Axiomatizing logics of finite Gödel-Kripke models
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918503648329728 |
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| author | Vidal, Amanda Rodriguez, Ricardo O. |
| author_facet | Vidal, Amanda Rodriguez, Ricardo O. |
| contents | We investigate completeness for modal Gödel logics with respect to finite Gödel-Kripke models, along with related aspects. It is well known that the logics studied in [4, 11] fail to be complete with respect to finite Gödel-Kripke models. We show that the natural candidate axiomatic extensions do not restore completeness, thereby resolving a 15 year open problem posed in the aforementioned works. We then provide new axiomatizations that are complete for finite models and characterize intermediate witnessing conditions that hold for the basic logics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15810 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Axiomatizing logics of finite Gödel-Kripke models Vidal, Amanda Rodriguez, Ricardo O. Logic We investigate completeness for modal Gödel logics with respect to finite Gödel-Kripke models, along with related aspects. It is well known that the logics studied in [4, 11] fail to be complete with respect to finite Gödel-Kripke models. We show that the natural candidate axiomatic extensions do not restore completeness, thereby resolving a 15 year open problem posed in the aforementioned works. We then provide new axiomatizations that are complete for finite models and characterize intermediate witnessing conditions that hold for the basic logics. |
| title | Axiomatizing logics of finite Gödel-Kripke models |
| topic | Logic |
| url | https://arxiv.org/abs/2605.15810 |