClaimsNet_019e4b0b-97b1-776c-8026-6c02e23c7e36_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 $6,064 and $10,523 and $2,945 and $3,025 for the three and six months ended June 30, 2026 and 2025, 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-20260630.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_019e4b0b-97b1-77a2-953c-1f60b9a858e6_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-20260630.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_logan_IncentiveFeeReceivable_019e4b0b-97b1-74e9-9203-7711e66b11d8_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-20260630.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_dei_DocumentInformationLineItems_019e4b0b-9859-758a-86f3-6cf351fe7dc6_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/2026/dei-2026.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_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/2026/ecd-2026.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_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_019e4b0b-97b1-7b10-a7f9-16127345e0b5_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Vested (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" 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, Vested in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_019e4b0b-97b1-7651-a386-9d83e7325110_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</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/2026/elts/us-gaap-2026.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_ReceivableTypeDomain_019fcdad-9964-766d-b4f9-825b8b340ad3_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivableTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable [Domain]</link:label>
    <link:label id="lab_us-gaap_ReceivableTypeDomain_label_en-US" xlink:label="lab_us-gaap_ReceivableTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivableTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReceivableTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivableTypeDomain" xlink:to="lab_us-gaap_ReceivableTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_019e4b0b-97b1-7501-9ef5-efec2571e844_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated amortization</link:label>
    <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">Intangible Asset, Finite-Lived, Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_IndefiniteLivedIntangibleAssetsAccumulatedImpairment_019e4b0b-9859-7ecb-bdb3-ff696de33646_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-20260630.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_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_019e4b0b-97b1-7db7-b772-f53fbc4ba1e0_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/2026/elts/us-gaap-2026.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_logan_DebtInstrumentInterestRatePayablePeriodAxis_019e4b0b-97b1-7703-af83-74d313613e00_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-20260630.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_ReinsuranceRecoverableCreditLossExpenseReversal_019e4b0b-98ea-7ddb-9a70-de25f3bee22a_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 (reversal) for reinsurance recoverable</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/2026/elts/us-gaap-2026.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_logan_NumberOfProductLines_019e4b0b-97b1-7439-80e4-40ebd15a7f49_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-20260630.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_logan_AdditionalLiabilityLongDurationInsuranceWeightedAverageDurationAtOriginalRate_019e4b0b-9859-7064-808d-cab9dc919372_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-20260630.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_us-gaap_InvestmentIncomeInvestmentExpense_019e4b0b-97b1-721a-8ffd-a3076a9503e9_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_019e4b0b-97b1-721d-9408-531257981341_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/2026/elts/us-gaap-2026.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_us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs_019e4b0b-9859-7ff6-8bc2-919e3199ca94_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/2026/elts/us-gaap-2026.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_NewAccountingPronouncementsPolicyPolicyTextBlock_019e4b0b-9859-7506-bd04-61aa02ffccf9_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 issued accounting pronouncements</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <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_AmortizationOfFinancingCosts_019e4b0b-9859-7ff5-a50b-255cb3dd3ea3_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/2026/elts/us-gaap-2026.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_UnsecuredDebtMember_019e4b0b-9859-72ae-b468-e5d4513fa7fd_terseLabel_en-US" xlink:label="lab_us-gaap_UnsecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured Debt</link:label>
    <link:label id="lab_us-gaap_UnsecuredDebtMember_label_en-US" xlink:label="lab_us-gaap_UnsecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnsecuredDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnsecuredDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnsecuredDebtMember" xlink:to="lab_us-gaap_UnsecuredDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InternalCreditAssessmentLevelFourMember_019e4b0b-96e1-7c9a-af4e-a68eac2252bf_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>
    <link:loc xlink:type="locator" xlink:label="loc_logan_InternalCreditAssessmentLevelFourMember" xlink:href="logan-20260630.xsd#logan_InternalCreditAssessmentLevelFourMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InternalCreditAssessmentLevelFourMember" xlink:to="lab_logan_InternalCreditAssessmentLevelFourMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_019e4b0b-97b1-7346-99ba-81a3474a8813_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_019e4b0b-97b1-7324-b45e-05b85d63a4d6_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/2026/elts/us-gaap-2026.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_LongTermDebt_019e4b0b-9859-7356-b42f-1c30e85b45bf_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_019e4b0b-9859-7970-a037-1b01aa0c8d7a_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_019e4b0b-9859-725d-99b7-c4dea7405868_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/2026/elts/us-gaap-2026.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_logan_StockIssuedDuringPeriodSharesShareBasedPaymentArrangement_019e4b0b-9859-744b-b322-e9f8d01d2c1e_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 (in shares)</link:label>
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    <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-20260630.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_019e4b0b-9859-79a1-85a5-c200cb695fbd_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-20260630.xsd#logan_ScheduleOfFuturePolicyBenefitsAndReinsuranceRecoverableTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ScheduleOfFuturePolicyBenefitsAndReinsuranceRecoverableTableTextBlock" xlink:to="lab_logan_ScheduleOfFuturePolicyBenefitsAndReinsuranceRecoverableTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e4b0b-97b1-73c6-8d6a-34a9110854bf_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/2026/elts/us-gaap-2026.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_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>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in the Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:to="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_019e4b0b-97b1-7349-a7db-9d460a1f9d0d_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/2026/elts/us-gaap-2026.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_CostsAndExpensesAbstract_019e4b0b-96e1-7693-abd1-b0f8dec59ba3_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/2026/elts/us-gaap-2026.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_dei_SecurityExchangeName_019e4b0b-97b1-7905-83cc-578d4690214c_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/2026/dei-2026.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_logan_PromissoryNoteDueOctober2040Member_019e4b0b-97b1-78d4-bc30-ea2766c50542_terseLabel_en-US" xlink:label="lab_logan_PromissoryNoteDueOctober2040Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Promissory Note due October 2040</link:label>
    <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-20260630.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_ReinsuranceRecoverablesGrossAbstract_019e4b0b-96e1-7bea-9eaf-afdeeb71ae0a_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/2026/elts/us-gaap-2026.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"/>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_019e4b0b-9859-7a76-9e8b-15563d1015ac_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/2026/elts/us-gaap-2026.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_NotesReceivableGross_019e4b0b-97b1-78e9-9442-3002a707901d_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_019e4b0b-97b1-74a4-8e88-23cba8899519_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/2026/elts/us-gaap-2026.xsd#us-gaap_NotesReceivableGross"/>
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    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_019e4b0b-97b1-77f5-909a-bb3d374d87d7_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/2026/elts/us-gaap-2026.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_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger_019e4b0b-9859-723b-a463-bd6c853d7a09_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/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger"/>
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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/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract"/>
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    <link:label id="lab_logan_InsuranceSolutionsSegmentMember_019e4b0b-97b1-7083-bab4-c8d4ce71e00e_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_019e4b0b-97b1-70f2-85d1-ba9a6a6ed67b_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-20260630.xsd#logan_InsuranceSolutionsSegmentMember"/>
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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>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryIndName"/>
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    <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>
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    <link:label id="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_019e4b0b-97b1-7666-8778-f9293b810a8a_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/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit"/>
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    <link:label id="lab_us-gaap_OtherLiabilitiesTableTextBlock_019e4b0b-9859-7165-9b87-dcb6c75270b2_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">Schedule of 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/2026/elts/us-gaap-2026.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_srt_SegmentGeographicalDomain_019e4b0b-97b1-7c1d-9a68-d8120aabfd23_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/2026/elts/srt-2026.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_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_019e4b0b-97b1-7f34-bbda-b369689c6985_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">Intangible Asset, Excluding Goodwill, Indefinite-Lived</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_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/2026/ecd-2026.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"/>
    <link:label id="lab_logan_APICShareBasedPaymentArrangementRestrictedStockDecreaseForStockRelease_019e4b0b-9859-7ef4-bc30-89b3441e11b9_terseLabel_en-US" xlink:label="lab_logan_APICShareBasedPaymentArrangementRestrictedStockDecreaseForStockRelease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted share units release</link:label>
    <link:label id="lab_logan_APICShareBasedPaymentArrangementRestrictedStockDecreaseForStockRelease_label_en-US" xlink:label="lab_logan_APICShareBasedPaymentArrangementRestrictedStockDecreaseForStockRelease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Restricted Stock, Decrease for Stock Release</link:label>
    <link:label id="lab_logan_APICShareBasedPaymentArrangementRestrictedStockDecreaseForStockRelease_documentation_en-US" xlink:label="lab_logan_APICShareBasedPaymentArrangementRestrictedStockDecreaseForStockRelease" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Restricted Stock, Decrease for Stock Release</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_APICShareBasedPaymentArrangementRestrictedStockDecreaseForStockRelease" xlink:href="logan-20260630.xsd#logan_APICShareBasedPaymentArrangementRestrictedStockDecreaseForStockRelease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_APICShareBasedPaymentArrangementRestrictedStockDecreaseForStockRelease" xlink:to="lab_logan_APICShareBasedPaymentArrangementRestrictedStockDecreaseForStockRelease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitUndiscountedBeforeReinsurance_019e4b0b-98ea-72ac-a382-28c7cff52a58_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/2026/elts/us-gaap-2026.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_PaidInKindInterestNet_019e4b0b-9859-7114-bb15-2c1edc5f7016_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-20260630.xsd#logan_PaidInKindInterestNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_PaidInKindInterestNet" xlink:to="lab_logan_PaidInKindInterestNet" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_ProfitSharingInterestDistributionEntitlementPercentage_019e4b0b-9859-712f-9c68-d1bc82576e49_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>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ProfitSharingInterestDistributionEntitlementPercentage" xlink:href="logan-20260630.xsd#logan_ProfitSharingInterestDistributionEntitlementPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ProfitSharingInterestDistributionEntitlementPercentage" xlink:to="lab_logan_ProfitSharingInterestDistributionEntitlementPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_RelatedPartyInterestIncomeMember_019e4b0b-96e1-7d1e-8023-4ce6e7100cc3_terseLabel_en-US" xlink:label="lab_logan_RelatedPartyInterestIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Interest Income</link:label>
