A real-time interval logic and its decision procedure

Abstract

Real-Time Future Interval Logic is a temporal logic in which formulæ have a natural graphical representation, resembling timing diagrams. It is a dense real-time logic that is based on two simple temporal primitives:interval modalities for the purely qualitative part andduration predicates for the quantitative part. This paper describes the logic and gives a decision procedure for satisfiability by reduction to the emptiness problem for Timed Büchi Automata. This decision procedure forms the core of an automated proof-checker for the logic. The logic does not admit instantaneous states, and is invariant under real-time stuttering, properties that facilitate proof methods based on abstraction and refinement. The logic appears to be as strong as one can hope for without sacrificing elementary decidability. Two natural extensions of the logic, along lines suggested in the literature, lead to either non-elementariness or undecidability.