First-order Modal Logic Via Logical Categories
Year: 2025
Type: article
Abstract: 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 a way to build syntactic categories out of first-order modal theories.
Source: Journal of Symbolic Logic
Authors: SILVIO GHILARDI, JÉRÉMIE MARQUÈS
Institution: University of Milan
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4415842339
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