    <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-20260630.xsd#logan_RelatedPartyInterestIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_RelatedPartyInterestIncomeMember" xlink:to="lab_logan_RelatedPartyInterestIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract_019e4b0b-96e1-76c1-9d60-d50de7b6db79_terseLabel_en-US" xlink:label="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental Disclosures of Non-Cash Investing and Financing Activities</link:label>
    <link:label id="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract_label_en-US" xlink:label="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash Investing and Financing Items [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoncashInvestingAndFinancingItemsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:to="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_019e4b0b-97b1-7c40-8a01-3d5dd4bee5e3_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/2026/elts/us-gaap-2026.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_us-gaap_DebtInstrumentCarryingAmount_019e4b0b-96e1-7bdf-8cad-f39cc91a1202_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_019e4b0b-96e1-782e-8c70-907c811fa5f7_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_019e4b0b-96e1-7f63-bd20-6ef8e7ac7915_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/2026/elts/us-gaap-2026.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_us-gaap_DebtSecuritiesMember_019e4b0b-97b1-74f9-9a34-03676b66ebfd_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/2026/elts/us-gaap-2026.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_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_019e4b0b-97b1-724c-8725-9ebcbdbeb76d_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/2026/elts/us-gaap-2026.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_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_logan_UnsecuredPromissoryNoteMember_019e4b0b-97b1-73fd-934d-bfbd313456ff_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-20260630.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_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/2026/ecd-2026.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_019e4b0b-9859-79da-86f8-b6b7c1396a09_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_019e4b0b-9859-7127-9de5-6300724cfd70_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/2026/elts/us-gaap-2026.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_WarrantMember_019e4b0b-9859-7ab2-ba60-8a50b2b27ad6_verboseLabel_en-US" xlink:label="lab_us-gaap_WarrantMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Warrants</link:label>
    <link:label id="lab_us-gaap_WarrantMember_019e4b0b-9859-7e9f-956b-ac2479eeeeef_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 unexercised 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/2026/elts/us-gaap-2026.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_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019e4b0b-97b1-79e2-948d-099cd0124a12_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_019e4b0b-97b1-7db9-bb6d-229e193cc7c6_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/2026/elts/us-gaap-2026.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_us-gaap_DisaggregationOfRevenueLineItems_019e4b0b-97b1-7a97-bac0-6515619943b8_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <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/2026/elts/us-gaap-2026.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_logan_IncomeLossFromContinuingOperationsBeforeIncomeTaxesNoncontrollingInterestAdjusted_019e4b0b-9859-7d1c-9df0-193b56de1681_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-20260630.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_019e4b0b-97b1-732d-ac5b-88bf21213060_terseLabel_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</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-20260630.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_dei_EntityEmergingGrowthCompany_019e4b0b-97b1-7421-9cd1-058a166d25cb_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/2026/dei-2026.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_us-gaap_RelatedPartyTransactionLineItems_019e4b0b-9859-73ab-9b90-a8c1cf9de21d_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/2026/elts/us-gaap-2026.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_ScheduleOfCededCreditRiskByReinsurerTextBlock_019e4b0b-9859-76e7-b36b-ae2451c16c57_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/2026/elts/us-gaap-2026.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_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseRemainderOfFiscalYear_019e4b0b-96e1-7c4f-a923-15282fdbbdd1_terseLabel_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remainder of 2026</link:label>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseRemainderOfFiscalYear_label_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense, Remainder Of Fiscal Year</link:label>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseRemainderOfFiscalYear_documentation_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense, Remainder Of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseRemainderOfFiscalYear" xlink:href="logan-20260630.xsd#logan_DeferredPolicyAcquisitionCostsAmortizationExpenseRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseRemainderOfFiscalYear" xlink:to="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableOriginatedInCurrentFiscalYear_019e4b0b-9859-7cea-931b-0e7903e7313a_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_CommercialPaperMember_019e4b0b-97b1-7f74-9a2e-33693b28f6cf_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/2026/elts/us-gaap-2026.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_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_019e4b0b-9859-71eb-a085-ac42612add2e_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>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount_019e4b0b-9859-739d-924c-f21b87e532b4_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/2026/elts/us-gaap-2026.xsd#us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:to="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromCollectionOfOtherReceivables_019e4b0b-97b1-71ec-a210-b26de4425b61_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromCollectionOfOtherReceivables" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from collection of receivables</link:label>
    <link:label id="lab_us-gaap_ProceedsFromCollectionOfOtherReceivables_label_en-US" xlink:label="lab_us-gaap_ProceedsFromCollectionOfOtherReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Collection of Other Receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromCollectionOfOtherReceivables" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromCollectionOfOtherReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromCollectionOfOtherReceivables" xlink:to="lab_us-gaap_ProceedsFromCollectionOfOtherReceivables" xlink:type="arc" order="1"/>
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    <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>
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    <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>
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    <link:label id="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit_019e4b0b-9859-77f9-9d40-2cd1e58c7eac_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_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">Intangible Asset, Goodwill and Other [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract"/>
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    <link:label id="lab_logan_UnrealizedGainLossOnInvestmentsAsAdjusted_documentation_en-US" xlink:label="lab_logan_UnrealizedGainLossOnInvestmentsAsAdjusted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) on Investments, As Adjusted</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYear_019e4b0b-97b1-7252-870f-d55bd9b563e2_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>
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    <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>
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    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Unsecured Debt</link:label>
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    <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">Intangible Asset, Indefinite-Lived, Class [Domain]</link:label>
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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_logan_A2019RSUPlanMember_documentation_en-US" xlink:label="lab_logan_A2019RSUPlanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2019 RSU Plan</link:label>
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    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants_019e4b0b-97b1-7c76-9891-8e4c2cca4d62_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>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_019e4b0b-9859-75f3-9ef9-0bede0768c58_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unvested, beginning balance (in dollars per share)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" 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/2026/ecd-2026.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_logan_ValuationTechniqueEnterpriseValueMember_019e4b0b-9859-78de-9d17-31b74491f485_terseLabel_en-US" xlink:label="lab_logan_ValuationTechniqueEnterpriseValueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Enterprise value</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ValuationTechniqueEnterpriseValueMember" xlink:href="logan-20260630.xsd#logan_ValuationTechniqueEnterpriseValueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ValuationTechniqueEnterpriseValueMember" xlink:to="lab_logan_ValuationTechniqueEnterpriseValueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_019e4b0b-98ea-7692-bbfd-cfd920a98aa7_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_AssetAcquisitionDomain_019e4b0b-96e1-7d42-b963-6d783e1aab92_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/2026/elts/us-gaap-2026.xsd#us-gaap_AssetAcquisitionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionDomain" xlink:to="lab_us-gaap_AssetAcquisitionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesTreasuryStockReissued_019e4b0b-97b1-70ce-ab68-31b4eed4c8c0_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesTreasuryStockReissued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common shares for vested Restricted Share Units (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesTreasuryStockReissued_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesTreasuryStockReissued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Treasury Stock Reissued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesTreasuryStockReissued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesTreasuryStockReissued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesTreasuryStockReissued" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesTreasuryStockReissued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_019e4b0b-97b1-7d4f-b533-7036ca84e29b_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>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" 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/2026/elts/us-gaap-2026.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_us-gaap_DeferredPolicyAcquisitionCostsAdditions_019e4b0b-97b1-7efb-924c-1fdd624761e7_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/2026/elts/us-gaap-2026.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_us-gaap_SegmentReportingDisclosureTextBlock_019e4b0b-97b1-788c-87dc-880dfd666346_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 [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.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_srt_MinimumMember_019e4b0b-9859-72fa-8464-7b9e482b40cb_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_019e4b0b-97b1-7e9d-8d44-ae733d9e4599_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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable"/>
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    <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/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueTableTextBlock"/>
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    <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/2026/elts/us-gaap-2026.xsd#us-gaap_VariableInterestEntityDisclosureTextBlock"/>
