3 papers
math.CT2025
A Completeness Theorem for Topological Doctrines
Silvio Ghilardi, Jérémie Marquès
We extend logical categories with fiberwise interior and closure operators so as to obtain an embedding theorem into powers of the category of topological spaces. The required axio…
cs.LO2025
First-Order Modal Logic via Logical Categories
Silvio Ghilardi, Jérémie Marquès
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…
math.LO2024
Unification with Simple Variable Restrictions and Admissibility of -rules
Rodrigo Nicolau Almeida, Silvio Ghilardi
We develop a method to recognize admissibility of -rules, relating this problem to a specific instance of the unification problem with linear constants restriction, called…