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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2505.10765 |
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| _version_ | 1866915289702072320 |
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| author | Takemura, Ryo |
| author_facet | Takemura, Ryo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A completeness theorem in proof-theoretic semantics via set-theoretic semantics Takemura, Ryo Logic 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. |
| title | A completeness theorem in proof-theoretic semantics via set-theoretic semantics |
| topic | Logic |
| url | https://arxiv.org/abs/2505.10765 |