Reasoning about Generalized Intervals: Horn Representability and Tractability

This paper organizes the topologic forms of the possible relations between generalized intervals. Working out generalized interval algebra on the pattern of point algebra and interval algebra, it introduces the concept of Horn representability just as the one of convexity. It gives the class of Horn representable relations a simple characterization based on the concept of strong preconvexity. Adapting the propagation techniques designed to solve the networks of constraints between points or between intervals, it shows that the issue of consistency of a Horn representable generalized interval network can be solved in polynomial time by means of the weak path-consistency algorithm, a new incomplete algorithm for computing a minimal set of temporal constraints.