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 the "natural scale" in any component of the model and by properly constraining the interactions between differently-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 finitely-layered metric temporal structures is shown to be decidable.
"Decidability Results for Metric and Layered Temporal Logics." Notre Dame J. Formal Logic 37 (2) 260 - 282, Spring 1996. https://doi.org/10.1305/ndjfl/1040046089