Abstract
For natural language understanding and generation, plan generation and recognition, and knowledge representation, it is necessary to represent qualitiave temporal information and to reason with it. Allen's interval calculus provides an appropriate framework for such a task. 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 machinegenerated case analysis, we show that the ORD-Horn subclass is a maximal tractable subclass of the full algebra (assuming P≠NP). In fact, it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations.
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