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294
On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus
 Artificial Intelligence
, 1997
"... The computational properties of qualitative spatial reasoning have been investigated to some degree. However, the question for the boundary between polynomial and NPhard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus" RCC8. ..."
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Cited by 108 (22 self)
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The computational properties of qualitative spatial reasoning have been investigated to some degree. However, the question for the boundary between polynomial and NPhard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus" RCC8. We extend Bennett's encoding of RCC8 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 RCC8 that contains all base relations. Further, we show that for this subset pathconsistency 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 socalled Region Connecti...
Integrating Metric and Qualitative Temporal Reasoning
 IN PROCEEDINGS OF AAAI91
, 1991
"... Research in Artificial Intelligence on constraintbased representations for temporal reasoning has largely concentrated on two kinds of formalisms: systems of simple linear inequalities to encode metric relations between time points, and systems of binary constraints in Allen's temporal calculus to ..."
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Cited by 106 (4 self)
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Research in Artificial Intelligence on constraintbased representations for temporal reasoning has largely concentrated on two kinds of formalisms: systems of simple linear inequalities to encode metric relations between time points, and systems of binary constraints in Allen's temporal calculus to encode qualitative relations between time intervals. Each formalism has certain advantages. Linear inequalities can represent dates, durations, and other quantitive information; Allen's qualitative calculus can express relations between time intervals, such as disjointedness, that are useful for constraint based approaches to planning. In this paper we demonstrate how metric and Allenstyle constraint networks can be integrated in a constraintbased reasoning system. The highlights of the work include a simple but powerful logical language for expressing both quantitative and qualitative information; translation algorithms between the metric and Allen sublanguages that entail minimal loss ...
Backtracking Algorithms for Disjunctions of Temporal Constraints
 Artificial Intelligence
, 1998
"... 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. W ..."
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Cited by 106 (2 self)
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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...
Time and time again: The many ways to represent time
 International Journal of Intelligent Systems
, 1991
"... 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 bri ..."
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Cited by 105 (0 self)
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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 realtime, say taken off the system clock
On Binary Constraint Problems
 Journal of the ACM
, 1994
"... The concepts of binary constraint satisfaction problems can be naturally generalized to the relation algebras of Tarski. The concept of pathconsistency plays a central role. Algorithms for pathconsistency can be implemented on matrices of relations and on matrices of elements from a relation algeb ..."
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Cited by 87 (2 self)
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The concepts of binary constraint satisfaction problems can be naturally generalized to the relation algebras of Tarski. The concept of pathconsistency plays a central role. Algorithms for pathconsistency can be implemented on matrices of relations and on matrices of elements from a relation algebra. We give an example of a 4by4 matrix of infinite relations on which no iterative local pathconsistency 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...
Complexity and Algorithms for Reasoning About Time: A GraphTheoretic Approach
, 1992
"... 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 ..."
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Cited by 86 (11 self)
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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 NPcomplete. 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 NPcomplete. This problem is als...
Situation recognition: Representation and algorithms
, 1993
"... The situation recognition system, to which this paper is devoted, receives as input a stream of timestamped 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 reasoni ..."
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Cited by 74 (4 self)
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The situation recognition system, to which this paper is devoted, receives as input a stream of timestamped 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 Reasoning with Constraint Networks and an Application to Plan Recognition
, 1992
"... Terminological systems, such as KLONE and KRep, 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 ..."
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Cited by 62 (5 self)
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Terminological systems, such as KLONE and KRep, 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 TREX system integrates terminological reasoning with constraint network reasoning to classify such plans, producing a "terminological" plan library. TREX 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 and global relational consistency
 THEORETICAL COMPUTER SCIENCE
, 1997
"... 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 relationbased, in contrast with the previous definition of local consiste ..."
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Cited by 61 (15 self)
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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 relationbased, in contrast with the previous definition of local consistency, which we characterize as variablebased. 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.
Solving Hard Qualitative Temporal Reasoning Problems: Evaluating the Efficiency of Using the ORDHorn Class
 Constraints
, 1997
"... While the worstcase computational properties of Allen's calculus for qualitative temporal reasoning have been analyzed quite extensively, the determination of the empirical efficiency of algorithms for solving the consistency problem in this calculus has received only little research attention. ..."
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Cited by 59 (6 self)
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While the worstcase computational properties of Allen's calculus for qualitative temporal reasoning have been analyzed quite extensively, the determination of the empirical efficiency of algorithms for solving the consistency problem in this calculus has received only little research attention. In this paper, we will demonstrate that using the ORDHorn class in Ladkin and Reinefeld's backtracking algorithm leads to performance improvements when deciding consistency of hard instances in Allen's calculus. For this purpose, we prove that Ladkin and Reinefeld's algorithm is complete when using the ORDHorn class, we identify phase transition regions of the reasoning problem, and compare the improvements of ORDHorn with other heuristic methods when applied to instances in the phase transition region. Finally, we give evidence that combining search methods orthogonally can dramatically improve the performance of the backtracking algorithm. Contents 1 Introduction 1 2 Allen's...