Complexity through Translations for Modal Logic with Recursion

Luca Aceto, Antonis Achilleos, Elli Anastasiadi, Adrian Francalanza, Anna Ingolfsdottir

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 a terminating tableau system for the logics we study, based on Kozen's tableau for the mu-calculus, and the one of Fitting and Massacci for modal logic.

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