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A short course of lectures
«Advances in Proof-Theoretic Semantics»





Self-contradictory Reasoning in N−=ArgumentsDecidabilityThe No-Assumptions ViewAbsolutenessValidity of ArgumentsFrege's QuestionA Completeness Result for Intuitionistic LogicExtending the Mapping Arg to BHK-Proofs of ACompleteness Results for Classical LogicProof-Theoretic Validity for Generalized Atomic SystemsBidirectionalityThe Liar ParadoxInternal and Intuitive TruthSelf-contradictory Reasoning in N−∀∃=Prawitz's ConjectureModel TheoryPremiss of I-Rule Discharges Some AssumptionsCategorical Harmony and Paradoxes in Proof-Theoretic SemanticsGentzen's Approach to MeaningStrong Normalization by Bar InductionFailure of CompletenessDefining Meanings: Specialise Then GeneraliseDeductions in Multicategories and PolycategoriesStratificationAuthor's Postscript, January 2015Propositional LogicUnknown StatementsReflectionGE Harmony: A Counter-ExampleInternalizationProof-Theoretic Semantics Beyond LogicAssessmentDefinition 18Goldfarb's Account of Dummett's ApproachLogic, Paradoxes, Partial DefinitionsThe Axiomatization of TThe Need for an Intensional Notion of HarmonyExplicit Composition and Its Application in Proofs of NormalizationNaïve Set TheoryAn Intuitionistic SolutionFailure of Strong CompletenessThe Language of TGeneralized Atomic SystemsOn Dummett's “Proof-Theoretic Justifications of Logical Laws”Extending the Mapping Proof to Arguments for ADefinition 7Argument StructuresTowards a Definition of Strong HarmonyEquality Versus IdentityFunctional Closure, Local Logic and the Notion of AbsolutenessComments on an OpinionThe Nature of Hypotheses and the Format of ProofsLocal LogicAnother [Counter-]ExampleFurther Development of Gentzen's IdeasDiagnosing the ParadoxSelf-Reference and TypingThe Paradox of Knowability from an Intuitionistic StandpointVariables and SubstitutionGE-Rules in GeneralOpen Proofs and the Placeholder ViewDefining Logical ConsequenceMeaning ConditionsSetsFailure of Completeness for Intuitionistic LogicTruth NotionsNeo-Verificationist ApproachesLocal and Global Proof-Theoretic SemanticsMappings of Valid Arguments on BHK-Proofs and Vice VersaA Strongly Differing Opinion on Proof-Theoretic Semantics?Concluding Remarks: From Semantic Dualism to DualityEqualityKreisel's Theory of Constructions, the Kreisel-Goodman Paradox, and the Second ClauseAnalysis of the MethodShifting OpinionsRules for DeductionsThe Reception of the Theory of Constructions and the Second ClauseHarmony Based on Generalised RulesOn the Relation Between Heyting's and Gentzen's Approaches to MeaningBoundary RulesWeak and Strong Validity and Their FeaturesProof-Theoretic SemanticsModel-Theoretic SemanticsCompleteness in Proof-Theoretic SemanticsDeductions in CategoriesThe Theory of Constructions and the Second ClauseAppendixThe Mode of PresentationNormal Deductions in a Fragment of NHow Is a Rational Discussion Possible?Background on General Elimination RulesFormalizing the BHK Interpretation in THarmony Based on EquivalenceSome Remarks on Proof-Theoretic SemanticsGuilt by Association?The Functional ClosureThe Problem of HarmonyTowards a Proof-Theoretic Semantics of EqualitiesThe Kreisel-Goodman ParadoxAn Overview of the Theory of ConstructionsComparison with Kripke SemanticsIn Other WordsMorning Star Versus Evening Star RevisitedDefinition 19Self-contradictory Reasoning in N−∃=Schematic InferencesCategorical Harmony in Comparison with Other PrinciplesRepresenting the MeaningDeductions Not Necessarily Based on PropositionsConcluding RemarksOn the Paths of CategoriesReductions of Deductions in N−=Definition 1Heyting's Approach to MeaningThe GE-rule for Implication and the Type-Theoretic Dependent Product TypeProof-Theoretic ValidityOpen Problems in Proof-Theoretic SemanticsPredicativity, Decidability, and the BHK InterpretationStrong Completeness ResultsSeveral I-Rules(21) is intuitionistically validA First Comparison Between Heyting's and Gentzen's ApproachesLemma 3Degrees of Paradoxicality of Logical ConstantsTarski's Definition of Logical ConsequenceRemarksOn the Proof-Theoretic Foundations of Set TheoryEquality of SensesFoundational IssuesSelf-contradictory ReasoningNotation for Natural DerivationsI-Rule Has Several PremissesConcluding Remarks and Further ApplicationsAppendixFunctions of LanguageSoundness, Completeness, and InternalizationA Proof-Theoretic InterpretationDefinitional ReflectionDefining SetsThe Principle of Categorical HarmonyOutlook: Applications and Extensions of Definitional ReflectionIs Bullet a Logical Constant?Defining Meanings in General
 
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