Decidability Results for Metric and Layered Temporal Logics

We study the decidability problem for metric and layered temporal logics. The logics we consider are suitable to model time granularity in various contexts, and they allow one to build granular temporal models by referring to thènatural scale' in any component of the model and by properly constraining the interactions between diierently-grained components. A monadic second-order language combining operators such as temporal contextualization and projection, together with the usual displacement operator of metric temporal logics, is considered, and the theory of nitely-layered metric temporal structures is shown to be decidable.