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





Categorical Harmony in Comparison with Other PrinciplesA Completeness Result for Intuitionistic LogicDegrees of Paradoxicality of Logical ConstantsEqualityA Strongly Differing Opinion on Proof-Theoretic Semantics?SetsBackground on General Elimination RulesStratificationCompleteness Results for Classical LogicSelf-Reference and TypingStrong Normalization by Bar InductionIs Bullet a Logical Constant?Open Problems in Proof-Theoretic 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 ConstructionsProof-Theoretic ValidityDefining Meanings in GeneralAnother [Counter-]ExampleFailure of CompletenessDeductions in Multicategories and PolycategoriesVariables and SubstitutionDefinitional ReflectionModel-Theoretic SemanticsReductions of Deductions in N−=InternalizationValidity of ArgumentsPrawitz's ConjectureLocal LogicStrong Completeness ResultsGE Harmony: A Counter-ExampleI-Rule Has Several PremissesProof-Theoretic Semantics Beyond LogicDecidabilityAppendixProof-Theoretic SemanticsPremiss of I-Rule Discharges Some AssumptionsNeo-Verificationist ApproachesSome Remarks on Proof-Theoretic SemanticsThe Language of TOn the Relation Between Heyting's and Gentzen's Approaches to MeaningFrege's QuestionMappings of Valid Arguments on BHK-Proofs and Vice VersaTowards a Definition of Strong HarmonyThe Paradox of Knowability from an Intuitionistic StandpointConcluding Remarks and Further ApplicationsBidirectionalityHeyting's Approach to MeaningOn the Proof-Theoretic Foundations of Set TheoryCompleteness in Proof-Theoretic SemanticsDefining SetsOn Dummett's “Proof-Theoretic Justifications of Logical Laws”Rules for DeductionsLemma 3The Problem of Harmony(21) is intuitionistically validSelf-contradictory Reasoning in N−=Defining Meanings: Specialise Then GeneraliseDefining Logical ConsequenceAssessmentInternal and Intuitive TruthHarmony Based on Generalised RulesNaïve Set TheoryEquality of SensesFoundational IssuesThe GE-rule for Implication and the Type-Theoretic Dependent Product TypeSelf-contradictory ReasoningRemarksDefinition 18Local and Global Proof-Theoretic 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 7GE-Rules in GeneralFailure of Strong CompletenessKreisel's Theory of Constructions, the Kreisel-Goodman Paradox, and the Second ClauseAppendixMorning Star Versus Evening Star RevisitedProof-Theoretic Validity for Generalized Atomic SystemsDefinition 1Equality Versus IdentityCategorical Harmony and Paradoxes in Proof-Theoretic SemanticsMeaning ConditionsDeductions Not Necessarily Based on PropositionsOpen Proofs and the Placeholder ViewPredicativity, Decidability, and the BHK InterpretationDiagnosing the ParadoxThe Kreisel-Goodman ParadoxFunctions of LanguageThe No-Assumptions ViewSelf-contradictory Reasoning in N−∀∃=Self-contradictory Reasoning in N−∃=Truth NotionsLogic, Paradoxes, Partial DefinitionsReflectionExtending the Mapping Arg to BHK-Proofs of AGentzen's Approach to MeaningThe Liar ParadoxPropositional LogicSeveral I-RulesConcluding Remarks: From Semantic Dualism to DualityComments on an OpinionA Proof-Theoretic InterpretationComparison with Kripke SemanticsRepresenting the MeaningDefinition 19Towards a Proof-Theoretic 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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