A Generalized Framework for Reasoning with Multi-Point Events

Allen's Interval Algebra (IA) and Vilain and Kautz's Point Algebra (PA) consider an interval and a point as basic temporal entities (i.e., events) respectively. However, in many real world situations we often need to deal with recurring events that include multiple points, multiple intervals or combinations of points and intervals. Recently, we presented a multiple-point event (MPE) framework to represent relations over recurring point events and showed that it can handle pointisable interval relations (SIA). We also showed that computing a minimal MPE network is a polynomial solvable problem. However, the MPE framework cannot correctly capture the relation between three points called a discontinuous point relation and this has not been satisfactorily addressed in the literature. In this paper, we extend MPE to a general framework that is expressive enough to represent discontinuous point relations and other complex situations which are relationships between single events (i.e., point-interval, and interval-interval relations), and clusters of events (i.e., recurring point-point and interval-interval relations). Further we developed a path-consistency algorithm for computing the minimal network for a generalised MPE network and improved our earlier path-consistency algorithm for MPE networks. We then present an analysis of experimental results on the implementation of these algorithms.