Reasoning about temporal relations : a maximal tractable subclass of Allen's interval algebra

Abstract

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