The Way to Go: Multi-Level Temporal Logics

In this paper we briefly survey the main contributions of our research on time granularity and outline some directions for current and future researches. The original motivation of our research was the design of a temporal logic embedding the notion of time granularity, suitable for the specification of complex real-time systems, whose components evolve according to different time units. However, there are significant similarities between the problems we encountered in pursuing our goal, and those addressed by current research on combining logics, theories, and structures. Furthermore, exploiting interesting connections between multi-level temporal logics and automata theory that we recently established, a complementary point of view on time granularity arises: time granularity can be viewed not only as an important feature of a representation language, but as well as a formal tool to investigate expressiveness and decidability properties of temporal theories. Finally, as a by-product of our work, we defined a uniform framework for time and states that ``reconciles'' the tense logic and the logic of program perspectives