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 office hours may consider things like the relative temporal ordering of the office hours and a number of other events in a given work day. The number of times office hours will actually be held may be unknown, even irrelevant, at the time of scheduling them. The objective of this article 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 offer a calculus of binary temporal relations for temporal collections based on a well-defined transformation of interval temporal relations into recurrence relations. Finally, we describe a reasoning framework based on manipulating knowledge stored in temporal relation networks, 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.