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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.07306 |
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| _version_ | 1866910740892352512 |
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| author | Chen, Zhicheng |
| author_facet | Chen, Zhicheng |
| contents | In this paper, we propose a relational semantics of propositional language, which unifies the relational semantics of intuitionistic logic, Visser's Basic Propositional Logic and orthologic. Working in language $\{\bot,\land,\neg\}$ and $\{\bot,\land,\to\}$ respectively, we axiomatize this basic logic as well as stronger ones corresponding to different combinations of frame conditions: reflexivity, symmetry, and transitivity. We also provide translations from these propositional logics into modal logics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_07306 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A unified relational semantics for BPL, IPL and OL -- axiomatization without disjunction Chen, Zhicheng Logic In this paper, we propose a relational semantics of propositional language, which unifies the relational semantics of intuitionistic logic, Visser's Basic Propositional Logic and orthologic. Working in language $\{\bot,\land,\neg\}$ and $\{\bot,\land,\to\}$ respectively, we axiomatize this basic logic as well as stronger ones corresponding to different combinations of frame conditions: reflexivity, symmetry, and transitivity. We also provide translations from these propositional logics into modal logics. |
| title | A unified relational semantics for BPL, IPL and OL -- axiomatization without disjunction |
| topic | Logic |
| url | https://arxiv.org/abs/2207.07306 |