EXPTIME tableaux for the coalgebraic mu-calculus

Corina Cirstea, Clemens Kupke, Dirk Pattinson

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The coalgebraic approach to modal logic provides a uniform framework that captures the semantics of a large class of structurally different modal logics, including e.g. graded and probabilistic modal logics and coalition logic. In this paper, we introduce the coalgebraic mu-calculus, an extension of the general (coalgebraic) framework with fixpoint operators. Our main results are completeness of the associated tableau calculus and EXPTIME decidability for guarded formulas. Technically, this is achieved by reducing satisfiability to the existence of non-wellfounded tableaux, which is in turn equivalent to the existence of winning strategies in parity games. Our results are parametric in the underlying class of models and yield, as concrete applications, previously unknown complexity bounds for the probabilistic mu-calculus and for an extension of coalition logic with fixpoints.
Original languageEnglish
Article number3
Number of pages33
JournalLogical Methods in Computer Science
Issue number3
Publication statusPublished - 11 Aug 2011


  • coalgebra
  • modal logic
  • tableau-based decision procedures
  • coalgebraic approach


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