Reasoning about Temporal Relations : A Maximal Tractable Subclassof

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 suucient for deciding satissability. 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 P6 =NP). In fact, it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations. (BMFT) under grant ITW 8901 8 as part of the WIP project and under grant ITW 9201 as part of the TACOS project.