Point-Based Description of Interval Relations

Temporal text understanding and question answering presupposes the availability of a component which computes the transitive closure of a set of statements about interval relations. Vilain and Kautz have addressed the question of computing the transitive closure by translating such statements into equivalent point-based descriptions. The problem is that there are basic statements about interval relations which have to be translated into disjunctions of point-based descriptions. Therefore, in order to handle the general case economically, it is necessary to have translations with a minimum number of disjuncts for each and every case. In this paper we present an algorithm which computes a best translation, i.e. a translation which consists of a minimal number of disjuncts. This number amounts at most to 5.