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Home arrow Philosophy arrow Advances in Proof-Theoretic Semantics

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





Prawitz's ConjectureSelf-Reference and TypingThe Need for an Intensional Notion of HarmonyFunctions of LanguageFurther Development of Gentzen's IdeasExtending the Mapping Proof to Arguments for AComments on an OpinionDeductions in CategoriesDegrees of Paradoxicality of Logical ConstantsShifting OpinionsModel-Theoretic SemanticsDefinition 7Concluding Remarks: From Semantic Dualism to DualityGoldfarb's Account of Dummett's ApproachDefining Meanings: Specialise Then GeneraliseOpen Proofs and the Placeholder ViewLocal and Global Proof-Theoretic SemanticsThe Reception of the Theory of Constructions and the Second ClauseCategorical Harmony in Comparison with Other PrinciplesA Proof-Theoretic InterpretationStratificationThe Kreisel-Goodman ParadoxNeo-Verificationist ApproachesOn the Relation Between Heyting's and Gentzen's Approaches to MeaningNormal Deductions in a Fragment of NDefinition 19Proof-Theoretic Validity for Generalized Atomic SystemsOpen Problems in Proof-Theoretic SemanticsOn Dummett's “Proof-Theoretic Justifications of Logical Laws”Unknown StatementsFoundational IssuesDecidabilityMeaning ConditionsReductions of Deductions in N−=Rules for DeductionsDiagnosing the ParadoxThe Problem of HarmonySeveral I-RulesProof-Theoretic Semantics Beyond LogicThe Functional ClosureTarski's Definition of Logical ConsequenceWeak and Strong Validity and Their FeaturesDeductions in Multicategories and PolycategoriesFailure of Completeness for Intuitionistic LogicAppendixGE Harmony: A Counter-ExampleFrege's QuestionModel TheoryPredicativity, Decidability, and the BHK InterpretationLogic, Paradoxes, Partial DefinitionsThe Mode of PresentationValidity of ArgumentsDefinitional ReflectionEquality of SensesThe Nature of Hypotheses and the Format of ProofsOn the Proof-Theoretic Foundations of Set TheoryRepresenting the MeaningBackground on General Elimination RulesMorning Star Versus Evening Star RevisitedIs Bullet a Logical Constant?(21) is intuitionistically validVariables and SubstitutionSoundness, Completeness, and InternalizationEqualityCategorical Harmony and Paradoxes in Proof-Theoretic SemanticsThe GE-rule for Implication and the Type-Theoretic Dependent Product TypePropositional LogicProof-Theoretic SemanticsSelf-contradictory ReasoningThe No-Assumptions ViewAn Intuitionistic SolutionKreisel's Theory of Constructions, the Kreisel-Goodman Paradox, and the Second ClauseEquality Versus IdentityExplicit Composition and Its Application in Proofs of NormalizationRemarksSome Remarks on Proof-Theoretic SemanticsStrong Completeness ResultsGuilt by Association?Outlook: Applications and Extensions of Definitional ReflectionConcluding RemarksThe Axiomatization of TConcluding Remarks and Further ApplicationsSelf-contradictory Reasoning in N−∀∃=Schematic InferencesNotation for Natural DerivationsFailure of CompletenessGentzen's Approach to MeaningNaïve Set TheoryAnalysis of the MethodAssessmentInternalizationStrong Normalization by Bar InductionGeneralized Atomic SystemsTowards a Proof-Theoretic Semantics of EqualitiesThe Paradox of Knowability from an Intuitionistic StandpointLocal LogicProof-Theoretic ValidityAbsolutenessSelf-contradictory Reasoning in N−=AppendixDefining Logical ConsequenceCompleteness Results for Classical LogicThe Principle of Categorical HarmonyAnother [Counter-]ExampleThe Theory of Constructions and the Second ClauseTowards a Definition of Strong HarmonyOn the Paths of CategoriesTruth NotionsMappings of Valid Arguments on BHK-Proofs and Vice VersaI-Rule Has Several PremissesHow Is a Rational Discussion Possible?Deductions Not Necessarily Based on PropositionsArgumentsSetsBidirectionalityA Completeness Result for Intuitionistic LogicAn Overview of the Theory of ConstructionsHeyting's Approach to MeaningA First Comparison Between Heyting's and Gentzen's ApproachesArgument StructuresThe Liar ParadoxDefining SetsThe Language of TPremiss of I-Rule Discharges Some AssumptionsDefining Meanings in GeneralBoundary RulesHarmony Based on Generalised RulesFunctional Closure, Local Logic and the Notion of AbsolutenessLemma 3ReflectionComparison with Kripke SemanticsInternal and Intuitive TruthSelf-contradictory Reasoning in N−∃=Extending the Mapping Arg to BHK-Proofs of AFormalizing the BHK Interpretation in TA Strongly Differing Opinion on Proof-Theoretic Semantics?GE-Rules in GeneralDefinition 18Harmony Based on EquivalenceCompleteness in Proof-Theoretic SemanticsIn Other WordsFailure of Strong CompletenessDefinition 1Author's Postscript, January 2015
 
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