Local Intuitionistic Modal Logics and Their Calculi
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910362186547200 |
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| author | Balbiani, Philippe Gao, Han Gencer, Çiğdem Olivetti, Nicola |
| author_facet | Balbiani, Philippe Gao, Han Gencer, Çiğdem Olivetti, Nicola |
| contents | We investigate intuitionistic modal logics with locally interpreted $\square$ and $\lozenge$. The basic logic LIK is stronger than constructive modal logic WK and incomparable with intuitionistic modal logic IK. We propose an axiomatization of LIK and some of its extensions. We propose bi-nested calculi for LIK and these extensions, thus providing both a decision procedure and a procedure of finite countermodel extraction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06772 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local Intuitionistic Modal Logics and Their Calculi Balbiani, Philippe Gao, Han Gencer, Çiğdem Olivetti, Nicola Logic in Computer Science We investigate intuitionistic modal logics with locally interpreted $\square$ and $\lozenge$. The basic logic LIK is stronger than constructive modal logic WK and incomparable with intuitionistic modal logic IK. We propose an axiomatization of LIK and some of its extensions. We propose bi-nested calculi for LIK and these extensions, thus providing both a decision procedure and a procedure of finite countermodel extraction. |
| title | Local Intuitionistic Modal Logics and Their Calculi |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2403.06772 |