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Temporal Reasoning Based on SemiIntervals
, 1992
"... A generalization of Allen's intervalbased approach to temporal reasoning is presented. The notion of `conceptual neighborhood' of qualitative relations between events is central to the presented approach. Relations between semiintervals rather than intervals are used as the basic units o ..."
Abstract

Cited by 235 (14 self)
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A generalization of Allen's intervalbased approach to temporal reasoning is presented. The notion of `conceptual neighborhood' of qualitative relations between events is central to the presented approach. Relations between semiintervals rather than intervals are used as the basic units of knowledge. Semiintervals correspond to temporal beginnings or endings of events. We demonstrate the advantages of reasoning on the basis of semiintervals: 1) semiintervals are rather natural entities both from a cognitive and from a computational point of view; 2) coarse knowledge can be processed directly; computational effort is saved; 3) incomplete knowledge about events can be fully exploited; 4) incomplete inferences made on the basis of complete knowledge can be used directly for further inference steps; 5) there is no tradeoff in computational strength for the added flexibility and efficiency; 6) for a natural subset of Allen's algebra, global consistency can be guaranteed in polynomial time; 7) knowledge about relations between events can be represented much more compactly.
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 ..."
Abstract

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...
Fast Algebraic Methods for Interval Constraint Problems
 Annals of Mathematics and Artificial Intelligence
, 1996
"... We describe an e#ective generic method for solving constraint problems, based on Tarski's relation algebra, using pathconsistency as a pruning technique. Weinvestigate the performance of this method on interval constraint problems. Time performance is a#ected strongly by the pathconsistenc ..."
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Cited by 21 (1 self)
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We describe an e#ective generic method for solving constraint problems, based on Tarski's relation algebra, using pathconsistency as a pruning technique. Weinvestigate the performance of this method on interval constraint problems. Time performance is a#ected strongly by the pathconsistency calculations, whichinvolve the calculation of compositions of relations. Weinvestigate various methods of tuning composition calculations, and also pathconsistency computations. Space performance is a#ected by the branching factor during search. Reducing this branching factor depends on the existence of `nice' subclasses of the constraint domain. Finally,we survey the statistics of consistency properties of interval constraint problems. Problems of up to 500 variables may be solved in expected cubic time. Evidence is presented that the `phase transition' occurs in the range 6 # n:c # 15, where n is the numberofvariables, and c is the ratio of nontrivial constraints to possible constra...
Temporal Query Processing With Indefinite Information
 Artificial Intelligence in Medicine
, 1991
"... Time is an important aspect of information in medical domains. In this paper, we adopt Allen's influential interval algebra framework for representing temporal information. The interval algebra allows the representation of indefinite and incomplete information which is necessary in many applica ..."
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Cited by 21 (1 self)
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Time is an important aspect of information in medical domains. In this paper, we adopt Allen's influential interval algebra framework for representing temporal information. The interval algebra allows the representation of indefinite and incomplete information which is necessary in many applications. However, answering interesting queries in this framework has been shown to be almost assuredly intractable. We show that when the representation language is sufficiently restricted we can develop efficient algorithms for answering interesting classes of queries including: (i) determining whether a formula involving temporal relations between events is possibly true and necessarily true; and (ii) answering aggregation questions where the set of all events that satisfy a formula are retrieved. We also show, by examining applications of the interval algebra discussed in the literature, that our restriction on the representation language often is not overly restrictive in practice. 1 Introduct...
1.1 Background
"... A generalization of Allen’s intervalbased approach to temporal reasoning is presented. The notion of ‘conceptual neighborhood ’ of qualitative relations between events is central to the presented approach. Relations between semiintervals rather than intervals are used as the basic units of knowled ..."
Abstract
 Add to MetaCart
A generalization of Allen’s intervalbased approach to temporal reasoning is presented. The notion of ‘conceptual neighborhood ’ of qualitative relations between events is central to the presented approach. Relations between semiintervals rather than intervals are used as the basic units of knowledge. Semiintervals correspond to temporal beginnings or endings of events. We demonstrate the advantages of reasoning on the basis of semiintervals: 1) semiintervals are rather natural entities both from a cognitive and from a computational point of view; 2) coarse knowledge can be processed directly; computational effort is saved; 3) incomplete knowledge about events can be fully exploited; 4) incomplete inferences made on the basis of complete knowledge can be used directly for further inference steps; 5) there is no tradeoff in computational strength for the added flexibility and efficiency; 6) for a natural subset of Allen’s algebra, global consistency can be guaranteed in polynomial time; 7) knowledge about relations between events can be represented much more compactly.