Uploaded May 2025 | Updated September 2026, 20 hours ago

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Recorded as part of the CFvW colloquium on May 28, 2025

A completeness theorem in proof-theoretic semantics via set-theoretic semantics - Ryo Takemura (Nihon University, Japan)

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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