Complexity results for modal logic with recursion via translations and tableaux

• 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.

Ämnesord

NATURVETENSKAP  -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences -- Computer Sciences (hsv//eng)

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

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