Reasoning about Temporal Relations: A Maximal Tractable Subclass of Allen’s Interval Algebra

Bernhard Nebel, Hans-Jürgen Bürckert

We introduce a new subclass of Allen’s interval algebra we call "ORD-Horn subclass," which is a strict superset of the "pointisable subclass." We prove that reasoning in the ORD-Horn subclass is a polynomial-time problem and show that the path-consistency method is sufficient for deciding satisfiability. Further, using an extensive machine-generated case analysis, we show that the ORD-Horn subclass is a maximal tractable subclass of the full algebra. In fact, it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations.

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