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A short course of lectures «Advances in ProofTheoretic Semantics»
Categorical Harmony in Comparison with Other PrinciplesA Completeness Result for Intuitionistic LogicDegrees of Paradoxicality of Logical ConstantsEqualityA Strongly Differing Opinion on ProofTheoretic Semantics?SetsBackground on General Elimination RulesStratificationCompleteness Results for Classical LogicSelfReference and TypingStrong Normalization by Bar InductionIs Bullet a Logical Constant?Open Problems in ProofTheoretic SemanticsGoldfarb's Account of Dummett's ApproachArgumentsOutlook: Applications and Extensions of Definitional ReflectionBoundary RulesThe Need for an Intensional Notion of HarmonyAn Overview of the Theory of ConstructionsProofTheoretic ValidityDefining Meanings in GeneralAnother [Counter]ExampleFailure of CompletenessDeductions in Multicategories and PolycategoriesVariables and SubstitutionDefinitional ReflectionModelTheoretic SemanticsReductions of Deductions in N−=InternalizationValidity of ArgumentsPrawitz's ConjectureLocal LogicStrong Completeness ResultsGE Harmony: A CounterExampleIRule Has Several PremissesProofTheoretic Semantics Beyond LogicDecidabilityAppendixProofTheoretic SemanticsPremiss of IRule Discharges Some AssumptionsNeoVerificationist ApproachesSome Remarks on ProofTheoretic SemanticsThe Language of TOn the Relation Between Heyting's and Gentzen's Approaches to MeaningFrege's QuestionMappings of Valid Arguments on BHKProofs and Vice VersaTowards a Definition of Strong HarmonyThe Paradox of Knowability from an Intuitionistic StandpointConcluding Remarks and Further ApplicationsBidirectionalityHeyting's Approach to MeaningOn the ProofTheoretic Foundations of Set TheoryCompleteness in ProofTheoretic SemanticsDefining SetsOn Dummett's “ProofTheoretic Justifications of Logical Laws”Rules for DeductionsLemma 3The Problem of Harmony(21) is intuitionistically validSelfcontradictory Reasoning in N−=Defining Meanings: Specialise Then GeneraliseDefining Logical ConsequenceAssessmentInternal and Intuitive TruthHarmony Based on Generalised RulesNaïve Set TheoryEquality of SensesFoundational IssuesThe GErule for Implication and the TypeTheoretic Dependent Product TypeSelfcontradictory ReasoningRemarksDefinition 18Local and Global ProofTheoretic SemanticsTarski's Definition of Logical ConsequenceWeak and Strong Validity and Their FeaturesAnalysis of the MethodFunctional Closure, Local Logic and the Notion of AbsolutenessExplicit Composition and Its Application in Proofs of NormalizationNotation for Natural DerivationsA First Comparison Between Heyting's and Gentzen's ApproachesThe Mode of PresentationThe Reception of the Theory of Constructions and the Second ClauseModel TheoryHarmony Based on EquivalenceNormal Deductions in a Fragment of NThe Functional ClosureHow Is a Rational Discussion Possible?Soundness, Completeness, and InternalizationAuthor's Postscript, January 2015Definition 7GERules in GeneralFailure of Strong CompletenessKreisel's Theory of Constructions, the KreiselGoodman Paradox, and the Second ClauseAppendixMorning Star Versus Evening Star RevisitedProofTheoretic Validity for Generalized Atomic SystemsDefinition 1Equality Versus IdentityCategorical Harmony and Paradoxes in ProofTheoretic SemanticsMeaning ConditionsDeductions Not Necessarily Based on PropositionsOpen Proofs and the Placeholder ViewPredicativity, Decidability, and the BHK InterpretationDiagnosing the ParadoxThe KreiselGoodman ParadoxFunctions of LanguageThe NoAssumptions ViewSelfcontradictory Reasoning in N−∀∃=Selfcontradictory Reasoning in N−∃=Truth NotionsLogic, Paradoxes, Partial DefinitionsReflectionExtending the Mapping Arg to BHKProofs of AGentzen's Approach to MeaningThe Liar ParadoxPropositional LogicSeveral IRulesConcluding Remarks: From Semantic Dualism to DualityComments on an OpinionA ProofTheoretic InterpretationComparison with Kripke SemanticsRepresenting the MeaningDefinition 19Towards a ProofTheoretic Semantics of EqualitiesThe Axiomatization of TArgument StructuresThe Theory of Constructions and the Second ClauseThe Nature of Hypotheses and the Format of ProofsIn Other WordsOn the Paths of CategoriesGuilt by Association?Extending the Mapping Proof to Arguments for AFurther Development of Gentzen's IdeasFailure of Completeness for Intuitionistic LogicFormalizing the BHK Interpretation in TDeductions in CategoriesThe Principle of Categorical HarmonyAbsolutenessGeneralized Atomic SystemsSchematic InferencesUnknown StatementsConcluding RemarksAn Intuitionistic SolutionShifting Opinions

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