2025/04/03 by Silvio Ghilardi, Ghilardi, Silvio, Jérémie Marquès +1 · 1 citation
Computer Science · #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Multi-Agent Systems and Negotiation
paper · pdf · doi:10.48550/arxiv.2504.02985
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.