A Tableau for Temporal Logic over the Reals

We provide a simple, sound, complete and terminating tableau decision procedure for the temporal logic of until and since over the real numbers model of time. This logic is an important basis for reasoning about concurrency, metric constraints and planning. Despite its usefulness and long history, there are no existing implementable reasoning techniques for it. The tableau uses a mosaic-based technique to translate the satisfiability problem into a question about the way that intervals of a real-flowed model relate to each other. It builds on top of recently developed reasoning tools for general linear time by applying some interesting but computationally simple checks.

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