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Journal of Logic and Computation

Volume 12, Issue 4, August 2002: pp. 583-606

Linear Tense Logics of Increasing Sets

Bernhard Heinemann1

1Fachbereich Informatik, FernUniversität Hagen, D-58084 Hagen, Germany. E-mail: Bernhard.Heinemann@fernuni-hagen.de

We provide an extension of the language of linear tense logic with future and past connectives F and P, respectively, by a modality that quantifies over the points of some set which is assumed to increase in the course of time. In this way we obtain a general framework for modelling growth qualitatively. We develop an appropriate logical system, prove a corresponding completeness and decidability result and discuss the various kinds of flow of time in the new context. We also consider decreasing sets briefly.

Keywords: Temporal reasoning; modal logics of time; modal logics of set spaces

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