Toward the van Benthem Characterization Theorem for Non-Distributive Modal Logic
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909163353800704 |
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| author | Ding, Yiwen Manoorkar, Krishna Panettiere, Mattia Wang, Ruoding |
| author_facet | Ding, Yiwen Manoorkar, Krishna Panettiere, Mattia Wang, Ruoding |
| contents | In this paper, we introduce the simulations and bisimulations on polarity-based semantics for non-distributive modal logic, which are natural generalizations of those notions on Kripke semantics for modal logic. We also generalize other important model-theoretic notions about Kripke semantics such as image-finite models, modally-saturated models, ultrafilter extension and ultrapower extension to the non-distributive setting. By using these generalizations, we prove the Hennessy-Milner theorem and the van Benthem characterization theorem for non-distributive modal logic based on polarity-based semantics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05574 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Toward the van Benthem Characterization Theorem for Non-Distributive Modal Logic Ding, Yiwen Manoorkar, Krishna Panettiere, Mattia Wang, Ruoding Logic 03G10 In this paper, we introduce the simulations and bisimulations on polarity-based semantics for non-distributive modal logic, which are natural generalizations of those notions on Kripke semantics for modal logic. We also generalize other important model-theoretic notions about Kripke semantics such as image-finite models, modally-saturated models, ultrafilter extension and ultrapower extension to the non-distributive setting. By using these generalizations, we prove the Hennessy-Milner theorem and the van Benthem characterization theorem for non-distributive modal logic based on polarity-based semantics. |
| title | Toward the van Benthem Characterization Theorem for Non-Distributive Modal Logic |
| topic | Logic 03G10 |
| url | https://arxiv.org/abs/2404.05574 |