Generalizing the Modal and Temporal Logic of Linear Time

Abstract

In the present paper we generalize two fundamental systems modelling the flow of time: the modal logic S4.3 and propositional linear time temporal logic. We allow to consider a whole set of states instead of only a single one at every time. Moreover, we assume that these sets increase in the course of time. Thus we get a basic formalism expressing a distinguished dynamic aspect of sets, growing. Our main results include completeness of the proposed axiomatizations and decidability of the set of all formally provable formulas.KeywordsModal LogicTemporal LogicCompleteness ProofAccessibility RelationCanonical ModelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.