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21
Constraint propagation algorithms for temporal reasoning
 Readings in Qualitative Reasoning about Physical Systems
, 1986
"... Abstract: This paper revises and expands upon a paper presented by two of the present authors at AAAI 1986 [Vilain & Kautz 1986]. As with the original, this revised document considers computational aspects of intervalbased and pointbased temporal representations. Computing the consequences of tempo ..."
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Cited by 371 (4 self)
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Abstract: This paper revises and expands upon a paper presented by two of the present authors at AAAI 1986 [Vilain & Kautz 1986]. As with the original, this revised document considers computational aspects of intervalbased and pointbased temporal representations. Computing the consequences of temporal assertions is shown to be computationally intractable in the intervalbased representation, but not in the pointbased one. However, a fragment of the interval language can be expressed using the point language and benefits from the tractability of the latter. The present paper departs from the original primarily in correcting claims made there about the point algebra, and in presenting some closely related results of van Beek [1989]. The representation of time has been a recurring concern of Artificial Intelligence researchers. Many representation schemes have been proposed for temporal reasoning; of these, one of the most attractive is James Allen's algebra of temporal intervals [Allen 1983]. This representation scheme is particularly appealing for its simplicity and for its ease of implementation with constraint propagation algorithms. Reasoners based on
Reasoning about Temporal Relations: A Maximal Tractable Subclass of Allen's Interval Algebra
 Journal of the ACM
, 1995
"... 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 ORDHorn subclass is a polynomialtime problem and show that the pathconsistency method is sufficient for deciding satisfiabil ..."
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Cited by 161 (9 self)
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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 ORDHorn subclass is a polynomialtime problem and show that the pathconsistency method is sufficient for deciding satisfiability. Further, using an extensive machinegenerated case analysis, we show that the ORDHorn 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 . . . "...
Reasoning about Qualitative Temporal Information
 Artificial Intelligence
, 1992
"... Representing and reasoning about incomplete and indefinite qualitative temporal information is an essential part of many artificial intelligence tasks. An intervalbased framework and a pointbased framework have been proposed for representing such temporal information. In this paper, we address ..."
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Cited by 137 (6 self)
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Representing and reasoning about incomplete and indefinite qualitative temporal information is an essential part of many artificial intelligence tasks. An intervalbased framework and a pointbased framework have been proposed for representing such temporal information. In this paper, we address two fundamental reasoning tasks that arise in applications of these frameworks: Given possibly indefinite and incomplete knowledge of the relationships between some intervals or points, (i) find a scenario that is consistent with the information provided, and (ii) find the feasible relations between all pairs of intervals or points. For the pointbased framework and a restricted version of the intervalbased framework, we give computationally efficient procedures for finding a consistent scenario and for finding the feasible relations. Our algorithms are marked improvements over the previously known algorithms. In particular, we develop an O(n 2 ) time algorithm for finding one co...
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...
Efficient Algorithms for Qualitative Reasoning about Time
 Artificial Intelligence
, 1995
"... 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 ..."
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Cited by 32 (6 self)
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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 (PArelations) and on a major extension to include binary disjunctions of PArelations (PAdisjunctions). 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 PAr...
Artificial Intelligence: A Computational Perspective
 Essentials in Knowledge Representation
, 1994
"... Although the computational perspective on cognitive tasks has always played a major role in Artificial Intelligence, the interest in the precise determination of the computational costs that are required for solving typical AI problems has grown only recently. In this paper, we will describe what in ..."
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Cited by 31 (1 self)
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Although the computational perspective on cognitive tasks has always played a major role in Artificial Intelligence, the interest in the precise determination of the computational costs that are required for solving typical AI problems has grown only recently. In this paper, we will describe what insights a computational complexity analysis can provide and what methods are available to deal with the complexity problem. This work was partially supported by the European Commission as part of DRUMSII, the ESPRIT Basic Research Project P6156. 1 Introduction It is wellknown that typical AI problems, such as natural language understanding, scene interpretation, planning, configuration, or diagnosis are computationally difficult. Hence, it seems to be worthless to analyze the computational complexity of these problems. In fact, some people believe that all AI problems are NPhard or even undecidable. Conceiving AI as a scientific field that has as its goal the analysis and synthesis of...
A Unifying Approach to Temporal Constraint Reasoning
 Artificial Intelligence
"... We present a formalism, Disjunctive Linear Relations (DLRs), for reasoning about temporal constraints. DLRs subsume most of the formalisms for temporal constraint reasoning proposed in the literature and is therefore computationally expensive. We also present a restricted type of DLRs, Horn DLRs ..."
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Cited by 31 (9 self)
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We present a formalism, Disjunctive Linear Relations (DLRs), for reasoning about temporal constraints. DLRs subsume most of the formalisms for temporal constraint reasoning proposed in the literature and is therefore computationally expensive. We also present a restricted type of DLRs, Horn DLRs, which have a polynomialtime satisfiability problem. We prove that most approaches to tractable temporal constraint reasoning can be encoded as Horn DLRs, including the ORDHorn algebra by Nebel and Burckert and the simple temporal constraints by Dechter et al. Thus, DLRs is a suitable unifying formalism for reasoning about temporal constraints. 1 Introduction Reasoning about temporal knowledge abounds in artificial intelligence applications and other areas, such as planning [4], natural language understanding [25] and molecular biology [6, 13]. In most applications, knowledge of temporal constraints is expressed in terms of collections of relations between time intervals or time po...
Reasoning About Temporal Relations: The Tractable Subalgebras Of Allen's Interval Algebra
 Journal of the ACM
, 2001
"... Allen's interval algebra is one of the best established formalisms for temporal reasoning. This paper is the final step in the classification of complexity in Allen's algebra. We show that the current knowledge about tractability in the interval algebra is complete, that is, this algebra contains ex ..."
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Cited by 30 (2 self)
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Allen's interval algebra is one of the best established formalisms for temporal reasoning. This paper is the final step in the classification of complexity in Allen's algebra. We show that the current knowledge about tractability in the interval algebra is complete, that is, this algebra contains exactly eighteen maximal tractable subalgebras, and reasoning in any fragment not entirely contained in one of these subalgebras is NPcomplete. We obtain this result by giving a new uniform description of the known maximal tractable subalgebras and then systematically using an algebraic technique for identifying maximal subalgebras with a given property.
Eight Maximal Tractable Subclasses of Allen's Algebra with Metric Time
, 1997
"... This paper combines two important directions of research in temporal resoning: that of finding maximal tractable subclasses of Allen's interval algebra, and that of reasoning with metric temporal information. Eight new maximal tractable subclasses of Allen's interval algebra are presented, some of t ..."
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Cited by 22 (10 self)
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This paper combines two important directions of research in temporal resoning: that of finding maximal tractable subclasses of Allen's interval algebra, and that of reasoning with metric temporal information. Eight new maximal tractable subclasses of Allen's interval algebra are presented, some of them subsuming previously reported tractable algebras. The algebras allow for metric temporal constraints on interval starting or ending points, using the recent framework of Horn DLRs. Two of the algebras can express the notion of sequentiality between intervals, being the first such algebras admitting both qualitative and metric time. 91 1 Introduction Reasoning about temporal knowledge abounds in artificial intelligence applications and other areas, such as planning [ Allen, 1991 ] , natural language understanding [ Song and Cohen, 1988 ] and molecular biology [ Benzer, 1959; Golumbic and Shamir, 1993 ] . However, since even the restricted problem of reasoning with pure qualitative ti...
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 applications ..."
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Cited by 21 (2 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...