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    <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/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAbstract"/>
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    <link:label id="lab_us-gaap_ClassOfWarrantOrRightAxis_019e4b0b-97b1-7a16-9898-c96f91d2a301_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/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfWarrantOrRightAxis"/>
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    <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>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DependentProbabilitiesMember_019e4b0b-97b1-7d83-8330-17bbd8a40af1_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-20260630.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_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_019e4b0b-9859-75ca-9ef6-519b02cbf767_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/2026/elts/us-gaap-2026.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_RepaymentsOfNotesPayable_019e4b0b-97b1-735a-bd40-0843bbdc8560_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>
    <link:label id="lab_us-gaap_RepaymentsOfNotesPayable_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfNotesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Notes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfNotesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfNotesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfNotesPayable" xlink:to="lab_us-gaap_RepaymentsOfNotesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure_019e4b0b-9859-7b41-9c57-4c2123b63b68_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/2026/elts/us-gaap-2026.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_us-gaap_DerivativeMember_019e4b0b-97b1-78a2-bd9d-2f25c3c7504c_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_019e4b0b-97b1-7f89-b15b-c312fd8453f8_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Derivative income (expense)</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/2026/elts/us-gaap-2026.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_BusinessAcquisitionLineItems_019e4b0b-97b1-74a8-a241-37143ab2c521_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/2026/elts/us-gaap-2026.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_CommonStockSharesAuthorized_019e4b0b-97b1-7874-a784-1278f05aae04_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/2026/elts/us-gaap-2026.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_AccumulatedOtherComprehensiveIncomeLossLineItems_019e4b0b-97b1-74b2-889d-338674b9d6ca_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/2026/elts/us-gaap-2026.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_ConcentrationRiskDisclosureTextBlock_019e4b0b-97b1-7d89-bdf2-6404f2f53636_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/2026/elts/us-gaap-2026.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_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock_019e4b0b-9859-7ee4-8dd9-a251ce5426c6_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">Schedule of 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/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue_019e4b0b-9859-7556-b17f-b1c6eaa9bae3_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_us-gaap_AvailableForSaleDebtSecuritiesGrossUnrealizedLoss_019e4b0b-9859-75f7-94f2-0cbe8b3a3214_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/2026/elts/us-gaap-2026.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_us-gaap_SegmentReportingInformationLineItems_019e4b0b-97b1-74db-ae29-558218a343e4_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 [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 [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.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_logan_LiabilityForFuturePolicyBenefitReinsuranceAssumed_019e4b0b-96e1-7f16-b1aa-ceb51d6a60cf_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-20260630.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_dei_DocumentQuarterlyReport_019e4b0b-9859-7730-9dee-69bc08c4a7a8_terseLabel_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:label id="lab_dei_DocumentQuarterlyReport_label_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentQuarterlyReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentQuarterlyReport"/>
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    <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/2026/ecd-2026.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
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    <link:label id="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember_019e4b0b-97b1-72ea-af23-558880745334_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_019e4b0b-97b1-7e74-9a46-e4a58bd8576f_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/2026/elts/us-gaap-2026.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_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock_019e4b0b-9859-71b3-8349-3d3017bbc3c5_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/2026/elts/us-gaap-2026.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_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_019f5a11-e18f-7b8f-af7d-6bcac811d0a9_terseLabel_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of Exchange Rate on Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_label_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effect of Exchange Rate on Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations"/>
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    <link:label id="lab_us-gaap_AccountsReceivableNet_019e4b0b-97b1-7756-a477-e596eda74ce6_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/2026/elts/us-gaap-2026.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_us-gaap_ReceivableInvestmentSale_019e4b0b-97b1-75ca-9729-3afffe1608d6_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/2026/elts/us-gaap-2026.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_RepaymentsOfLongTermDebt_019e4b0b-96e1-7bfa-ac70-d3e55661c8ea_terseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repayments of long-term debt</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfLongTermDebt" xlink:to="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSalesAndRepayments_019e4b0b-96e1-742d-b65e-951b8736d59c_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-20260630.xsd#logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSalesAndRepayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSalesAndRepayments" xlink:to="lab_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSalesAndRepayments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_019e4b0b-97b1-7c90-8163-df205bd9d956_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/2026/elts/us-gaap-2026.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_logan_ScheduleOfFinancialAssetsTableTextBlock_019e4b0b-97b1-78f5-98f2-42310a7daa16_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-20260630.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_DeferredPolicyAcquisitionCosts_019e4b0b-9859-700b-98c6-a294a90f50f3_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_019e4b0b-9859-7d7a-9665-f1da30b0d0b2_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_019e4b0b-9859-7b58-adb2-e64357760806_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_019e4b0b-9859-7a46-a4a4-b596b1a0ebf1_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/2026/elts/us-gaap-2026.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_MeasurementInputTypeDomain_019e4b0b-96e1-733c-b1c1-0c75f4b22611_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/2026/elts/us-gaap-2026.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_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1_019e4b0b-985a-70f6-b7a6-bfd72118df0f_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_srt_RepurchaseAgreementCounterpartyNameDomain_019e4b0b-9859-7eb3-b62c-4da562050ec7_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/2026/elts/srt-2026.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_PolicyholderAccountBalanceMinimumGuaranteedInterestRates_019e4b0b-9859-76dd-bac5-007c456e2763_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-20260630.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_ScenarioPlanMember_019e4b0b-97b1-7cf8-a075-da2c6cd599e7_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/2026/elts/us-gaap-2026.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_us-gaap_FairValueConcentrationOfRiskInvestments_019e4b0b-9859-72b8-93c5-02123651546c_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/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueConcentrationOfRiskInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueConcentrationOfRiskInvestments" xlink:to="lab_us-gaap_FairValueConcentrationOfRiskInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidInsurance_019e4b0b-9859-7aba-b74a-e3ac07acfd01_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/2026/elts/us-gaap-2026.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_us-gaap_ReinsuranceEffectOnClaimsAndBenefitsIncurredAmountAssumed_019e4b0b-97b1-7d14-bcd2-1bfcdf075d21_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceEffectOnClaimsAndBenefitsIncurredAmountAssumed" 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_ReinsuranceEffectOnClaimsAndBenefitsIncurredAmountAssumed_label_en-US" xlink:label="lab_us-gaap_ReinsuranceEffectOnClaimsAndBenefitsIncurredAmountAssumed" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Benefits and Claims Incurred, Assumed</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceEffectOnClaimsAndBenefitsIncurredAmountAssumed" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsuranceEffectOnClaimsAndBenefitsIncurredAmountAssumed"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceEffectOnClaimsAndBenefitsIncurredAmountAssumed" xlink:to="lab_us-gaap_ReinsuranceEffectOnClaimsAndBenefitsIncurredAmountAssumed" 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/2026/ecd-2026.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_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/2026/ecd-2026.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_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/2026/ecd-2026.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_OperatingLeaseLiability_019e4b0b-9859-7aaf-b02c-dbdb7e1be7e5_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/2026/elts/us-gaap-2026.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_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_019e4b0b-9859-7139-a497-808d99907edb_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/2026/elts/us-gaap-2026.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_us-gaap_InterestIncomeOperating_019e4b0b-97b1-76db-b177-36d2128ec01a_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/2026/elts/us-gaap-2026.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_logan_SharesIssuedRestrictedStockReleaseShares_019e4b0b-9859-7d35-b55c-e7ba4f493f8f_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 share unit 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-20260630.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_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/2026/ecd-2026.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"/>
    <link:label id="lab_us-gaap_RepaymentsOfDebt_019e4b0b-97b1-75aa-a6cb-0b557f95bf24_terseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repayments of debt</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfDebt" xlink:to="lab_us-gaap_RepaymentsOfDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitReinsuranceRecoverableExcludedFromComputation_019e4b0b-97b1-7644-9568-62805d0e49cc_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-20260630.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_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum_019e4b0b-97b1-763e-a97f-07f8b7c99bf6_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/2026/elts/us-gaap-2026.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_BusinessAcquisitionAcquireeDomain_019e4b0b-9859-76a2-b44d-bafe4988c4e5_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/2026/elts/us-gaap-2026.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_CommitmentsAndContingenciesDisclosureTextBlock_019e4b0b-9859-7ef1-a238-6bf9194a780e_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/2026/elts/us-gaap-2026.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_ecd_CompActuallyPaidVsNetIncomeTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsNetIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_019e4b0b-9859-7155-8f5e-81cc6abac151_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/2026/elts/us-gaap-2026.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_RestrictedStockUnitsRSUMember_019e4b0b-9859-7411-a724-1823f6fd515b_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_019e4b0b-9859-725c-ac53-e2e6871fa225_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/2026/elts/us-gaap-2026.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_us-gaap_PolicyholderAccountBalancePolicyCharge_019e4b0b-9859-726d-9982-0cd34912325c_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/2026/elts/us-gaap-2026.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_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_019e4b0b-97b1-7f11-b808-b64ef1f4649e_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>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:to="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_InsuranceSolutionsSegmentConsolidatedVIEsMember_019e4b0b-9859-7ce9-a78f-117b4e99fab6_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-20260630.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_srt_WeightedAverageMember_019e4b0b-97b1-7429-9f8c-eebc58713f47_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/2026/elts/srt-2026.xsd#srt_WeightedAverageMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_WeightedAverageMember" xlink:to="lab_srt_WeightedAverageMember" 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/2026/ecd-2026.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"/>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_019e4b0b-96e1-762c-af56-bb98fecfc5dd_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/2026/elts/us-gaap-2026.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_us-gaap_BusinessAcquisitionAxis_019e4b0b-9859-7a9e-8d11-e7d6a09b26dd_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/2026/elts/us-gaap-2026.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_FinancingCostsPaidAndDeferred_019e4b0b-9859-7a4e-b8b7-df18783ddf19_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-20260630.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_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e4b0b-9859-7a79-b585-50597172e164_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
