Efficient Algorithms for Qualitative Reasoning about Time

Reasoning about temporal information is an important task in many areas of Artiicial Intelligence. In this paper we address the problem of scal-ability in temporal reasoning by providing a collection of new algorithms for eeciently managing large sets of qualitative temporal relations. We focus on the class of relations forming the Point Algebra (PA-relations) and on a major extension to include binary disjunctions of PA-relations (PA-disjunctions). Such disjunctions add a great deal of expressive power, including the ability to stipulate disjointness of temporal intervals, which is important in planning applications. Our representation of time is based on timegraphs, graphs partitioned into a set of chains on which the search is supported by a metagraph data structure. The approach is an extension of the time representation proposed by Schubert, Taugher and Miller in the context of story comprehension. The algorithms herein enable construction of a timegraph from a given set of PA-relations, querying a timegraph, and eeciently checking the consistency of a timegraph augmented by a set of PA-disjunctions. Experimental results illustrate the eeciency of the proposed approach.