Spatial and Temporal Workshop DOMAIN INDEPENDENT TEMPORAL REASONING WITH RECURRING EVENTS

Numerous examples of temporal reasoning involve a process of abstraction from the number of times an event is to occur, or the number of times events stand in a temporal relation. For example, scheduling a recurring event such as one's ooce hours may consider things like the relative temporal ordering of the ooce hours and a number of other events in a given work day. The number of times ooce hours will actually be held may be unknown, even irrelevant, at the time of scheduling them. The objective of this paper is to formulate a domain-independent framework for reasoning about recurring events and their relations. To achieve this end, we propose an ontology of recurrence based on the model-theoretic structure underlying collective predication using plural noun phrases. We ooer a calculus of binary temporal relations for temporal collections based on a well-deened transformation of interval temporal relations into recurrence relations. Finally, we describe a reasoning framework based on manipulating knowledge stored in temporal relation networks (Van Beek 1990), which is in turn a specialization of the CSP (Constraint Satisfaction Problem) framework. The reasoner manipulates recurrence relations in the network to determine the network's consistency, or to generate scenarios. 1. SETTING THE STAGE 1.1. Motivation and Potential Applications The work here is motivated by the observation that many applications of temporal reasoning seem to require manipulation of recurring events. This section provides examples from scheduling, planning, and managing temporal data for illustration. First, consider a scheduling problem. In certain domains such as telescope observation scheduling (Drummond 1994), an eeective scheduler should be responsive to the tendency for a schedule to \break" during execution. Breakage is due to the temporal uncertainty of the initial knowledge about the durations of events to be scheduled. This uncertainty can be measured in terms of statistical data that characterize the mean and standard deviation of the duration of each event. This data is generated from observations of repeated executions of the events. Hence the eeective scheduling and rescheduling of future events (as a result of schedule failure during execution) requires a representation and manipulation of recurring events. More generally, planning and scheduling tasks might involve constraints in which the number, and even the ordering of the events are unspeciied. For example, consider the constraint on a schedule imposed by the sentence OOce hours should be held once a week on teaching days, preferably before the hour …