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arXiv · 2305.11015

COOL 2 -- A Generic Reasoner for Modal Fixpoint Logics

Oliver Görlitz·Daniel Hausmann·Merlin Humml·Dirk Pattinson·Simon Prucker·Lutz Schröder
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Abstract

There is a wide range of modal logics whose semantics goes beyond relational structures, and instead involves, e.g., probabilities, multi-player games, weights, or neighbourhood structures. Coalgebraic logic serves as a unifying semantic and algorithmic framework for such logics. It provides uniform reasoning algorithms that are easily instantiated to particular, concretely given logics. The COOL 2 reasoner provides an implementation of such generic algorithms for coalgebraic modal fixpoint logics. As concrete instances, we obtain in particular reasoners for the aconjunctive and alternation-free fragments of the graded $\mu$-calculus and the alternating-time $\mu$-calculus. We evaluate the tool on standard benchmark sets for fixpoint-free graded modal logic and alternating-time temporal logic (ATL), as well as on a dedicated set of benchmarks for the graded $\mu$-calculus.

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Oliver Görlitz, Daniel Hausmann, Merlin Humml, Dirk Pattinson, Simon Prucker, Lutz Schröder. 2023-05-18. COOL 2 -- A Generic Reasoner for Modal Fixpoint Logics. https://arxiv.org/abs/2305.11015

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