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Conjunction introductionPropositional logicInference ruleDisjunctionRule of inferencePredicate logicAxiom of regularityModus tollensDisjunctSymbolic logicIntensional logicNatural deductionResolutionQuantum logicAxiomatic systemFirst-order logicSecond-order logicContrapositionExistential generalizationSymmetric differenceSequent calculusLaw of total probabilityLogical consequenceSyllogismAxiom of extensionalityProof systemPropositional functionLogical connectiveProof by contradictionAxiom schema of specificationDisjunctive normal formDouble negationModal logicInverse function ruleBoolean logicAbstract algebraic logicAxiom of pairingRelevance logicPredicate calculusClassical logicProbabilistic logicPrinciple of compositionalityArgumentation theoryProduct ruleDistributive propertySet theoryChain ruleExtensionalityHypothetical syllogismQuotient ruleTheoremImplicationMonadic second-order logicProlog syntax and semanticsDisjoint unionInformal logicTruth valueMaterial implicationNegationEpisyllogismMathematical proofDe morgan's lawCausal inferenceExclusive orIncidence algebraDerivationCountable additivityClauseDisjunctive syllogismIntuitionistic logicFormulaLogicismImpredicativityAxiom of infinityAnalytical hierarchyHorn clauseAlgebraic logicMathematical logicCombinatory logicElementary equivalenceHoare logicMany-valued logicConditional proofLambda calculusIntegro-differential equationHerbrand's theoremIntegration by substitutionPeirce's lawPropositional variableDomain of discourseValuationSelection ruleBayes' theoremDe morgan's lawsExclusive disjunctionAxiom schemaGödel's incompleteness theoremNecessity and sufficiencyDivision algebraBinary operation