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A short course of lectures «Advances in ProofTheoretic Semantics»
Selfcontradictory Reasoning in N−=ArgumentsDecidabilityThe NoAssumptions ViewAbsolutenessValidity of ArgumentsFrege's QuestionA Completeness Result for Intuitionistic LogicExtending the Mapping Arg to BHKProofs of ACompleteness Results for Classical LogicProofTheoretic Validity for Generalized Atomic SystemsBidirectionalityThe Liar ParadoxInternal and Intuitive TruthSelfcontradictory Reasoning in N−∀∃=Prawitz's ConjectureModel TheoryPremiss of IRule Discharges Some AssumptionsCategorical Harmony and Paradoxes in ProofTheoretic 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 CounterExampleInternalizationProofTheoretic 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 “ProofTheoretic 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 ParadoxSelfReference and TypingThe Paradox of Knowability from an Intuitionistic StandpointVariables and SubstitutionGERules in GeneralOpen Proofs and the Placeholder ViewDefining Logical ConsequenceMeaning ConditionsSetsFailure of Completeness for Intuitionistic LogicTruth NotionsNeoVerificationist ApproachesLocal and Global ProofTheoretic SemanticsMappings of Valid Arguments on BHKProofs and Vice VersaA Strongly Differing Opinion on ProofTheoretic Semantics?Concluding Remarks: From Semantic Dualism to DualityEqualityKreisel's Theory of Constructions, the KreiselGoodman 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 FeaturesProofTheoretic SemanticsModelTheoretic SemanticsCompleteness in ProofTheoretic 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 ProofTheoretic SemanticsGuilt by Association?The Functional ClosureThe Problem of HarmonyTowards a ProofTheoretic Semantics of EqualitiesThe KreiselGoodman ParadoxAn Overview of the Theory of ConstructionsComparison with Kripke SemanticsIn Other WordsMorning Star Versus Evening Star RevisitedDefinition 19Selfcontradictory 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 GErule for Implication and the TypeTheoretic Dependent Product TypeProofTheoretic ValidityOpen Problems in ProofTheoretic SemanticsPredicativity, Decidability, and the BHK InterpretationStrong Completeness ResultsSeveral IRules(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 ProofTheoretic Foundations of Set TheoryEquality of SensesFoundational IssuesSelfcontradictory ReasoningNotation for Natural DerivationsIRule Has Several PremissesConcluding Remarks and Further ApplicationsAppendixFunctions of LanguageSoundness, Completeness, and InternalizationA ProofTheoretic 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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