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Generic Infinite Traces and Path-Based Coalgebraic Temporal Logics

Generic Infinite Traces and Path-Based Coalgebraic Temporal Logics
Generic Infinite Traces and Path-Based Coalgebraic Temporal Logics
This paper gives a general coalgebraic account of the notions of possibly infinite trace and possibly infinite execution in state-based, dynamical systems, by extending the generic theory of finite traces and executions developed by Hasuo and coauthors [8]. The systems we consider are modelled as coalgebras of endofunctors obtained as the composition of a computational type (e.g. nondeterministic or stochastic) with a general transition type. This generalises existing work by Jacobs [10] that only accounts for a nondeterministic computational type. We subsequently introduce path-based temporal (including fixpoint) logics for coalgebras of such endofunctors, whose semantics is based upon the notion of possibly infinite execution. Our approach instantiates to both nondeterministic and stochastic computations, yielding, in particular, path-based fixpoint logics in the style of CTL* for nondeterministic systems, as well as generalisations of the logic PCTL for probabilistic systems.
coalgebra, trace semantics, temporal logic, nondeterminism, probability
83-103
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Jacobs, B.P.F.
10000303-7bbc-4a90-a88a-2ca9f51a8375
Niqui, M.
282ae186-f1e4-48b5-9e90-a65cc1cbeade
Rutten, J.J.M.M.
bf112f10-cf0d-4e6b-9bec-a86df7c8c53d
Silva, A.
7ae1cc5b-6099-4f8d-9288-d328b2de87ec
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Jacobs, B.P.F.
10000303-7bbc-4a90-a88a-2ca9f51a8375
Niqui, M.
282ae186-f1e4-48b5-9e90-a65cc1cbeade
Rutten, J.J.M.M.
bf112f10-cf0d-4e6b-9bec-a86df7c8c53d
Silva, A.
7ae1cc5b-6099-4f8d-9288-d328b2de87ec

Cirstea, Corina, (2010) Generic Infinite Traces and Path-Based Coalgebraic Temporal Logics Jacobs, B.P.F., Niqui, M., Rutten, J.J.M.M. and Silva, A. (eds.) At Coalgebraic Methods in Computer Science 2010. , pp. 83-103.

Record type: Conference or Workshop Item (Paper)

Abstract

This paper gives a general coalgebraic account of the notions of possibly infinite trace and possibly infinite execution in state-based, dynamical systems, by extending the generic theory of finite traces and executions developed by Hasuo and coauthors [8]. The systems we consider are modelled as coalgebras of endofunctors obtained as the composition of a computational type (e.g. nondeterministic or stochastic) with a general transition type. This generalises existing work by Jacobs [10] that only accounts for a nondeterministic computational type. We subsequently introduce path-based temporal (including fixpoint) logics for coalgebras of such endofunctors, whose semantics is based upon the notion of possibly infinite execution. Our approach instantiates to both nondeterministic and stochastic computations, yielding, in particular, path-based fixpoint logics in the style of CTL* for nondeterministic systems, as well as generalisations of the logic PCTL for probabilistic systems.

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Published date: 2010
Venue - Dates: Coalgebraic Methods in Computer Science 2010, 2010-01-01
Keywords: coalgebra, trace semantics, temporal logic, nondeterminism, probability
Organisations: Electronic & Software Systems

Identifiers

Local EPrints ID: 271026
URI: http://eprints.soton.ac.uk/id/eprint/271026
PURE UUID: 5452cd45-447f-4abd-9155-9a9502489126

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Date deposited: 07 May 2010 10:09
Last modified: 18 Jul 2017 06:47

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Contributors

Author: Corina Cirstea
Editor: B.P.F. Jacobs
Editor: M. Niqui
Editor: J.J.M.M. Rutten
Editor: A. Silva

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