Game semantics for lattice-based modal {\mu}-calculus
Logic
2024-08-14 v3
Abstract
In this paper, we generalize modal -calculus to the non-distributive (lattice-based) modal -calculus and formalize some scenarios regarding categorization using it. We also provide a game semantics for the developed logic. The proof of adequacy of this game semantics proceeds by generalizing the unfolding games on the power-set algebras to the arbitrary lattices and showing that these games can be used to determine the least and the greatest fixed points of a monotone operator on a lattice. Finally, we define a notion of bisimulations on the polarities and show invariance of non-distributive modal -calculus under them.
Cite
@article{arxiv.2310.13944,
title = {Game semantics for lattice-based modal {\mu}-calculus},
author = {Yiwen Ding and Krishna Manoorkar and Mattia Panettiere and Apostolos Tzimoulis and Ruoding Wang},
journal= {arXiv preprint arXiv:2310.13944},
year = {2024}
}