A Fast Algorithm and Lower Bound for Temporal Reasoning

We introduce two new tractable temporal constraint languages, which both strictly contain the Ord-Horn language of Bürkert and Nebel. The algorithm we present for these languages decides whether a given set of constraints is consistent in time that is quadratic in the input size. We also prove that (unlike Ord-Horn) the two languages cannot be solved by Datalog or by establishing local consistency.

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