First-Order Modal Logic via Logical Categories

Fuente: arXiv
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Autori principali: Ghilardi, Silvio, Marquès, Jérémie
Natura: Preprint
Pubblicazione: 2025
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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