Reasoning with Multi-Point Events

Recent research on qualitative reasoning has focussed on representing and reasoning about events that occur repeatedly. Allen's interval algebra has been modiied to model events that are collections of convex intervals|a non-convex interval. Using the modiied version of Allen's algebra, constraint-based algorithms have been investigated for nding feasible relations in a network of non-convex intervals. In this paper, we propose to model reoccuring events as multi-point events by extending Vilain and Kautz's point algebra. We then propose an exact algorithm (based on van Beek's exact algorithm) for nding feasible relations for multi-point event networks. The complexity of our method is compared with previously known results both for reoccuring and non-reoccuring events. We identify the special cases for which our multi-point based algorithm can nd exact solution. Finally, we summarise our paper with brief discussion on ongoing and future research.