EXPTIME Tableaux for the Coalgebraic Mu-Calculus
EXPTIME Tableaux for the Coalgebraic Mu-Calculus
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.
179-193
Cirstea, Corina
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Kupke, Clemens
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Pattinson, Dirk
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Grädel, Erich
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Kahle, Reinhard
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2009
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Kupke, Clemens
903c8340-ea04-43d6-aefa-e613e5a2034d
Pattinson, Dirk
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Grädel, Erich
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Kahle, Reinhard
550a354f-4aef-4f6b-9711-01b1a3df1e38
Cirstea, Corina, Kupke, Clemens and Pattinson, Dirk
(2009)
EXPTIME Tableaux for the Coalgebraic Mu-Calculus.
Grädel, Erich and Kahle, Reinhard
(eds.)
Computer Science Logic 2009.
.
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.
Text
csl2009final.pdf
- Accepted Manuscript
More information
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
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Date deposited: 22 Jul 2009 12:57
Last modified: 15 Mar 2024 03:18
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Contributors
Author:
Corina Cirstea
Author:
Clemens Kupke
Author:
Dirk Pattinson
Editor:
Erich Grädel
Editor:
Reinhard Kahle
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