Temporal Constraint Reasoning With Preferences

A number of reasoning problems involving the manipulation of temporal information can naturally be viewed as implicitly inducing an ordering of potential local decisions involving time (specifically, associated with durations or orderings of events) on the basis of preferences. For example. a pair of events might be constrained to occur in a certain order, and, in addition. it might be preferable that the delay between them be as large, or as small, as possible. This paper explores problems in which a set of temporal constraints is specified, where each constraint is associated with preference criteria for making local decisions about the events involved in the constraint, and a reasoner must infer a complete solution to the problem such that, to the extent possible, these local preferences are met in the best way. A constraint framework for reasoning about time is generalized to allow for preferences over event distances and durations, and we study the complexity of solving problems in the resulting formalism. It is shown that while in general such problems are NP-hard, some restrictions on the shape of the preference functions, and on the structure of the preference set, can be enforced to achieve tractability. In these cases, a simple generalization of a single-source shortest path algorithm can be used to compute a globally preferred solution in polynomial time.