Two types of filtrations for $\mathrm{wK4}$ and its relatives
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915340013797376 |
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| author | Kudinov, Andrey Shapirovsky, Ilya |
| author_facet | Kudinov, Andrey Shapirovsky, Ilya |
| contents | We study the finite model property of subframe logics with expressible transitive reflexive closure modality. For $m>0$, let $\mathrm{L}_m$ be the logic defined by axiom $\lozenge^{m+1} p\to \lozenge p\vee p$. We construct filtrations for the logics $\mathrm{L}_m$. It follows that these logics and their tense counterparts have the finite model property. Then we show that every canonical subframe logic that contains $\mathrm{L}_m$ have the finite model property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00457 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Two types of filtrations for $\mathrm{wK4}$ and its relatives Kudinov, Andrey Shapirovsky, Ilya Logic 03B45 We study the finite model property of subframe logics with expressible transitive reflexive closure modality. For $m>0$, let $\mathrm{L}_m$ be the logic defined by axiom $\lozenge^{m+1} p\to \lozenge p\vee p$. We construct filtrations for the logics $\mathrm{L}_m$. It follows that these logics and their tense counterparts have the finite model property. Then we show that every canonical subframe logic that contains $\mathrm{L}_m$ have the finite model property. |
| title | Two types of filtrations for $\mathrm{wK4}$ and its relatives |
| topic | Logic 03B45 |
| url | https://arxiv.org/abs/2401.00457 |