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...

This paper focuses on the optimization of the navigation through voluminous subsumption hierarchies of topics employed by Portal Catalogs like Netscape Open Directory (ODP). Weadvocate for the use of labeling schemes for modeling these hierarchies in order to efficiently answer queries such as subsumption check, descendants, ancestors or nearest common ancestor, which usually require costly transitive closure computations. We first give a qualitative comparison of three main families of schemes, namely bit vector, prefix and interval based schemes. We then show that two labeling schemes are good candidates for an efficient implementation of label querying using standard relational DBMS, namely, the Dewey Prefix scheme[6] and an Interval scheme byAgrawal, Borgida and Jagadish[1] We compare their storage and query evaluation performance for the 16 ODP hierarchies using the PostgreSQL engine.

This paper presents a logical formalism for representing and reasoning with statistical knowledge. One of the key features of the formalism is its ability to deal with qualitative statistical information. It is argued that statistical knowledge, especially that of a qualitative nature, is an important component of our world knowledge and that such knowledge is used in many different reasoning tasks. The work is further motivated by the observation that previous formalisms for representing probabilistic information are inadequate for representing statistical knowledge. The representation mechanism takes the form of a logic that is capable of representing a wide variety of statistical knowledge, and that possesses an intuitive formal semantics based on the simple notions of sets of objects and probabilities defined over those sets. Furthermore, a proof theory is developed and is shown to be sound and complete. The formalism offers a perspicuous and powerful representational tool for stat...

We analyze the problem of computing the minimal labels for a network of temporal relations in the Point Algebra. van Beek proposes an algorithm for accomplishing this task which takes O(max(n 3 ; n 2 \Delta m)) time (for n points and m 6=-relations). We show that the proof of the correctness of this algorithm given by van Beek and Cohen is faulty, and we provide a new proof showing that the algorithm is indeed correct. Keywords: temporal reasoning, Point Algebra, constraint networks, reasoning with inequations The work of the first author was carried out in part during a visit at the Computer Science Department of the University of Rochester (NY) supported by the Italian National Research Council (CNR), and in part at IRST in the context of the MAIA project and CNR projects "Sistemi Informatici e Calcolo Parallelo" and "Pianificazione Automatica". The second author was supported by Rome Lab Contract F30602-91-C-0010. 1 Introduction The Interval Algebra (IA) (Allen 1983) and t...

This paper focuses on the optimization of the navigation through voluminous subsumption hierarchies of topics employed byPortal Catalogs like Netscape Open Directory (ODP). We advocate for the use of labeling schemes for modeling these hierarchies in order to efficiently answer queries such as subsumption check, descendants, ancestors or nearest common ancestor, which usually require costly transitive closure computations. Wefirstgive a qualitative comparison of three main families of schemes, namely bit vector, prefix and interval based schemes. We then show that two labeling schemes are good candidates for an efficientimplementation of label querying using standard relational DBMS, namely the Dewey Prefix scheme and an Interval scheme by Agrawal, Borgida and Jagadish. We compare their storage and query evaluation performance for the 16 ODP hierarchies using the PostgreSQL engine.

Locational reasoning plays an important role in many applications of AI problem-solving systems, yet has remained a relatively unexplored area of research. This paper addresses both theoretical and practical issues relevant to reasoning about locations. We de ne several theories of location designed for use in various settings, along with a sound and complete belief revision calculus for each that maintains a STRIPS-style database of locational facts. Techniques for the e cient oper-ationalization of the belief revision rules in planning frameworks are presented. These techniques were developed during application of the location theories to several large-scale planning tasks within the SIPE{2 planning framework.

Efficient knowledge representation and reasoning is an important component of intelligent activity, and is a crucial aspect in the design of large-scale intelligent systems. This dissertation explores the design, analysis, and implementation of massively parallel knowledge representation and reasoning systems which can encode very large knowledge bases and respond to a class of queries in real-time, with reasoning episodes expected to span a fraction of a second. The dissertation attempts to design efficient, large-scale knowledge base systems by: (i) exploiting massive parallelism; and (ii) constraining representational and inferential capabilities to achieve tractability, while still retaining sufficient expressive power to capture a broad class of reasoning in intelligent systems. To this end, shruti, a connectionist reasoning system which models reflexive--- i.e., effortless and spontaneous---reasoning serves as the knowledge representation and reasoning framework. Shruti-based mas...

We address the problems of determining consistency and of finding a solution for sets of 3-point relations expressing exclusion of a point from an interval, and for sets of 4-point relations expressing interval disjointness. Availability of these relations is an important requirement for dealing with the sorts of temporal constraints encountered in many AI applications such as plan reasoning. We prove that consistency testing is NP-complete and finding a solution is NP-hard. Keywords: temporal reasoning, complexity of reasoning, planning, reasoning with disjunctions The work of the first author was carried out in part during a visit at the Computer Science Department of the University of Rochester (NY) supported by the Italian National Research Council (CNR), and in part at IRST in the context of the MAIA project and CNR projects "Sistemi Informatici e Calcolo Parallelo" and "Pianificazione Automatica". The second author was supported by Rome Lab Contract F30602-91-C-0010. 1 Introd...

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 ...