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arXiv · 2505.10765

A completeness theorem in proof-theoretic semantics via set-theoretic semantics

Ryo Takemura
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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.

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Ryo Takemura. 2025-05-16. A completeness theorem in proof-theoretic semantics via set-theoretic semantics. https://arxiv.org/abs/2505.10765

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