A completeness theorem in proof-theoretic semantics via set-theoretic semantics
Logic
2025-05-19 v1
Abstract
We investigate the completeness of intuitionistic logic with respect to Prawitz's proof-theoretic validity. As an intuitionistic natural deduction system, we apply atomic second-order intuitionistic propositional logic. By developing phase semantics with proof-terms introduced by Okada & Takemura (2007), we construct a special phase model whose domain consists of closed terms. We then discuss how our phase semantics can be regarded as proof-theoretic semantics, and we prove completeness with respect to proof-theoretic semantics via our phase semantics.
Keywords
Cite
@article{arxiv.2505.10765,
title = {A completeness theorem in proof-theoretic semantics via set-theoretic semantics},
author = {Ryo Takemura},
journal= {arXiv preprint arXiv:2505.10765},
year = {2025}
}