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Maximal traces and path-based coalgebraic temporal logics

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
0304-3975
5025-5042
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
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), pp. 5025-5042. (doi:10.1016/j.tcs.2011.04.025).

Record type: Article

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: 18 Jul 2017 06:33

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Author: Corina Cirstea

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