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Canonical coalgebraic linear time logics

Canonical coalgebraic linear time logics
Canonical coalgebraic linear time logics
We extend earlier work on linear time fixpoint logics for coalgebras with branching, by showing how propositional operators arising from the choice of branching monad can be canonically added to these logics. We then consider two semantics for the uniform modal fragments of such logics: the previously-proposed, step-wise semantics and a new semantics akin to those of path-based logics. We prove that the two semantics are equivalent, and show that the canonical choice made for resolving branching in these logics is crucial for this property. We also state conditions under which similar, non-canonical logics enjoy the same property – this applies both to the choice of a branching modality and to the choice of linear time modalities. Our logics allow reasoning about linear time behaviour in systems with non-deterministic, probabilistic or weighted branching. In all these cases, the logics enhanced with propositional operators gain in expressiveness. Another contribution of our work is a reformulation of fixpoint semantics, which applies to any coalgebraic modal logic whose semantics arises from a one-step semantics.
coalgebra, linear time logic, fix point logic
1868-8969
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea

Cirstea, Corina (2015) Canonical coalgebraic linear time logics Leibniz International Proceedings in Informatics (LIPIcs)

Record type: Article

Abstract

We extend earlier work on linear time fixpoint logics for coalgebras with branching, by showing how propositional operators arising from the choice of branching monad can be canonically added to these logics. We then consider two semantics for the uniform modal fragments of such logics: the previously-proposed, step-wise semantics and a new semantics akin to those of path-based logics. We prove that the two semantics are equivalent, and show that the canonical choice made for resolving branching in these logics is crucial for this property. We also state conditions under which similar, non-canonical logics enjoy the same property – this applies both to the choice of a branching modality and to the choice of linear time modalities. Our logics allow reasoning about linear time behaviour in systems with non-deterministic, probabilistic or weighted branching. In all these cases, the logics enhanced with propositional operators gain in expressiveness. Another contribution of our work is a reformulation of fixpoint semantics, which applies to any coalgebraic modal logic whose semantics arises from a one-step semantics.

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Accepted/In Press date: 7 May 2015
Keywords: coalgebra, linear time logic, fix point logic
Organisations: Electronic & Software Systems

Identifiers

Local EPrints ID: 380300
URI: http://eprints.soton.ac.uk/id/eprint/380300
ISSN: 1868-8969
PURE UUID: d6cb9e49-223d-4524-a9a9-aeaa2036ff22

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Date deposited: 14 Sep 2015 11:14
Last modified: 17 Jul 2017 20:36

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Contributors

Author: Corina Cirstea

University divisions

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