Toward the van Benthem Characterization Theorem for Non-Distributive Modal Logic
Logic
2024-04-09 v1
Abstract
In this paper, we introduce the simulations and bisimulations on polarity-based semantics for non-distributive modal logic, which are natural generalizations of those notions on Kripke semantics for modal logic. We also generalize other important model-theoretic notions about Kripke semantics such as image-finite models, modally-saturated models, ultrafilter extension and ultrapower extension to the non-distributive setting. By using these generalizations, we prove the Hennessy-Milner theorem and the van Benthem characterization theorem for non-distributive modal logic based on polarity-based semantics.
Cite
@article{arxiv.2404.05574,
title = {Toward the van Benthem Characterization Theorem for Non-Distributive Modal Logic},
author = {Yiwen Ding and Krishna Manoorkar and Mattia Panettiere and Ruoding Wang},
journal= {arXiv preprint arXiv:2404.05574},
year = {2024}
}