Lyndon interpolation property for extensions of $\mathbf{S4}$ and intermediate propositional logics
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909615428468736 |
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| author | Kurahashi, Taishi |
| author_facet | Kurahashi, Taishi |
| contents | We study the Lyndon interpolation property (LIP) and the uniform Lyndon interpolation property (ULIP) for extensions of $\mathbf{S4}$ and intermediate propositional logics. We prove that among the 18 consistent normal modal logics of finite height extending $\mathbf{S4}$ known to have CIP, 11 logics have LIP and 7 logics do not. We also prove that for intermediate propositional logics, the Craig interpolation property, LIP, and ULIP are equivalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00505 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lyndon interpolation property for extensions of $\mathbf{S4}$ and intermediate propositional logics Kurahashi, Taishi Logic We study the Lyndon interpolation property (LIP) and the uniform Lyndon interpolation property (ULIP) for extensions of $\mathbf{S4}$ and intermediate propositional logics. We prove that among the 18 consistent normal modal logics of finite height extending $\mathbf{S4}$ known to have CIP, 11 logics have LIP and 7 logics do not. We also prove that for intermediate propositional logics, the Craig interpolation property, LIP, and ULIP are equivalent. |
| title | Lyndon interpolation property for extensions of $\mathbf{S4}$ and intermediate propositional logics |
| topic | Logic |
| url | https://arxiv.org/abs/2407.00505 |