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    <link:label id="lab_logan_ConsolidatedBalanceIncludingVariableInterestEntityMember_019e4b0b-9859-70dc-97dc-dcec5a738a89_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-20260630.xsd#logan_ConsolidatedBalanceIncludingVariableInterestEntityMember"/>
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    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefits_019e4b0b-97b1-7b7e-9ee8-a7ec6657ad80_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_019e4b0b-97b1-767d-b43e-39763c321079_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_019e4b0b-97b1-764b-b1f8-6cdb1af4c2f8_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/2026/elts/us-gaap-2026.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_StockholdersEquityAbstract_019e4b0b-9859-7c49-937d-96a45994941a_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/2026/elts/us-gaap-2026.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_dei_DocumentTransitionReport_019e4b0b-96e1-7e5f-b0cd-7092bc874376_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/2026/dei-2026.xsd#dei_DocumentTransitionReport"/>
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    <link:label id="lab_us-gaap_GainLossOnInvestments_019e4b0b-97b1-7e8e-8e7d-8141a51b458d_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net realized and change in unrealized gains (losses) from investment activities</link:label>
    <link:label id="lab_us-gaap_GainLossOnInvestments_019e4b0b-97b1-75bc-9506-e7b351a2223d_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 realized and change in unrealized 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/2026/elts/us-gaap-2026.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_IntersegmentEliminationMember_019e4b0b-96e1-7b17-af63-9411d34c6f4e_terseLabel_en-US" xlink:label="lab_us-gaap_IntersegmentEliminationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intersegment Eliminations</link:label>
    <link:label id="lab_us-gaap_IntersegmentEliminationMember_label_en-US" xlink:label="lab_us-gaap_IntersegmentEliminationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intersegment Eliminations [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntersegmentEliminationMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IntersegmentEliminationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntersegmentEliminationMember" xlink:to="lab_us-gaap_IntersegmentEliminationMember" xlink:type="arc" order="1"/>
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    <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/2026/elts/us-gaap-2026.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
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    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_019e4b0b-9859-7f2f-83c8-fa361f58fd79_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 Intangible Asset, Finite-Lived</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">Intangible Asset, Finite-Lived [Table Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsNetOfValuationAllowanceAbstract_019e4b0b-97b1-7674-9570-491831c4e147_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/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxAssetsNetOfValuationAllowanceAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsNetOfValuationAllowanceAbstract" xlink:to="lab_us-gaap_DeferredTaxAssetsNetOfValuationAllowanceAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverables_019e4b0b-97b1-739d-bf93-44291a57e1e5_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_019e4b0b-97b1-7f0f-8cfa-b19ba86ebde9_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/2026/elts/us-gaap-2026.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_OtherCommitmentsDomain_019e4b0b-97b1-740e-b1cc-dfd6a3000a06_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>
    <link:label id="lab_us-gaap_OtherCommitmentsDomain_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitmentsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentsDomain" xlink:to="lab_us-gaap_OtherCommitmentsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_019e4b0b-98ea-75f9-a666-170229a6db76_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/2026/dei-2026.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_BusinessCombinationConsiderationTransferredShares_019e4b0b-9859-763f-90ad-61011f52c31c_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-20260630.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_SharesIssuedSharesShareBasedPaymentArrangementAfterForfeitureNet_019e4b0b-97b1-7012-87dd-de410a3b28a2_terseLabel_en-US" xlink:label="lab_logan_SharesIssuedSharesShareBasedPaymentArrangementAfterForfeitureNet" 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_SharesIssuedSharesShareBasedPaymentArrangementAfterForfeitureNet_label_en-US" xlink:label="lab_logan_SharesIssuedSharesShareBasedPaymentArrangementAfterForfeitureNet" 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, Net</link:label>
    <link:label id="lab_logan_SharesIssuedSharesShareBasedPaymentArrangementAfterForfeitureNet_documentation_en-US" xlink:label="lab_logan_SharesIssuedSharesShareBasedPaymentArrangementAfterForfeitureNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Shares Issued, Shares, Share-Based Payment Arrangement, after Forfeiture, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_SharesIssuedSharesShareBasedPaymentArrangementAfterForfeitureNet" xlink:href="logan-20260630.xsd#logan_SharesIssuedSharesShareBasedPaymentArrangementAfterForfeitureNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_SharesIssuedSharesShareBasedPaymentArrangementAfterForfeitureNet" xlink:to="lab_logan_SharesIssuedSharesShareBasedPaymentArrangementAfterForfeitureNet" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_SurplusNotesMember_019e4b0b-97b1-7fe3-b3eb-1dfa452a1d22_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-20260630.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_logan_DebtInstrumentDebentureUnitsIssued_019e4b0b-96e1-737a-8dff-ff9631a02f13_terseLabel_en-US" xlink:label="lab_logan_DebtInstrumentDebentureUnitsIssued" 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_DebtInstrumentDebentureUnitsIssued_label_en-US" xlink:label="lab_logan_DebtInstrumentDebentureUnitsIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Debenture Units, Issued</link:label>
    <link:label id="lab_logan_DebtInstrumentDebentureUnitsIssued_documentation_en-US" xlink:label="lab_logan_DebtInstrumentDebentureUnitsIssued" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Debenture Units, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_DebtInstrumentDebentureUnitsIssued" xlink:href="logan-20260630.xsd#logan_DebtInstrumentDebentureUnitsIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_DebtInstrumentDebentureUnitsIssued" xlink:to="lab_logan_DebtInstrumentDebentureUnitsIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationTable_019e4b0b-97b1-7044-9b61-af1ac78139ec_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>
    <link:label id="lab_dei_DocumentInformationTable_label_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationTable" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentInformationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationTable" xlink:to="lab_dei_DocumentInformationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_019e4b0b-97b1-7f64-a7b0-ea8ab0401ed1_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent events</link:label>
    <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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_NetInvestmentIncomeTextBlock_019e4b0b-97b1-735d-9db7-45743845371d_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-20260630.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_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/2026/ecd-2026.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_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_019e4b0b-97b1-7da0-8a8b-dd92b8e44e29_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>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" 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, Weighted Average Grant Date Fair Value [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_019e4b0b-97b1-7492-aac8-0243350d791a_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/2026/dei-2026.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_EffectiveIncomeTaxRateReconciliationLineItems_019e4b0b-9859-7548-8b3d-4213cff876ef_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/2026/elts/us-gaap-2026.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalLiabilityLongDurationInsuranceTableTextBlock_019e4b0b-97b1-7ad8-ac6c-ab672b8ab0a5_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">Schedule of 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/2026/elts/us-gaap-2026.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_PolicyholderAccountBalanceTable_019e4b0b-97b1-7eac-9fb2-027ff4b7f3aa_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/2026/elts/us-gaap-2026.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_logan_TransactionWithServicingFeesMember_019e4b0b-9859-73b1-a0a0-b80c6f22a2c1_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-20260630.xsd#logan_TransactionWithServicingFeesMember"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MortgagesHeldForSaleFairValueDisclosure"/>
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    <link:label id="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearOne_019e4b0b-97b1-7911-91d8-d2cae1e4d29f_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">2027</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearOne" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearOne"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_019e4b0b-985a-7a68-9469-c28cb21f52d8_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/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherOperatingAssets"/>
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    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitAfterReinsurance_019e4b0b-9859-7203-bf19-9141cad3b7b2_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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitAfterReinsurance" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForFuturePolicyBenefitAfterReinsurance"/>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
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    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract_019e4b0b-96e1-71b4-a2eb-4f716e81dae2_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>
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    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_019e4b0b-9859-7f35-93c4-40a87edcd088_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/2026/elts/us-gaap-2026.xsd#us-gaap_AllocatedShareBasedCompensationExpense"/>
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    <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/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
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    <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/2026/elts/us-gaap-2026.xsd#us-gaap_StockRepurchasedAndRetiredDuringPeriodShares"/>
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    <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/2026/elts/us-gaap-2026.xsd#us-gaap_ReportingUnitAxis"/>
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    <link:label id="lab_us-gaap_Investments_019e4b0b-97b1-7764-a2b5-80c2661cb178_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_019e4b0b-97b1-706a-8eeb-15ba8b22dd34_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">Intersegment 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>
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    <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>
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    <link:label id="lab_srt_RestatementDomain_019fc6ab-a7b1-73ab-9657-eb301403f118_terseLabel_en-US" xlink:label="lab_srt_RestatementDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Domain]</link:label>
