arXiv Open Access 2025

First-Order Modal Logic via Logical Categories

Silvio Ghilardi Jérémie Marquès

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Abstrak

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.

Topik & Kata Kunci

cs.LO math.LO

Penulis (2)

Silvio Ghilardi

Jérémie Marquès

Format Sitasi

APA MLA BibTeX

Ghilardi, S., Marquès, J. (2025). First-Order Modal Logic via Logical Categories. https://arxiv.org/abs/2504.02985

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Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