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 by Lehmann and Shelah (Information and Control 53, 165-198 (1982)), but we give it a different 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 the "co-meagre" family of paths, where the term "co-meagre" refers to a set whose complement is of the first category in Baire's classification 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 finite model property; namely, every sentence having a model has a finite model.