    <link:label id="lab_srt_RestatementDomain_label_en-US" xlink:label="lab_srt_RestatementDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RestatementDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RestatementDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RestatementDomain" xlink:to="lab_srt_RestatementDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_019e4b0b-9859-7ce7-a7f2-ccd11cf1cf7c_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/2026/elts/us-gaap-2026.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_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYear_019e4b0b-96e1-7878-9d71-33eb5e11f0ce_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/2026/elts/us-gaap-2026.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_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember_019e4b0b-97b1-758f-b253-55a1b19f7eee_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_019e4b0b-9859-7a15-9f87-5a7e8b1cf1fe_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/2026/elts/us-gaap-2026.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_us-gaap_PaymentsOfDebtIssuanceCosts_019e4b0b-9859-77bd-9e3f-c95aaff38981_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/2026/elts/us-gaap-2026.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_AccumulatedOtherComprehensiveIncomeLossTable_019e4b0b-97b1-79da-b800-2d12669ee8ae_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/2026/elts/us-gaap-2026.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_logan_CommonSharesPurchaseWarrantsMember_019e4b0b-97b1-7f78-a8c4-0a908e1068ab_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>
    <link:label id="lab_logan_CommonSharesPurchaseWarrantsMember_label_en-US" xlink:label="lab_logan_CommonSharesPurchaseWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Shares Purchase Warrants [Member]</link:label>
    <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:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_CommonSharesPurchaseWarrantsMember" xlink:to="lab_logan_CommonSharesPurchaseWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_019e4b0b-97b1-710e-946c-eb3acdc8d69e_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e4b0b-96e1-7eae-bd3b-21301d653644_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>
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    <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>
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    <link:label id="lab_us-gaap_CashFlowHedgingMember_019e4b0b-9859-793b-9975-fe30abf464ef_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/2026/elts/us-gaap-2026.xsd#us-gaap_CashFlowHedgingMember"/>
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    <link:label id="lab_logan_InvestmentCommitmentsMember_019e4b0b-96e1-70a8-aeef-df95c8b769d0_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-20260630.xsd#logan_InvestmentCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_InvestmentCommitmentsMember" xlink:to="lab_logan_InvestmentCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYear_019e4b0b-9859-7041-8dd2-90ac230bb125_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>
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    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock_019e4b0b-9859-7b45-8257-645427e6d01d_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>
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    <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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProvisionForLoanLeaseAndOtherLosses"/>
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    <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/2026/elts/us-gaap-2026.xsd#us-gaap_OffBalanceSheetCreditLossLiability"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract_019e4b0b-97b1-781b-95a8-033f634aa514_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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract"/>
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    <link:label id="lab_srt_AMBestARatingMember_019e4b0b-97b1-7922-b439-ae7dc68928d4_terseLabel_en-US" xlink:label="lab_srt_AMBestARatingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">A</link:label>
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    <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/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
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    <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/2026/ecd-2026.xsd#ecd_AllTradingArrangementsMember"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_019e4b0b-97b1-7736-8ee0-7687f6097822_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_019e4b0b-97b1-76aa-80a2-ea1eff2d0f23_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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months_019e4b0b-9859-79f1-9190-dfc191723814_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/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months"/>
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    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock_019e4b0b-97b1-7bf3-8a3e-5de001beed26_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value Measurements, Recurring and Nonrecurring</link:label>
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    <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>
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    <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_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/2026/dei-2026.xsd#dei_CurrentFiscalYearEndDate"/>
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    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitCurrentWeightedAverageDiscountRate_019e4b0b-9859-71ef-b9c6-262f3f4ba265_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>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
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    <link:label id="lab_us-gaap_DerivativeLineItems_019e4b0b-97b1-74ba-b837-72917ab6bb11_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
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    <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>
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    <link:label id="lab_logan_LiabilityForFuturePolicyBenefitsDirect_019e4b0b-9859-76f5-b45a-795e02bcd4bb_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-20260630.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_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/2026/ecd-2026.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_019e4b0b-9859-7b3e-a187-c5eddab8a5cd_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 (in dollars 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/2026/elts/us-gaap-2026.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_dei_EntityFileNumber_019e4b0b-97b1-7b56-a21b-ed7852fdfe4c_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_019e4b0b-9859-7a54-b610-9a44d57eeb9e_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/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearTwo_019e4b0b-97b1-789c-bdb8-054d0a28c5d7_terseLabel_en-US" xlink:label="lab_logan_DeferredPolicyAcquisitionCostsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</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-20260630.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_logan_ProductChargeRevenue_019e4b0b-9859-7c46-9ffb-b8820220718b_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-20260630.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_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput_019e4b0b-9859-7df1-9957-1916ce788ad9_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/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput" 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/2026/ecd-2026.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_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/2026/ecd-2026.xsd#ecd_MeasureAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureAxis" xlink:to="lab_ecd_MeasureAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_019e4b0b-9859-725d-8537-f1a50cd07ce3_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/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_RelatedPartyTransactionTermOfContract_019fd08e-f985-72ed-abdb-01dc9171e10b_terseLabel_en-US" xlink:label="lab_logan_RelatedPartyTransactionTermOfContract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term of contract</link:label>
    <link:label id="lab_logan_RelatedPartyTransactionTermOfContract_label_en-US" xlink:label="lab_logan_RelatedPartyTransactionTermOfContract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Term Of Contract</link:label>
    <link:label id="lab_logan_RelatedPartyTransactionTermOfContract_documentation_en-US" xlink:label="lab_logan_RelatedPartyTransactionTermOfContract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Term Of Contract</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_RelatedPartyTransactionTermOfContract" xlink:href="logan-20260630.xsd#logan_RelatedPartyTransactionTermOfContract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_RelatedPartyTransactionTermOfContract" xlink:to="lab_logan_RelatedPartyTransactionTermOfContract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumsEarnedNet_019e4b0b-97b1-706f-9cc0-99807de7183a_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_019e4b0b-97b1-70fb-8586-4ed24e3415f9_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/2026/elts/us-gaap-2026.xsd#us-gaap_PremiumsEarnedNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PremiumsEarnedNet" xlink:to="lab_us-gaap_PremiumsEarnedNet" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_DividendEquivalentUnitsMember_019e4b0b-9859-7322-ba69-b4986b2bcb07_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-20260630.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_019e4b0b-96e1-7010-91b6-01f88c2ab521_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-20260630.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_FundsHeldUnderReinsuranceAgreementsLiability_019e4b0b-97b1-7a24-b8a8-cc6aacafbd2f_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_019e4b0b-97b1-7c55-9a37-8ab2f808114d_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/2026/elts/us-gaap-2026.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_StatementEquityComponentsAxis_019e4b0b-9859-7831-bd1d-5a53fc610137_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/2026/elts/us-gaap-2026.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_us-gaap_IncrementalCommonSharesAttributableToContingentlyIssuableShares_019e4b0b-97b1-76ee-99f5-f7477f278f48_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/2026/elts/us-gaap-2026.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_logan_ProceedsFromBorrowingsOfInsuranceBusiness_019e4b0b-9859-76cf-96f1-a480fded467b_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-20260630.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_RelatedPartyMember_019e4b0b-97b1-77af-8c9f-d14fdf950c9f_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/2026/elts/us-gaap-2026.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"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_019e4b0b-9859-7809-b0cc-257c35dedbae_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_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 Tax Paid, after Refund Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.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_us-gaap_DeferredTaxAssetsValuationAllowance_019e4b0b-97b1-7cee-b01a-48237178c9bb_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/2026/elts/us-gaap-2026.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_dei_EntityInteractiveDataCurrent_019e4b0b-9859-7697-90a6-b023d4ed019c_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/2026/dei-2026.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_us-gaap_EffectsOfReinsuranceLineItems_019e4b0b-9859-74ce-8d89-1f5799c99e57_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/2026/elts/us-gaap-2026.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_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_019e4b0b-97b1-7aa6-b044-43866fba74d3_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/2026/elts/us-gaap-2026.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_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract_019e4b0b-9859-747e-932b-c84317172479_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/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract"/>
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    <link:label id="lab_dei_EntitySmallBusiness_019e4b0b-97b1-7b42-a403-862a5481901e_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/2026/dei-2026.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_logan_InsuranceRegulationCapitalConservationBufferTotalRiskBasedCapitalActual_019e4b0b-9859-7c49-a3e7-77d93f066096_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-20260630.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_ComprehensiveIncomeNetOfTax_019e4b0b-97b1-762f-b4fd-52a1704dccd4_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/2026/elts/us-gaap-2026.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_EffectiveIncomeTaxRateReconciliationTable_019e4b0b-96e1-7cf6-88cf-9fc1e16d4644_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation [Table]</link:label>
