The Temporal Reasoning Systems TimeGraph I-II Alfonso Gerevini1 2
Lenhart Schubert2
;
1
Stephanie Schae er3
IRST - Istituto per la Ricerca Scienti ca e Tecnologica, 38050 Povo TN, Italy E-mail:
[email protected] Phone:+39 461 814333 Fax:+39 461 302040
2
Computer Science Department University of Rochester, Rochester, NY 14627, USA E-mail: gerevini,schubert @cs.rochester.edu f
3
g
Computing Science Department, University of Alberta Edmonton, Alberta T6G 2H1, Canada E-mail:
[email protected]
{ Technical report 494 {
Abstract
We describe two domain-independent temporal reasoning systems called TimeGraph I and II which can be used in AI-applications as tools for eciently managing large sets of relations in the Point Algebra, in the Interval Algebra, and metric information such as absolute times and durations. Our representation of time is based on timegraphs, graphs partitioned into a set of chains on which the search is supported by a metagraph data structure. TimeGraph I was originally developed by Taugher, Schubert and Miller in the context of story comprehension. TimeGraph II provides useful extensions, including ecient algorithms for handing inequations, and relations expressing point-interval exclusion and interval disjointness. These extensions make the system much more expressive in the representation of qualitative information and suitable for a large class of applications.
Keywords: Temporal reasoning systems, Point algebra, Interval Algebra, Scalable systems 1
1 Introduction We are interested in developing temporal reasoning tools for eciently managing large data sets of temporal information. Our approach was originally developed by Schubert, Taugher and Schae er (formerly Miller) in the context of natural language comprehension [28, 29, 22], and then extended with the aim of making it suitable for a larger class of Arti cial Intelligence applications including, in particular, planning [10, 12]. In natural language applications such as story understanding, reasoning about the temporal structure of episodes is an important task which requires specialized temporal inference methods [22]. For example, to answer a question like \Was the wolf alive at any time after everyone (the human characters in the story of Little Red Riding Hood) talked or after everyone ate the goodies?" requires detection of an an inconsistency between a presumed \alive" episode and a semi-in nite \not alive" episode that starts with the death of wolf at the hands of the woodcutter, an event known to precede both the \talking" and \goodie eating" episodes [22]. In planning, constraint-propagation approaches like Allen and Koomen's [3, 2] and nonlinear planners like ucpop rely on a temporal reasoning module for eciency [25, 35]. In fact, the rst requires an ecient method for managing relations in the Interval Algebra (IA) formed from subsets of thirteen basic relation (see 1); the second requires a specialized reasoning module to maintain the consistency of a temporal database of point relations expressing strict ordering and point-interval exclusion, i.e., relations of the form \p1 < p2", and \p3 < p4 or p5 < p3", where t4 < t5 .1 In this paper we present two domain-independent temporal reasoning systems called TimeGraph I (TG-I) and TimeGraph II (TG-II). These systems can eciently handle point relations in
the Point Algebra (PA), the interval relations in the subclass of IA called SIA [31], and metric information such as constraints involving absolute times and durations. Moreover, a recent extension 1 The \
