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arXiv · 2306.16881

Complexity results for modal logic with recursion via translations and tableaux

Luca Aceto·Antonis Achilleos·Elli Anastasiadi·Adrian Francalanza·Anna Ingólfsdóttir
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Abstract

This paper studies the complexity of classical modal logics and of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complexity results for multi-agent logics via translations to and from the $\mu$-calculus and modal logic, which allow us to transfer known upper and lower bounds. We also use these translations to introduce terminating and non-terminating tableau systems for the logics we study, based on Kozen's tableau for the $\mu$-calculus and the one of Fitting and Massacci for modal logic. Finally, we describe these tableaux with $\mu$-calculus formulas, thus reducing the satisfiability of each of these logics to the satisfiability of the $\mu$-calculus, resulting in a general 2EXP upper bound for satisfiability testing.

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Luca Aceto, Antonis Achilleos, Elli Anastasiadi, Adrian Francalanza, Anna Ingólfsdóttir. 2023-06-29. Complexity results for modal logic with recursion via translations and tableaux. https://doi.org/10.46298/lmcs-20(3%3A14)2024

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