# An automata-theoretic decision procedure for Future Interval Logic

## Abstract

Graphical Interval Logic (GIL) is a temporal logic in which all reasoning is done by means of diagrammatic formulæ. It is a discrete linear-time modal logic in which the basic temporal modality is the interval. Future Interval Logic (FIL) provides the logical foundation for GIL. In this paper we present an automata-theoretic decision procedure for FIL with complexity *DTIME*\((2^{O(n^k )} )\), where *n* is the size of the formula and *k* is the depth of interval nesting. For formulæ with bounded depth but length unbounded, the satisfiability problem for FIL is shown to be *PSPACE*-complete. We believe that this is the first result giving a direct decision procedure of elementary complexity for an interval logic. We also show that the logic is transparent to finite stuttering over the class of *ω*-sequences, a feature that is useful for composition and refinement.

## Keywords

Temporal Logic Decision Procedure World Model Propositional Dynamic Logic Interval Logic## Preview

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