EXPTIME Tableaux for the Coalgebraic μ-Calculus [chapter]

Corina Cîrstea, Clemens Kupke, Dirk Pattinson
2009 Lecture Notes in Computer Science  
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 µ-calculus, an extension of the general (coalgebraic) framework with fixpoint operators. Our main results are completeness of the associated tableau calculus and EXPTIME decidability. Technically, this is achieved by reducing
more » ... tisfiability 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 µ-calculus and for an extension of coalition logic with fixpoints.
doi:10.1007/978-3-642-04027-6_15 fatcat:tdqe46nv6jdp3p6s2sfxu2tjpu