An Application of Temporal Projection to Interleaving Concurrency

Abstract

We revisit the earliest temporal projection operator Π in discrete-time Propositional Interval Temporal Logic (PITL) and use it to formalise interleaving concurrency. The logical properties of Π as a normal modality and a way to eliminate it in both PITL and conventional point-based Linear-Time Temporal Logic (LTL), which can be viewed as a PITL subset, are examined. We also formalise concurrency without Π, and relate the two approaches. Furthermore, Π and another standard PITL projection operator are interdefinable and both suitable for reasoning about different time granularities. We mention other (mostly interval-based) temporal logics with similar forms of projection, as well as some related applications and international standards.