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Temporalising tableaux

Roman Kontchakov, Carsten Lutz, Frank Wolter & Michael Zakharyaschev

Studia Logica 76 (1):91 - 134 (2004)

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Tableaux-based decision method for single-agent linear time synchronous temporal epistemic logics with interacting time and knowledge.Mai Ajspur & Valentin Goranko - 2013 - In Kamal Lodaya (ed.), Logic and Its Applications. Springer. pp. 80--96.details Temporal epistemic logics are known, from results of Halpern and Vardi, to have a wide range of complexities of the satisfiability problem: from PSPACE, through non-elementary, to highly undecidable. These complexities depend on the choice of some key parameters specifying, inter alia, possible interactions between time and knowledge, such as synchrony and agents' abilities for learning and recall. In this work we develop practically implementable tableau-based decision procedures for deciding satisfiability in single-agent synchronous temporal-epistemic logics with interactions between time and (...) Download Export citation Bookmark
Temporal logic.Antony Galton - 2008 - Stanford Encyclopedia of Philosophy.details Download Export citation Bookmark 9 citations
A general tableau method for propositional interval temporal logics: Theory and implementation.V. Goranko, A. Montanari, P. Sala & G. Sciavicco - 2006 - Journal of Applied Logic 4 (3):305-330.details In this paper we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema's \cdt\ logic interpreted over partial orders (\nsbcdt\ for short). It combines (...) Download Export citation Bookmark 5 citations
Temporal logic.Temporal Logic - forthcoming - Stanford Encyclopedia of Philosophy.details Download Export citation Bookmark
Non-primitive recursive decidability of products of modal logics with expanding domains.David Gabelaia, Agi Kurucz, Frank Wolter & Michael Zakharyaschev - 2006 - Annals of Pure and Applied Logic 142 (1):245-268.details We show that—unlike products of ‘transitive’ modal logics which are usually undecidable—their ‘expanding domain’ relativisations can be decidable, though not in primitive recursive time. In particular, we prove the decidability and the finite expanding product model property of bimodal logics interpreted in two-dimensional structures where one component—call it the ‘flow of time’—is • a finite linear order or a finite transitive tree and the other is composed of structures like • transitive trees/partial orders/quasi-orders/linear orders or only finite such structures expanding (...) Download Export citation Bookmark 10 citations
Tableaux for logics of time and knowledge with interactions relating to synchrony.Clare Dixon, Cláudia Nalon & Michael Fisher - 2004 - Journal of Applied Non-Classical Logics 14 (4):397-445.details The paper describes tableaux based proof methods for temporal logics of knowledge allowing non-trivial interaction axioms between the modal and temporal components, namely those of synchrony and no learning and synchrony and perfect recall. The interaction axioms allow the description of how knowledge evolves over time and makes reasoning in such logics theoretically more complex. Such logics can be used to specify systems that involve the knowledge of processes or agents and which change over time, for example agent based systems, (...) Download Export citation Bookmark 2 citations

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