Maximal traces and path-based coalgebraic temporal logics
Maximal traces and path-based coalgebraic temporal logics
This paper gives a general coalgebraic account of temporal logics whose semantics involves a notion of computation path. Examples of such logics include the logic CTL* for transition systems and the logic PCTL for probabilistic transition systems. Our path-based temporal logics are interpreted over coalgebras of endofunctors obtained as the composition of a computation type (e.g. nondeterministic or stochastic) with a general transition type. The semantics of such logics relies on the existence of execution maps similar to the trace maps introduced by Jacobs and co-authors as part of the coalgebraic theory of finite traces [1]. We consider both finite execution maps derived from the theory of finite traces, and a new notion of maximal execution map that accounts for maximal, possibly infinite executions. The latter is needed to recover the logics CTL* and PCTL as specific path-based logics.
coalgebra, trace semantics, computation path, temporal logic, nondeterminism, probability
5025-5042
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
2 September 2011
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Cirstea, Corina
(2011)
Maximal traces and path-based coalgebraic temporal logics.
[in special issue: CMCS Tenth Anniversary Meeting]
Theoretical Computer Science, 412 (38), .
(doi:10.1016/j.tcs.2011.04.025).
Abstract
This paper gives a general coalgebraic account of temporal logics whose semantics involves a notion of computation path. Examples of such logics include the logic CTL* for transition systems and the logic PCTL for probabilistic transition systems. Our path-based temporal logics are interpreted over coalgebras of endofunctors obtained as the composition of a computation type (e.g. nondeterministic or stochastic) with a general transition type. The semantics of such logics relies on the existence of execution maps similar to the trace maps introduced by Jacobs and co-authors as part of the coalgebraic theory of finite traces [1]. We consider both finite execution maps derived from the theory of finite traces, and a new notion of maximal execution map that accounts for maximal, possibly infinite executions. The latter is needed to recover the logics CTL* and PCTL as specific path-based logics.
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Published date: 2 September 2011
Keywords:
coalgebra, trace semantics, computation path, temporal logic, nondeterminism, probability
Organisations:
Electronic & Software Systems
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Local EPrints ID: 272229
URI: http://eprints.soton.ac.uk/id/eprint/272229
ISSN: 0304-3975
PURE UUID: 27e011f5-db7a-4027-8598-2a363004c9bf
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Date deposited: 27 Apr 2011 10:16
Last modified: 15 Mar 2024 03:18
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Author:
Corina Cirstea
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