    <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/2026/elts/us-gaap-2026.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationTable" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTable_019e4b0b-9859-7553-990e-708f218922eb_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_IncomeTaxReconciliationNondeductibleExpense_019e4b0b-97b1-7ae4-84b5-6d0bccbf41a5_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/2026/elts/us-gaap-2026.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_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitInterestExpense_019e4b0b-9859-7e0d-9905-800809ba4a20_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/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitInterestExpense"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract_019e4b0b-9859-767d-ac9a-ddd9e3141963_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/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract"/>
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    <link:label id="lab_dei_DocumentType_019e4b0b-97b1-7d9b-ba6f-78e809cf9c78_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_NetAssetsGeographicAreaMember_019e4b0b-9859-7abc-b50f-17569689bbf6_terseLabel_en-US" xlink:label="lab_us-gaap_NetAssetsGeographicAreaMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographic Area</link:label>
    <link:label id="lab_us-gaap_NetAssetsGeographicAreaMember_label_en-US" xlink:label="lab_us-gaap_NetAssetsGeographicAreaMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Assets, Geographic Area [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetAssetsGeographicAreaMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetAssetsGeographicAreaMember"/>
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    <link:label id="lab_logan_FeeRelatedCompensation_019e4b0b-97b1-709a-a46c-4dbb8851e145_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-20260630.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_us-gaap_GainsLossesOnExtinguishmentOfDebt_019e4b0b-9859-7d99-8ec3-606477357df0_terseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss on extinguishment of debt</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_019e4b0b-9859-716b-b3b7-94bb35c5653e_verboseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Loss on extinguishment of debt</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_label_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Extinguishment of Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainsLossesOnExtinguishmentOfDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:to="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanAccumulatedBenefitObligation_019e4b0b-97b1-7680-923d-ddbb2469402f_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/2026/elts/us-gaap-2026.xsd#us-gaap_DefinedBenefitPlanAccumulatedBenefitObligation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanAccumulatedBenefitObligation" xlink:to="lab_us-gaap_DefinedBenefitPlanAccumulatedBenefitObligation" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_OtherThanFairValueAbstractAbstract_019e4b0b-9859-7b7a-a821-85867a617e2a_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-20260630.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_ScheduleOfIndefiniteLivedIntangibleAssetsTableTextBlock_019e4b0b-96e1-7beb-b2f2-59de9094126a_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 Intangible Asset, Indefinite-Lived</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">Intangible Asset, Indefinite-Lived [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_FinancialAssets_019e4b0b-97b1-783e-95ab-42c659dee4f4_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-20260630.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_logan_ClassOfWarrantOrRightWarrantExchangeRate_019e4b0b-9859-781f-8b64-55c2e9ae3a6e_terseLabel_en-US" xlink:label="lab_logan_ClassOfWarrantOrRightWarrantExchangeRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrant exchange rate (in dollars per share)</link:label>
    <link:label id="lab_logan_ClassOfWarrantOrRightWarrantExchangeRate_label_en-US" xlink:label="lab_logan_ClassOfWarrantOrRightWarrantExchangeRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Warrant Exchange Rate</link:label>
    <link:label id="lab_logan_ClassOfWarrantOrRightWarrantExchangeRate_documentation_en-US" xlink:label="lab_logan_ClassOfWarrantOrRightWarrantExchangeRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Warrant Exchange Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_ClassOfWarrantOrRightWarrantExchangeRate" xlink:href="logan-20260630.xsd#logan_ClassOfWarrantOrRightWarrantExchangeRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_ClassOfWarrantOrRightWarrantExchangeRate" xlink:to="lab_logan_ClassOfWarrantOrRightWarrantExchangeRate" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_OtherAssetsAndOtherLiabilitiesLineItems_019e4b0b-96e1-71b1-84cb-7269f6db3023_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-20260630.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_SubsequentEventLineItems_019e4b0b-96e1-73cc-9079-858955c37cb4_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_label_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventLineItems" xlink:to="lab_us-gaap_SubsequentEventLineItems" 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/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable_019e4b0b-9859-7bcd-92f7-46df6c4cd483_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/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:to="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_019e4b0b-9859-7098-837e-8381f191642d_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/2026/dei-2026.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_country_CA_019e4b0b-9859-7466-bab3-88f0a0c464e8_verboseLabel_en-US" xlink:label="lab_country_CA" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">CANADA</link:label>
    <link:label id="lab_country_CA_019e4b0b-9859-7877-bf34-33e90a8b6eef_terseLabel_en-US" xlink:label="lab_country_CA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cayman Islands</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/2026/country-2026.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_logan_ProbabilityWeightedExpectedReturnMethodMember_019e4b0b-9859-73f3-8043-2c46275fb645_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-20260630.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_us-gaap_DeferredIncomeTaxLiabilities_019e4b0b-96e1-7861-8c48-334abb7e3169_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/2026/elts/us-gaap-2026.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_logan_LineOfCreditIncreaseDecreaseInBorrowingCapacity_019e4b0b-9859-75a7-8be5-03f380604729_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-20260630.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_019e4b0b-9859-76ad-8bc2-30bee9f0a641_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-20260630.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_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract_019e4b0b-9859-72b0-9142-763f8e2fcf08_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/2026/elts/us-gaap-2026.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_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent_019e4b0b-97b1-7b08-829c-f94768177822_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_019e4b0b-97b1-7b39-b368-1aeaa1b653ce_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/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e4b0b-9859-729b-ac4f-4e0208f69d71_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_019e4b0b-9859-752e-8214-dc3a4dcb471c_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_019e4b0b-9859-7615-90cd-48a71004b49d_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/2026/elts/us-gaap-2026.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_us-gaap_CommitmentsAndContingencies_019e4b0b-9859-79f3-868e-fd90e7f4f6d3_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/2026/elts/us-gaap-2026.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_us-gaap_AntidilutiveSecuritiesNameDomain_019e4b0b-97b1-7121-82f8-9caaca8a0a99_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_019e4b0b-97b1-7ede-9e00-863edf0b03ca_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">2030</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">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.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_PolicyholderFunds_019e4b0b-97b1-7e1b-b155-bc1dcf80fbae_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_019e4b0b-97b1-716b-9161-171daf3ca72d_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_019e4b0b-97b1-7e42-a26b-099dde8260af_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/2026/elts/us-gaap-2026.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_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFour_019e4b0b-97b1-7793-bc9d-582527f56bcb_terseLabel_en-US" xlink:label="lab_logan_FinancingReceivableBeforeAllowanceForCreditLossMaturityYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</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-20260630.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_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ExecutiveCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ExecutiveCategoryAxis" xlink:to="lab_ecd_ExecutiveCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceIssuance_019e4b0b-97b1-79ba-9b76-cc11e4193769_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_019e4b0b-97b1-7c82-a0f9-a1bad0b05fc4_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/2026/elts/us-gaap-2026.xsd#us-gaap_PolicyholderAccountBalanceIssuance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyholderAccountBalanceIssuance" xlink:to="lab_us-gaap_PolicyholderAccountBalanceIssuance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_019fcdad-9964-71a3-ad95-fd364a53e2a6_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable Type [Axis]</link:label>
    <link:label id="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_label_en-US" xlink:label="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis"/>
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    <link:label id="lab_srt_CounterpartyNameAxis_019e4b0b-97b1-7076-a39d-f55c73952900_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/2026/elts/srt-2026.xsd#srt_CounterpartyNameAxis"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableforsaleAmortizedCostAbstract_019e4b0b-9859-7f7c-9a5d-2b7fb104e7e6_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/2026/elts/us-gaap-2026.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_us-gaap_ReinsuranceTextBlock_019e4b0b-97b1-74fc-9e24-4c36e3c48ee1_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/2026/elts/us-gaap-2026.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_LoansHeldForSaleMeasurementInput_019e4b0b-9859-7532-861b-e37b6fb7bbe6_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/2026/elts/us-gaap-2026.xsd#us-gaap_LoansHeldForSaleMeasurementInput"/>
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    <link:label id="lab_us-gaap_AccountsPayableOtherCurrentAndNoncurrent_019e4b0b-9859-7fc5-85b5-521ad7910ac1_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeReinsuranceAfterDiscountRateChange_019e4b0b-97b1-79e7-a895-6aa8778a1b1d_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeReinsuranceAfterDiscountRateChange" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Beginning Balance</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeReinsuranceAfterDiscountRateChange_019e4b0b-97b1-7dfc-a0b1-fe06a9355f59_periodEndLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeReinsuranceAfterDiscountRateChange" 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_LiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeReinsuranceAfterDiscountRateChange_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeReinsuranceAfterDiscountRateChange" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefit, Expected Net Premium, before Reinsurance, after Discount Rate Change</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeReinsuranceAfterDiscountRateChange" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeReinsuranceAfterDiscountRateChange"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeReinsuranceAfterDiscountRateChange" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedNetPremiumBeforeReinsuranceAfterDiscountRateChange" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightOutstanding_019e4b0b-97b1-7334-b359-b7260fdb906c_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/2026/elts/us-gaap-2026.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_ScheduleOfVariableInterestEntitiesTable_019e4b0b-97b1-7516-99a4-9102bb9f9e49_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/2026/elts/us-gaap-2026.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_SupplementalCashFlowInformationAbstract_019e4b0b-97b1-7f83-830d-5f5332fdc0c2_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/2026/elts/us-gaap-2026.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_logan_ReinsuranceRecoverablesExcludingFundsHeldUnderReinsuranceContracts_019e4b0b-9859-7c60-81ba-0dc21b43d30f_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-20260630.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_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent_019e4b0b-97b1-724b-b303-31bf3141df41_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_AccruedLiabilitiesAndOtherLiabilities_019e4b0b-97b1-7abb-bdb0-aef03636bd47_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_019e4b0b-97b1-7362-a3ba-5dc5eac70dec_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/2026/elts/us-gaap-2026.