Quantitative Structural Temporal Constraints on Repeating Events

This paper presents a model of the temporal structure of repeating events. This model allows for the representation of quantitative temporal constraints for repeating events, viz., those dealing with their part-whole structure. The temporal structure of repeating events is viewed as being composed of ve properties: number, sub-interval duration, gap duration, period and extent. A set of constraints involving these properties collectively speciies the conditions under which repeating events can be assigned times, and thus partially formalizes the scheduling problem for repeating events. The consistency and tightness of a set of such constraints can be tested by nding a solution to linear equations relating these properties to one another. These equations can also be used to infer constraints about one structural property from the others, when one or more of these constraints is unknown. This paper also introduces a new category of quantitative temporal constraints involving repeating events which speciies that the duration or period of events be distributed randomly over a set of values. Finally, integrating previous work by the same authors, rules are formulated which allow the inferring of structural constraints of one repeating event from those of another, as well as from binary relational constraints between the events.