Using Constraint Propagation to Reason about UnsynchronizedClocks

• Authors: Rita V. Rodriguez;Frank D. Anger
• Venue: Constraints
• Year: 1998

Numerous AI problems in planning, robot motion, distributedsystems, cooperating agents, and intelligence gathering havedomains with sub-collections of events or actions over time whichare measured on incomparable or unsynchronized time scales fromone to another. In such situations, a temporal model providingonly a partial order on time moments is appropriate. Unlike abranching-time model, no sense of a common past and divergentfutures occurs; unlike a ’’parallel worlds‘‘ model, check pointsor intercommunication between the sub-collections of events mayexist, providing a true, rich partially ordered set of temporalinformation. In applications for which temporal intervals andtheir relations are appropriate, constraint propagation is arecognized reasoning tool. We discuss several temporal intervalmodels and their relationship to one another but particularlyfocus on the general partial order model. In each model the emphasisis on the atomic relations, so we amplify on the meaning ofatomic and show that what is atomic in one model may not be soin another. Utilizing results established earlier about the latticeproperties of the models, the paper describes the closure ofthe atomic relations under composition and conjunction, relatingthe structures of relations in linear time, partially orderedtime, and relativistic time. Lattice and algebraic isomorphismsexplain what appeared to be only coincidental similarities betweendifferent models. The results are shown to provide especiallyefficient representations for constraint propagation algorithms.