First-Order Modal Logic via Logical Categories
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913775619145728 |
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| author | Ghilardi, Silvio Marquès, Jérémie |
| author_facet | Ghilardi, Silvio Marquès, Jérémie |
| contents | We extend the logical categories framework to first order modal logic. In our modal categories, modal operators are applied directly to subobjects and interact with the background factorization system. We prove a Joyal-style representation theorem into relational structures formalizing a `counterpart' notion. We investigate saturation conditions related to definability questions and we enrich our framework with quotients and disjoint sums, thus leading to the notion of a modal (quasi) pretopos. We finally show how to build syntactic categories out of first order modal theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02985 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | First-Order Modal Logic via Logical Categories Ghilardi, Silvio Marquès, Jérémie Logic in Computer Science Logic 03B45, 03G30, 03B70 We extend the logical categories framework to first order modal logic. In our modal categories, modal operators are applied directly to subobjects and interact with the background factorization system. We prove a Joyal-style representation theorem into relational structures formalizing a `counterpart' notion. We investigate saturation conditions related to definability questions and we enrich our framework with quotients and disjoint sums, thus leading to the notion of a modal (quasi) pretopos. We finally show how to build syntactic categories out of first order modal theories. |
| title | First-Order Modal Logic via Logical Categories |
| topic | Logic in Computer Science Logic 03B45, 03G30, 03B70 |
| url | https://arxiv.org/abs/2504.02985 |