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About the temporal decrease of sets

This paper is about a simple general framework for modelling decrease. We provide an extension of propositional linear time temporal logic with operators expressing 'next-time' and 'henceforth', by a modality that quantifies over the points of some set X. This set changes in the course of time; actually X is assumed to shrink little by little. We develop an appropriate logical language, give a sound and complete axiomatization of the set of validities, and prove decidability of this set. Moreover the computational complexity of the logic is determined.