A completeness theorem in proof-theoretic semantics via set-theoretic semantics
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915289702072320 |
|---|---|
| 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 |