Process semantics of temporal logic specification

A process semantics for temporal logic specification is provided by relating a category of temporal theories and interpretations between theories where specification configuration and interconnection is achieved via colimits of diagrams, and a category of algebraic models of processes where parallel composition is explained in terms of limits of diagrams. This semantics is proved to be exact in the sense that given a diagram in the categories of theories and a model of it as a diagram in the category of processes, the limit of the process diagram is a model of the colimit of the theory diagram. In fact, any denotation of a system of interconnected specifications corresponds to a configuration of their denotations as a system of interconnected processes.