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_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_019e4b0b-9859-72b1-86df-992013460091_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:to="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" 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/2026/ecd-2026.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_dei_EntityTaxIdentificationNumber_019e4b0b-9859-7d1d-99cf-aa9a0f4519d3_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/2026/dei-2026.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_BelowInvestmentGradeMember_019e4b0b-98ea-716a-b38f-b501caf09fc9_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-20260630.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_us-gaap_PastDueFinancingReceivablesTableTextBlock_019e4b0b-97b1-7c56-86ba-1093f88bcc8b_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/2026/elts/us-gaap-2026.xsd#us-gaap_PastDueFinancingReceivablesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:to="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialAssetNotPastDueMember_019e4b0b-9859-7e1d-b549-e994f25fa998_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/2026/elts/us-gaap-2026.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_logan_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsNet_019e4b0b-9859-7a95-bad8-f14ee583df8a_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-20260630.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_logan_OtherInvestedAssetsMember_019e4b0b-97b1-7f14-8b8f-3693144c27f0_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_019e4b0b-97b1-78e9-b8cd-d783c5bbd7d6_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-20260630.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_019e4b0b-97b1-7af4-9907-77a47fc190bb_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_019e4b0b-97b1-77c7-b137-711cc126f454_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-20260630.xsd#logan_AmortizationAndImpairmentOfIntangibleAssets"/>
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    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross_019e4b0b-9859-7642-b265-29eb562bce84_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">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/2026/elts/us-gaap-2026.xsd#us-gaap_PolicyholderBenefitsAndClaimsIncurredGross"/>
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    <link:label id="lab_us-gaap_PolicyholderAccountBalanceBenefitPayment_019e4b0b-97b1-7266-affd-d114e2edf69e_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>
    <link:label id="lab_us-gaap_PolicyholderAccountBalanceBenefitPayment_label_en-US" xlink:label="lab_us-gaap_PolicyholderAccountBalanceBenefitPayment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Account Balance, Benefit Payment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderAccountBalanceBenefitPayment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PolicyholderAccountBalanceBenefitPayment"/>
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    <link:label id="lab_dei_EntityIncorporationStateCountryCode_019e4b0b-97b1-71d0-b879-e516358a2b4f_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/2026/dei-2026.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"/>
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    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
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    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:to="lab_ecd_MtrlTermsOfTrdArrTextBlock" 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/2026/ecd-2026.xsd#ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember"/>
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    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_019e4b0b-98ea-7e1a-8c2f-71e87abaa9b0_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_019e4b0b-9859-7030-a074-e04c54401554_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/2026/elts/us-gaap-2026.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_SubsequentEventTable_019e4b0b-97b1-7b92-979e-02999bdb174c_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/2026/elts/us-gaap-2026.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"/>
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    <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/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensation"/>
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    <link:label id="lab_us-gaap_LaborAndRelatedExpense_019e4b0b-9859-73ec-9b19-99409de04694_terseLabel_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" 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_LaborAndRelatedExpense_019e4b0b-9859-7edd-a331-27b2af22bbcb_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_019e4b0b-9859-7c0d-b378-2add703fe03b_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>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_label_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Labor and Related Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LaborAndRelatedExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LaborAndRelatedExpense"/>
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    <link:label id="lab_logan_MedicoInsuranceCompanyMember_019e4b0b-9859-7c06-aa54-dafa04ba5a4a_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_019e4b0b-9859-7734-91d2-a3369373d4bb_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>
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    <link:loc xlink:type="locator" xlink:label="loc_logan_MedicoInsuranceCompanyMember" xlink:href="logan-20260630.xsd#logan_MedicoInsuranceCompanyMember"/>
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    <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>
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    <link:label id="lab_us-gaap_CashSurrenderValueDuePolicyholdersAmount_019e4b0b-98ea-77d6-a294-e7f878fc9886_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/2026/elts/us-gaap-2026.xsd#us-gaap_CashSurrenderValueDuePolicyholdersAmount"/>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction_019e4b0b-97b1-76fe-aad7-7c5b037775d1_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing fees</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Amounts of Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionAmountsOfTransaction"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.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_logan_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross_019e4b0b-97b1-75ba-acd0-cab2ca3be454_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-20260630.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_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_019e4b0b-96e1-7ee1-92ff-a35bf471719e_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_019e4b0b-96e1-7cf9-a912-b13e4d3ed13e_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_019e4b0b-96e1-7cc0-bbc0-952f27ababbc_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/2026/elts/us-gaap-2026.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_logan_Second10YearsMember_019e4b0b-9859-7b7b-b639-151d16007ddb_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-20260630.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_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/2026/ecd-2026.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_us-gaap_FairValueDisclosureItemAmountsDomain_019e4b0b-97b1-7631-a5ee-2586ed58811e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <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/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:to="lab_us-gaap_FairValueDisclosureItemAmountsDomain" 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/2026/ecd-2026.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_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/2026/dei-2026.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_logan_NicholInternationalReinsuranceS.A.CLtdMember_019e4b0b-97b1-721b-a46a-412c28eda1bb_terseLabel_en-US" xlink:label="lab_logan_NicholInternationalReinsuranceS.A.CLtdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nichol International Reinsurance (S.A.C), Ltd</link:label>
    <link:label id="lab_logan_NicholInternationalReinsuranceS.A.CLtdMember_019e4b0b-97b1-7d1c-8186-788b388aae70_verboseLabel_en-US" xlink:label="lab_logan_NicholInternationalReinsuranceS.A.CLtdMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Nichol International Reinsurance (S.A.C), Ltd.</link:label>
    <link:label id="lab_logan_NicholInternationalReinsuranceS.A.CLtdMember_label_en-US" xlink:label="lab_logan_NicholInternationalReinsuranceS.A.CLtdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nichol International Reinsurance (S.A.C), Ltd [Member]</link:label>
    <link:label id="lab_logan_NicholInternationalReinsuranceS.A.CLtdMember_documentation_en-US" xlink:label="lab_logan_NicholInternationalReinsuranceS.A.CLtdMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Nichol International Reinsurance (S.A.C), Ltd</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_NicholInternationalReinsuranceS.A.CLtdMember" xlink:href="logan-20260630.xsd#logan_NicholInternationalReinsuranceS.A.CLtdMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_NicholInternationalReinsuranceS.A.CLtdMember" xlink:to="lab_logan_NicholInternationalReinsuranceS.A.CLtdMember" 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/2026/elts/us-gaap-2026.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_logan_AssetManagementRevenueAbstract_019e4b0b-97b1-7533-9482-9a58aa4eb2b0_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-20260630.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_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable_019e4b0b-9859-7c5d-95e6-91ca9c4c39a0_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_019e4b0b-97b1-7645-98c2-dd60dcd6b4b7_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/2026/elts/us-gaap-2026.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_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/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssumedPremiumsEarned_019e4b0b-9859-7a38-9772-01447c4932c6_terseLabel_en-US" xlink:label="lab_us-gaap_AssumedPremiumsEarned" 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_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssumedPremiumsEarned" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssumedPremiumsEarned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssumedPremiumsEarned" xlink:to="lab_us-gaap_AssumedPremiumsEarned" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingRelationshipDomain_019e4b0b-97b1-7215-ade0-a9b638d88350_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/2026/elts/us-gaap-2026.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_DeferredTaxAssetsLiabilitiesNet_019e4b0b-97b1-755c-a1d2-11fcb7e8de53_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/2026/elts/us-gaap-2026.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_PlanNameAxis_019fc6e9-4eeb-7d06-aee7-de204433a33b_terseLabel_en-US" xlink:label="lab_us-gaap_PlanNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plan Name [Axis]</link:label>
    <link:label id="lab_us-gaap_PlanNameAxis_label_en-US" xlink:label="lab_us-gaap_PlanNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Plan Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PlanNameAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PlanNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PlanNameAxis" xlink:to="lab_us-gaap_PlanNameAxis" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accounts, Notes, Loans and Financing Receivable [Table Text Block]</link:label>
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    <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/2026/elts/us-gaap-2026.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_us-gaap_FiniteLivedIntangibleAssetsNetAbstract_019e4b0b-9859-72c8-b188-fccc2cc43034_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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsNetAbstract"/>
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    <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/2026/elts/us-gaap-2026.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_AdditionalLiabilityLongDurationInsuranceWeightedAverageDuration_019e4b0b-9859-736b-8cc3-e1b279c26b36_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/2026/elts/us-gaap-2026.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"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod"/>
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    <link:loc xlink:type="locator" xlink:label="loc_logan_DebtCovenantAmendmentFeeAsAPercentageOfOutstandingPrincipal" xlink:href="logan-20260630.xsd#logan_DebtCovenantAmendmentFeeAsAPercentageOfOutstandingPrincipal"/>
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    <link:label id="lab_us-gaap_HedgingDesignationDomain_019e4b0b-9859-7545-83f0-01a12b505a33_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/2026/elts/us-gaap-2026.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_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>
