Generalizing the Modal and Temporal Logic of Linear Time

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.