From Proof-theoretic Validity to Base-extension Semantics for Intuitionistic Propositional Logic

Proof-theoretic semantics (P-tS) is the approach to meaning in logic based on 'proof' (as opposed to 'truth'). There are two major approaches to P-tS: proof-theoretic validity (P-tV) and base-extension semantics (B-eS). The former is a semantics of arguments, and the latter is a...

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Bibliographic Details
Published inarXiv.org
Main Authors Gheorghiu, Alexander V, Pym, David J
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.09.2024
Subjects
Semantics
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Summary:Proof-theoretic semantics (P-tS) is the approach to meaning in logic based on 'proof' (as opposed to 'truth'). There are two major approaches to P-tS: proof-theoretic validity (P-tV) and base-extension semantics (B-eS). The former is a semantics of arguments, and the latter is a semantics of logical constants. This paper demonstrates that the B-eS for intuitionistic propositional logic (IPL) encapsulates the declarative content of a version of P-tV based on the elimination rules. This explicates how the B-eS for IPL works, and shows the completeness of this version of P-tV.
ISSN:2331-8422