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EXPTIME tableaux for the coalgebraic µ-Calculus

Cirstea, Corina, Kupke, Clemens and Pattinson, Dirk (2011) EXPTIME tableaux for the coalgebraic µ-Calculus Logical Methods in Computer Science, 7, (3:03), pp. 1-33. (doi:10.2168/LMCS-7(3:3)2011).

Record type: Article

Abstract

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. 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.

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More information

Published date: 10 August 2011
Keywords: coalgebra, modal logic, µ-calculus, tableau-based decision procedures
Organisations: Electronic & Software Systems

Identifiers

Local EPrints ID: 271027
URI: http://eprints.soton.ac.uk/id/eprint/271027
PURE UUID: 2518786e-b158-45ed-a16a-4add74c0ad09

Catalogue record

Date deposited: 07 May 2010 10:28
Last modified: 18 Jul 2017 06:47

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Contributors

Author: Corina Cirstea
Author: Clemens Kupke
Author: Dirk Pattinson

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