Reasoning about Temporal Relatio A Maximal Tractable Su of Alllen’s Interval Algebra*

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 (assuming P#NP). In fact, it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations.