A Temporal Logic for Proving Properties of Topologically General Executions

We present a generalization of the temporal propositional logic of linear time which is useful for stating and proving properties of the generic execution sequence of a parallel program or a non-deterministic program. The formal system we present is exactly that same as the third of three logics presented in [LS82], but we give it a di erent semantics. The models are tree models of arbitrary size similar to those used in branching time temporal logic. The formulation we use allows us to state properties of \co-meagre" family of paths, where the term \co-meagre" refers to a set whose complement is of the rst category in Baire's classi cation, looking at the set of paths in the model as a metric space. Our system is decidable, sound and complete for models of arbitrary size, but it has the nite model property, namely every sentence having a model has a nite model. 2