We introduce a new subclass of Allen's interval algebra we call "ORDHorn subclass," which is a strict superset of the "pointisable subclass." We prove that reasoning in the ORD-Horn subclass is a polynomial-time problem and show that the path-consistency method is sufficient for deciding satisfiability. Further, using an extensive machine-generated case analysis, we show that the ORD-Horn subclass is a maximal tractable subclass of the full algebra (assuming<F NaN> P6=NP). In fact, it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations. This work has been supported by the German Ministry for Research and Technology (BMFT) under grant ITW 8901 8 as part of the WIP project and under grant ITW 9201 as part of the TACOS project. 1 1 Introduction Temporal information is often conveyed qualitatively by specifying the relative positions of time intervals such as ". . . point to the figure while explaining the performance of the system . . . "...

In this paper we address the problem of scalability in temporal reasoning. In particular, new algorithms for efficiently managing large sets of relations in the Point Algebra are provided. Our representation of time is based on timegraphs, graphs partitioned into a set of chains on which the search is supported by a rnetagraph data structure. The approach is an extension of the time representation proposed by Schubert, Taugher and Miller in the context of story comprehension. The algorithms presented in this work concern the construction of a timegraph from a given set of relations and are implemented in a temporal reasoning system called TG-II. Experimental results show that our approach is very efficient, especially when the given relations admit representation as a collection of chains connected by relatively few cross-chain links. 1

Reasoning about temporal information is an important task in many areas of Artificial Intelligence. In this paper we address the problem of scalability in temporal reasoning by providing a collection of new algorithms for efficiently managing large sets of qualitative temporal relations. We focus on the class of relations forming the Point Algebra (PA-relations) and on a major extension to include binary disjunctions of PA-relations (PA-disjunctions). Such disjunctions add a great deal of expressive power, including the ability to stipulate disjointness of temporal intervals, which is important in planning applications. 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. The approach is an extension of the time representation proposed by Schubert, Taugher and Miller in the context of story comprehension. The algorithms herein enable construction of a timegraph from a given set of PA-r...

We describe two domain-independent temporal reasoning systems called TimeGraph I and II which can be used in AI-applications as tools for efficiently 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 efficient 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 ...