A real-time interval logic and its decision procedure

Abstract

Real-Time Future Interval Logic is a visual logic in which formulæ have a natural graphical representation, resembling timing diagrams. It is a dense real-time temporal logic that is based on two simple temporal primitives: interval modalities for the purely qualitative part and duration predicates for the quantitative part. We give a decision procedure for the logic by reduction to the emptiness problem for Timed Büchi Automata. The decision procedure forms the core of a proof checker for the logic that we have recently implemented. The logic does not admit instantaneous states, and is invariant under realtime stuttering. These properties facilitate proof methods based on abstraction and refinement. Two natural extensions of the logic lead to nonelementariness and undecidability.