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EXPTIME Tableaux for the Coalgebraic Mu-Calculus

Cirstea, Corina, Kupke, Clemens and Pattinson, Dirk, (2009) EXPTIME Tableaux for the Coalgebraic Mu-Calculus Grädel, Erich and Kahle, Reinhard (eds.) At Computer Science Logic 2009. , pp. 179-193.

Record type: Conference or Workshop Item (Paper)

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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Published date: 2009
Venue - Dates: Computer Science Logic 2009, 2009-01-01
Organisations: Electronic & Software Systems

Identifiers

Local EPrints ID: 267695
URI: http://eprints.soton.ac.uk/id/eprint/267695
PURE UUID: b7f078df-50b9-46e5-9090-667607871a10

Catalogue record

Date deposited: 22 Jul 2009 12:57
Last modified: 18 Jul 2017 07:00

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Contributors

Author: Corina Cirstea
Author: Clemens Kupke
Author: Dirk Pattinson
Editor: Erich Grädel
Editor: Reinhard Kahle

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