A comparison of point-based approaches to qualitative temporal reasoning

Abstract

We address the problem of implementing general, qualitative, point-based temporal reasoning. Given a database of assertions concerning relative occurrences of points in time, we are interested in various operations on this database, including compiling the assertions into a representation that supports efficient reasoning, determining whether a database is consistent, and computing the strongest entailed relation between two points. We begin by specifying a set of operations and their corresponding algorithms, applicable to general point-based temporal domains. We next consider a special-purpose reasoner, based on series-parallel graphs, which performs very well in a temporal domain with a particular restricted structure. We discuss the notion of a metagraph, which encapsulates local structure inside metaedges and uses special purpose algorithms within such local structures, to obtain a fast general point-based reasoner. That is, specifically, we use a very fast, series-parallel graph reasoner to speed u p general point-based reasoning. We also analyse the TimeGraph reasoner of Gerevini and Schubert. For purposes of comparison, we have implemented four approaches: a generic point-based reasoner, the generic point-based reasoner with a ranking heuristic, a reasoner based on series-parallel graphs, and a version of Gerevini and Schubert's TimeGraph reasoner. We compare these different approaches, as well as the original TimeGraph-II reasoner of Gerevini and Schubert, on different data sets. We conclude that the series-parallel graph reasoner provides the best overall performance: our results show that it dominated on domains exhibiting structure, and it degraded gracefully when conditions were less than ideal, in that it did worse than the generic approach by only a constant factor in this case. © 2001 Elsevier Science B.V. All rights reserved.