Using Constraint Propagation to Reason about Unsynchronized Clocks

Abstract

Numerous AI problems in planning, robot motion, distributed systems, cooperating agents, and intelligence gathering have domains with sub-collections of events or actions over time which are measured on incomparable or unsynchronized time scales from one to another. In such situations, a temporal model providing only a partial order on time moments is appropriate. Unlike a branching-time model, no sense of a common past and divergent futures occurs; unlike a “parallel worlds” model, check points or intercommunication between the sub-collections of events may exist, providing a true, rich partially ordered set of temporal information. In applications for which temporal intervals and their relations are appropriate, constraint propagation is a recognized reasoning tool. We discuss several temporal interval models and their relationship to one another but particularly focus on the general partial order model. In each model the emphasis is on the atomic relations, so we amplify on the meaning of atomic and show that what is atomic in one model may not be so in another. Utilizing results established earlier about the lattice properties of the models, the paper describes the closure of the atomic relations under composition and conjunction, relating the structures of relations in linear time, partially ordered time, and relativistic time. Lattice and algebraic isomorphisms explain what appeared to be only coincidental similarities between different models. The results are shown to provide especially efficient representations for constraint propagation algorithms.