Completeness of Tableau Calculi for Two-Dimensional Hybrid Logics
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912966387957760 |
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| author | Nishimura, Yuki |
| author_facet | Nishimura, Yuki |
| contents | Hybrid logic is one of the extensions of modal logic. The many-dimensional product of hybrid logic is called hybrid product logic (HPL). We construct a sound and complete tableau calculus for two-dimensional HPL. Also, we made a tableau calculus for hybrid dependent product logic (HdPL), where one dimension depends on the other. In addition, we add a special rule to the tableau calculus for HdPL and show that it is still sound and complete. All of them lack termination, however. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_09630 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Completeness of Tableau Calculi for Two-Dimensional Hybrid Logics Nishimura, Yuki Logic Logic in Computer Science 03B60 Hybrid logic is one of the extensions of modal logic. The many-dimensional product of hybrid logic is called hybrid product logic (HPL). We construct a sound and complete tableau calculus for two-dimensional HPL. Also, we made a tableau calculus for hybrid dependent product logic (HdPL), where one dimension depends on the other. In addition, we add a special rule to the tableau calculus for HdPL and show that it is still sound and complete. All of them lack termination, however. |
| title | Completeness of Tableau Calculi for Two-Dimensional Hybrid Logics |
| topic | Logic Logic in Computer Science 03B60 |
| url | https://arxiv.org/abs/2210.09630 |