From Proof-theoretic Validity to Base-extension Semantics for Intuitionistic Propositional Logic
Logic in Computer Science
2024-09-13 v4 Logic
Abstract
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.
Cite
@article{arxiv.2210.05344,
title = {From Proof-theoretic Validity to Base-extension Semantics for Intuitionistic Propositional Logic},
author = {Alexander V. Gheorghiu and David J. Pym},
journal= {arXiv preprint arXiv:2210.05344},
year = {2024}
}