The computational properties of qualitative spatial reasoning have been investigated to some degree. However, the question for the boundary between polynomial and NP-hard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus" RCC-8. We extend Bennett's encoding of RCC-8 in modal logic. Based on this encoding, we prove that reasoning is NPcomplete in general and identify a maximal tractable subset of the relations in RCC-8 that contains all base relations. Further, we show that for this subset path-consistency is sufficient for deciding consistency. 1 Introduction When describing a spatial configuration or when reasoning about such a configuration, often it is not possible or desirable to obtain precise, quantitative data. In these cases, qualitative reasoning about spatial configurations may be used. One particular approach in this context has been developed by Randell, Cui, and Cohn [20], the so-called Region Connecti...

We define formal notions of temporal domain and temporal database, and use them to survey a wide spectrum of temporal query languages. We distinguish between an abstract temporal database and its concrete representations, and accordingly between abstract and concrete temporal query languages. We also address the issue of incomplete temporal information. 1 Introduction A temporal database is a repository of temporal information. A temporal query language is any query language for temporal databases. In this paper we propose a formal notion of temporal database and use this notion in surveying a wide spectrum of temporal query languages. The need to store temporal information arises in many computer applications. Consider, for example, records of various kinds: financial [37], personnel, medical [98], or judicial. Also, monitoring data, e.g., in telecommunications network management [4] or process control, has often a temporal dimension. There has been a lot of research in temporal dat...

We extend the framework of simple temporal problems studied originally by Dechter, Meiri and Pearl to consider constraints of the form x1 \Gamma y1 r1 : : : xn \Gamma yn rn , where x1 : : : xn ; y1 : : : yn are variables ranging over the real numbers, r1 : : : rn are real constants, and n 1. We have implemented four progressively more efficient algorithms for the consistency checking problem for this class of temporal constraints. We have partially ordered those algorithms according to the number of visited search nodes and the number of performed consistency checks. Finally, we have carried out a series of experimental results on the location of the hard region. The results show that hard problems occur at a critical value of the ratio of disjunctions to variables. This value is between 6 and 7. Introduction Reasoning with temporal constraints has been a hot research topic for the last fifteen years. The importance of this problem has been demonstrated in many areas of artifici...

issues remain essentially the same. One of the most crucial problems in any computer system that involves representing the world is the representation of time. This includes applications such as databases, simulation, expert systems and applications of Artificial Intelligence in general. In this brief paper, I will give a survey of the basic techniques available for representing time, and then talk about temporal reasoning in a general setting as needed in AI applications. Quite different representations of time are usable depending on the assumptions that can be made about the temporal information to be represented. The most crucial issue is the degree of certainty one can assume. Can one assume that a time stamp can be assigned to each event, or barring that, that the events are fully ordered? Or can we only assume that a partial ordering of events is known? Can events be simultaneous? Can they overlap in time and yet not be simultaneous? If they are not instantaneous, do we know the durations of events? Different answers to each of these questions allow very different representations of time. I. Representations Based on Dating Schemes A good representation of time for instantaneous events, if it is possible, is using an absolute dating system. This involves time stamping each event with an absolute real-time, say taken off the system clock

Temporal events are regarded here as intervals on a time line. This paper deals with problems in reasoning about such intervals when the precise topological relationship between them is unknown or only partially specified. This work unifies notions of interval algebras in artificial intelligence with those of interval orders and interval graphs in combinatorics. The satisfiability, minimal labeling, all solutions and all realizations problems are considered for temporal (interval) data. Several versions are investigated by restricting the possible interval relationships yielding different complexity results. We show that even when the temporal data comprises of subsets of relations based on intersection and precedence only, the satisfiability question is NP-complete. On the positive side, we give efficient algorithms for several restrictions of the problem. In the process, the interval graph sandwich problem is introduced, and is shown to be NP-complete. This problem is als...

The concepts of binary constraint satisfaction problems can be naturally generalized to the relation algebras of Tarski. The concept of path-consistency plays a central role. Algorithms for path-consistency can be implemented on matrices of relations and on matrices of elements from a relation algebra. We give an example of a 4-by-4 matrix of infinite relations on which no iterative local path-consistency algorithm terminates. We give a class of examples over a fixed finite algebra on which all iterative local algorithms, whether parallel or sequential, must take quadratic time. Specific relation algebras arising from interval constraint problems are also studied: the Interval Algebra, the Point Algebra, and the Containment Algebra. 1 Introduction The logical study of binary relations is classical [8], [9], [51], [52], [56], [53], [54]. Following this tradition, Tarski formulated the theory of binary relations as an algebraic theory called relation algebra [59] 1 . Constraint satis...

The situation recognition system, to which this paper is devoted, receives as input a stream of time-stamped events; it performs recognition of instances of occurring situations, as they are developing, and it generates as output deduced events and actions to trigger. It is mainly a temporal reasoning system. It is predictive in the sense that it predicts forthcoming events relevant to its task, it focuses its attention on them and it maintains their temporal windows of relevance. Its main functionality is to recognize efficiently complex temporal patterns on the fly, while they are taking place. This system has been tested for the surveillance of an environment by a multisensory perception machine; it is being applied to monitoring a complex dynamic system. 1

Terminological systems, such as KL-ONE and K-Rep, are widely used in AI to represent and reason with concept descriptions. They compute subsumption relations between concepts and automatically classify concepts into a taxonomy. Each concept in the taxonomy describes a set of possible instances which are a superset of those described by its descendants. One limitation of current systems is their inability to handle complex compositions of concepts, such as constraint networks where each node is described by an associated concept. For example, plans are often represented (in part) as collections of actions related by a rich variety of temporal constraints. The T-REX system integrates terminological reasoning with constraint network reasoning to classify such plans, producing a "terminological" plan library. T-REX also introduces a new view of plan recognition as a process which dynamically partitions the plan library by modalities, e.g., necessary, possible and impo...

Local consistency has proven to be an important concept in the theory and practice of constraint networks. In this paper, we present a new definition of local consistency, called relational consistency. The new definition is relation-based, in contrast with the previous definition of local consistency, which we characterize as variable-based. We show the conceptual power of the new definition by showing how it unifies known elimination operators such as resolution in theorem proving, joins in relational databases, and variable elimination for solving linear inequalities. Algorithms for enforcing various levels of relational consistency are introduced and analyzed. We also show the usefulness of the new definition in characterizing relationships between properties of constraint networks and the level of local consistency needed to ensure global consistency.

As multimedia systems deal with a variety of temporally interrelated media items, synchronization is an important issue in those systems. One part of synchronization is the representation of temporal information. In contrast to traditional computing tasks, multimedia imposes new requirements on the representation of time. Specifically, a fine-grained and a flexible temporal model is required. Therefore, a number of temporal models have been suggested by various authors. However, there is not any temporal model that has been agreed on for multimedia. This paper evaluates and classifies a selection of the most common existing models applying fundamental statements of the time theory and temporal logic. Learning from the deficits of the existing models, a new temporal model based on interval operators is proposed for multimedia systems. 1.