Journal of Logic, Language and Information 11 (4):389-425 (2002)
AbstractTemporal logic can be used to describe processes: their behaviour ischaracterized by a set of temporal models axiomatized by a temporaltheory. Two types of models are most often used for this purpose: linearand branching time models. In this paper a third approach, based onsocalled joint closure models, is studied using models which incorporateall possible behaviour in one model. Relations between this approach andthe other two are studied. In order to define constructions needed torelate branching time models, appropriate algebraic notions are defined(in a category theoretical manner) and exploited. In particular, thenotion of joint closure is used to construct one model subsuming a setof models. Using this universal algebraic construction we show that aset of linear models can be merged to a unique branching time model.Logical properties of the described algebraic constructions are studied.The proposed approach has been successfully aplied to obtain anappropriate semantics for non-monotonic reasoning processes based ondefault logic. References are discussed that show the details of theseapplications.
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References found in this work
Adding a Temporal Dimension to a Logic System.Marcelo Finger & Dov M. Gabbay - 1992 - Journal of Logic, Language and Information 1 (3):203-233.
The Logic of Time: A Model-Theoretic Investigation Into the Varieties of Temporal Ontology and Temporal Discourse.Johan van Benthem - 1982 - Dordrecht, Netherland: Kluwer Academic Publishers.
The Logic of Time: A Model-Theoretic Investigation Into the Varieties of Temporal Ontology and Temporal Discourse.J. F. A. K. van Benthem - 1984 - Journal of Philosophical Logic 13 (3):235-248.
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