Polytopological Semantics for Intuitionistic Modal Logics
Logic
2026-04-28 v1
Abstract
We develop polytopological semantics for various constructive, intuitionistic, and G\"odel--Dummett variations of and . In our models, intuitionistic and modal operators are interpreted via various topologies over a single set, equipped with either the closure or derivative operators. We identify regularity conditions to ensure that spaces validate each of our target logics and prove that all the logics considered are sound and strongly complete with respect to their respective semantics.
Keywords
Cite
@article{arxiv.2604.23234,
title = {Polytopological Semantics for Intuitionistic Modal Logics},
author = {Juan P. Aguilera and David Fernández-Duque and Leonardo Pacheco},
journal= {arXiv preprint arXiv:2604.23234},
year = {2026}
}