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- Aceto, Luca, et al.
(författare)
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Complexity results for modal logic with recursion via translations and tableaux
- 2024
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Ingår i: Logical Methods in Computer Science. - : LOGICAL METHODS COMPUTER SCIENCE. - 1860-5974. ; 30:3
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Tidskriftsartikel (refereegranskat)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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