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Luca Aceto ; Antonis Achilleos ; Elli Anastasiadi ; Adrian Francalanza ; Anna Ingólfsdóttir - Complexity results for modal logic with recursion via translations and tableaux
lmcs:11525 - Logical Methods in Computer Science, August 7, 2024, Volume 20, Issue 3 - https://doi.org/10.46298/lmcs-20(3:14)2024This 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.