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arXiv · 2310.13944

Game semantics for lattice-based modal {\mu}-calculus

Yiwen Ding·Krishna Manoorkar·Mattia Panettiere·Apostolos Tzimoulis·Ruoding Wang
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Abstract

In this paper, we generalize modal $\mu$-calculus to the non-distributive (lattice-based) modal $\mu$-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 $\mu$-calculus under them.

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Yiwen Ding, Krishna Manoorkar, Mattia Panettiere, Apostolos Tzimoulis, Ruoding Wang. 2023-10-21. Game semantics for lattice-based modal {\mu}-calculus. https://arxiv.org/abs/2310.13944

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