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    <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_us-gaap_OtherCommitment_019e4b0b-9859-73d3-a53c-cc451ad89b38_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment commitments</link:label>
    <link:label id="lab_us-gaap_OtherCommitment_label_en-US" xlink:label="lab_us-gaap_OtherCommitment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitment</link:label>
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    <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>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition_019e4b0b-97b1-7e01-bc02-a03a08ffe6f5_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>
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    <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/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
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    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_019e4b0b-97b1-7af7-a4dd-cbbcab098301_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/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivablesPeriodPastDueAxis"/>
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    <link:label id="lab_us-gaap_EquityMethodInvestmentDividendsOrDistributions_019e4b0b-97b1-7742-8b40-efc8b6fa421b_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/2026/elts/us-gaap-2026.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_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract"/>
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    <link:label id="lab_us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract_019e4b0b-97b1-7ec6-8f6d-9b093f8ef6b2_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/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract"/>
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    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisChangeInUnrealizedGainLoss_019e4b0b-97b1-7042-83c5-f69d6587034b_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>
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    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_019e4b0b-9859-7d75-b339-973a525609ec_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/2026/elts/us-gaap-2026.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_GrossInvestmentIncomeOperating_019e4b0b-9859-7de0-9992-5bf74a9ad63f_verboseLabel_en-US" xlink:label="lab_us-gaap_GrossInvestmentIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Gross investment income</link:label>
    <link:label id="lab_us-gaap_GrossInvestmentIncomeOperating_019e4b0b-9859-7f70-b604-591a691be21c_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>
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    <link:label id="lab_us-gaap_BusinessAcquisitionSharePrice_019e4b0b-97b1-75b5-bbde-f933740a8e77_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/2026/elts/us-gaap-2026.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_logan_DebtInstrumentDebentureUnitsPricePerUnit_019e4b0b-97b1-7b24-805d-31faa2ecc6a4_terseLabel_en-US" xlink:label="lab_logan_DebtInstrumentDebentureUnitsPricePerUnit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument issued denomination (per unit)</link:label>
    <link:label id="lab_logan_DebtInstrumentDebentureUnitsPricePerUnit_label_en-US" xlink:label="lab_logan_DebtInstrumentDebentureUnitsPricePerUnit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Debenture Units, Price Per Unit</link:label>
    <link:label id="lab_logan_DebtInstrumentDebentureUnitsPricePerUnit_documentation_en-US" xlink:label="lab_logan_DebtInstrumentDebentureUnitsPricePerUnit" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Debenture Units, Price Per Unit</link:label>
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    <link:label id="lab_us-gaap_DerivativeLiabilities_019e4b0b-9859-72f8-80e5-b7f9f89c8bdb_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_019e4b0b-9859-76dd-9e60-ff3374dd652e_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_019e4b0b-9859-779b-aeb6-7132ccaa5750_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>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilities" xlink:to="lab_us-gaap_DerivativeLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_019e4b0b-97b1-7fc4-b9f0-e23126f160e1_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>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue_019e4b0b-9859-7c0f-8ef6-9b5e3572b846_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vested (in dollars per share)</link:label>
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    <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>
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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>
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    <link:label id="lab_us-gaap_OtherNonoperatingIncome_019fdc25-9231-7819-abef-7b516b27b63a_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncome" 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_OtherNonoperatingIncome_019e4b0b-97b1-7602-b3ae-31a63728dfbc_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other fee-related income</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncome_019e4b0b-97b1-78c1-ac51-73c6c478db83_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 fee-related 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/2026/elts/us-gaap-2026.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_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeReinsuranceAfterDiscountRateChange_019e4b0b-9859-7074-8628-79c3490de481_periodStartLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeReinsuranceAfterDiscountRateChange" 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_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeReinsuranceAfterDiscountRateChange_019e4b0b-9859-78b0-8dcb-3c2cbca79da2_periodEndLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeReinsuranceAfterDiscountRateChange" 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_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeReinsuranceAfterDiscountRateChange_019e4b0b-9859-784e-b70c-3507ffce6171_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeReinsuranceAfterDiscountRateChange" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Benefit payments, Discounted</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeReinsuranceAfterDiscountRateChange_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeReinsuranceAfterDiscountRateChange" 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, before Reinsurance, after Discount Rate Change</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeReinsuranceAfterDiscountRateChange" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeReinsuranceAfterDiscountRateChange"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeReinsuranceAfterDiscountRateChange" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFuturePolicyBenefitBeforeReinsuranceAfterDiscountRateChange" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_019e4b0b-9859-7991-a68e-67630bbdac0f_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/2026/elts/us-gaap-2026.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_VariableInterestEntityPrimaryBeneficiaryMember_019e4b0b-9859-76c9-ace4-112903fb454f_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/2026/elts/us-gaap-2026.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_country_KY_019e4b0b-98ea-7e5f-b68f-a4d28d9d9f4a_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>
    <link:label id="lab_country_KY_label_en-US" xlink:label="lab_country_KY" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CAYMAN ISLANDS</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_KY" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_KY"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_KY" xlink:to="lab_country_KY" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward_019e4b0b-9859-757f-a318-614227ae0a87_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>
    <link:label id="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward_label_en-US" xlink:label="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent, Net of Tax [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AOCIAttributableToParentNetOfTaxRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:to="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_019e4b0b-97b1-7caf-a484-7f63b957549f_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/2026/elts/us-gaap-2026.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_us-gaap_StatementTable_019e4b0b-9859-7e91-94d3-2581faba7c8f_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/2026/elts/us-gaap-2026.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_MaterialReconcilingItemsMember_019e4b0b-9859-7b87-927a-b3bfac734b4f_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/2026/elts/us-gaap-2026.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_logan_NumberOfReinsurers_019e4b0b-9859-7052-b393-36d4893a178f_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-20260630.xsd#logan_NumberOfReinsurers"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_NumberOfReinsurers" xlink:to="lab_logan_NumberOfReinsurers" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_019e4b0b-97b1-74d3-afa5-66c93146ea5c_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" 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_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/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIncomeInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeInterest" xlink:to="lab_us-gaap_InvestmentIncomeInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_TransactionCosts_019e4b0b-97b1-7fd2-b117-dc5939e80a12_terseLabel_en-US" xlink:label="lab_logan_TransactionCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transaction costs</link:label>
    <link:label id="lab_logan_TransactionCosts_019f1430-1fbd-7579-b8e9-c07673174236_negatedLabel_en-US" xlink:label="lab_logan_TransactionCosts" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Transaction costs</link:label>
    <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-20260630.xsd#logan_TransactionCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_TransactionCosts" xlink:to="lab_logan_TransactionCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_FinancingReceivableBeforeAllowanceForCreditLossMaturityTableTextBlock_019e4b0b-97b1-7308-be5b-f03554a6e45e_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>
    <link:label id="lab_srt_FinancingReceivableBeforeAllowanceForCreditLossMaturityTableTextBlock_label_en-US" xlink:label="lab_srt_FinancingReceivableBeforeAllowanceForCreditLossMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss, Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_FinancingReceivableBeforeAllowanceForCreditLossMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_FinancingReceivableBeforeAllowanceForCreditLossMaturityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_FinancingReceivableBeforeAllowanceForCreditLossMaturityTableTextBlock" xlink:to="lab_srt_FinancingReceivableBeforeAllowanceForCreditLossMaturityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_logan_LongTermCareMember_019e4b0b-97b1-78f1-b674-9021a1874e81_verboseLabel_en-US" xlink:label="lab_logan_LongTermCareMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">LTC</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-20260630.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_logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFourAndThereafter_019e4b0b-96e1-7ba5-b172-a29268a8ca49_terseLabel_en-US" xlink:label="lab_logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFourAndThereafter" 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_FiniteLivedIntangibleAssetExpectedAmortizationYearFourAndThereafter_label_en-US" xlink:label="lab_logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFourAndThereafter" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Four and Thereafter</link:label>
    <link:label id="lab_logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFourAndThereafter_documentation_en-US" xlink:label="lab_logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFourAndThereafter" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Four and Thereafter</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFourAndThereafter" xlink:href="logan-20260630.xsd#logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFourAndThereafter"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFourAndThereafter" xlink:to="lab_logan_FiniteLivedIntangibleAssetExpectedAmortizationYearFourAndThereafter" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitExpectedFutureGrossPremiumDiscountedBeforeReinsurance_019e4b0b-9859-7e05-ba0b-da0adb752c51_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/2026/elts/us-gaap-2026.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_LoansHeldForSaleFairValueDisclosure_019e4b0b-97b1-7efa-958a-df34b1f1fec4_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>
    <link:label id="lab_us-gaap_LoansHeldForSaleFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LoansHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan, Held-for-Sale, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansHeldForSaleFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoansHeldForSaleFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansHeldForSaleFairValueDisclosure" xlink:to="lab_us-gaap_LoansHeldForSaleFairValueDisclosure" xlink:type="arc" order="1"/>
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