EXPTIME tableaux for the coalgebraic µ-Calculus
EXPTIME tableaux for the coalgebraic µ-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.
coalgebra, modal logic, µ-calculus, tableau-based decision procedures
1-33
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Kupke, Clemens
903c8340-ea04-43d6-aefa-e613e5a2034d
Pattinson, Dirk
b6607852-21d6-492c-a334-475ad5a7e7b4
10 August 2011
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Kupke, Clemens
903c8340-ea04-43d6-aefa-e613e5a2034d
Pattinson, Dirk
b6607852-21d6-492c-a334-475ad5a7e7b4
Cirstea, Corina, Kupke, Clemens and Pattinson, Dirk
(2011)
EXPTIME tableaux for the coalgebraic µ-Calculus.
Logical Methods in Computer Science, 7 (3:03), .
(doi:10.2168/LMCS-7(3:3)2011).
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: 10 August 2011
Keywords:
coalgebra, modal logic, µ-calculus, tableau-based decision procedures
Organisations:
Electronic & Software Systems
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Local EPrints ID: 271027
URI: http://eprints.soton.ac.uk/id/eprint/271027
PURE UUID: 2518786e-b158-45ed-a16a-4add74c0ad09
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Date deposited: 07 May 2010 10:28
Last modified: 15 Mar 2024 03:18
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Author:
Corina Cirstea
Author:
Clemens Kupke
Author:
Dirk Pattinson
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