Following all the rules: Intuitionistic completeness for generalized proof-theoretic validity
Will Stafford, Victor Nascimento
Abstract
Abstract Prawitz conjectured that the proof-theoretically valid logic is intuitionistic logic. Recent work on proof-theoretic validity has disproven this. In fact, it has been shown that proof-theoretic validity is not even closed under substitution. In this paper, we make a minor modification to the definition of proof-theoretic validity found in Prawitz’s 1973paper ‘Towards a foundation of a general proof theory’ and refined by Schroeder-Heister in ‘Validity concepts in proof-theoretic semantics’ (2006). We will call the new notion generalized proof-theoretic validity and show that the logic of generalized proof-theoretic validity is intuitionistic logic.
Topics & Concepts
Structural proof theoryProof theoryMathematicsCompleteness (order theory)Intuitionistic logicCalculus (dental)Discrete mathematicsLinear logicMathematical proofMathematical analysisMedicineGeometryDentistryLogic, programming, and type systemsLogic, Reasoning, and KnowledgeAdvanced Algebra and Logic