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Modular Construction of Complete Coalgebraic Logics

Modular Construction of Complete Coalgebraic Logics
Modular Construction of Complete Coalgebraic Logics
We present a modular approach to defining logics for a wide variety of state-based systems. The systems are modelled by coalgebras, and we use modal logics to specify their observable properties. We show that the syntax, semantics and proof systems associated to such logics can all be derived in a modular fashion. Moreover, we show that the logics thus obtained inherit soundness, completeness and expressiveness properties from their building blocks. We apply these techniques to derive sound, complete and expressive logics for a wide variety of probabilistic systems, for which no complete axiomatisation has been obtained so far.
Coalgebra, Modal Logic, Completeness, Probabilistic automata, Modularity
0304-3975
83-108
Cirstea, C
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Pattinson, D
e0a15626-4d02-428d-ab3e-a0385a5f3dfe
Cirstea, C
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Pattinson, D
e0a15626-4d02-428d-ab3e-a0385a5f3dfe

Cirstea, C and Pattinson, D (2007) Modular Construction of Complete Coalgebraic Logics Theoretical Computer Science, 388, pp. 83-108.

Record type: Article

Abstract

We present a modular approach to defining logics for a wide variety of state-based systems. The systems are modelled by coalgebras, and we use modal logics to specify their observable properties. We show that the syntax, semantics and proof systems associated to such logics can all be derived in a modular fashion. Moreover, we show that the logics thus obtained inherit soundness, completeness and expressiveness properties from their building blocks. We apply these techniques to derive sound, complete and expressive logics for a wide variety of probabilistic systems, for which no complete axiomatisation has been obtained so far.

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Published date: 2007
Keywords: Coalgebra, Modal Logic, Completeness, Probabilistic automata, Modularity
Organisations: Electronic & Software Systems

Identifiers

Local EPrints ID: 262612
URI: http://eprints.soton.ac.uk/id/eprint/262612
ISSN: 0304-3975
PURE UUID: ef50043b-e215-469a-b3b5-75a687cca279

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Date deposited: 19 May 2006
Last modified: 18 Jul 2017 08:49

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Contributors

Author: C Cirstea
Author: D Pattinson

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