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35
Maintaining knowledge about temporal intervals
 Communication of ACM
, 1983
"... The problem of representing temporal knowledge arises ill many areas of computer science. In applications in which such knowledge is imprecise or relative, current representations based on date lines or time instants are inadequate. An intervalbased temporal logic is introduced, together WiUl a com ..."
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Cited by 2278 (9 self)
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The problem of representing temporal knowledge arises ill many areas of computer science. In applications in which such knowledge is imprecise or relative, current representations based on date lines or time instants are inadequate. An intervalbased temporal logic is introduced, together WiUl a computationally effective reasoning algorithm based on constraint propagation. This system is notable in offering a delicate balance between expressive power and the efficiency of its deductive engine. A notion of reference intervals is introduced which captures the temporal hierarchy implicit in many domains, and which can be used to precisely control the amount of deduction performed automatically by the system. Examples.are provided for a data base containing historical data, a d<lta base. used for modeling processes and process interaction, and a data base for an interactive system where the present moment is continually being updated.
Combining Qualitative and Quantitative Constraints in Temporal Reasoning
 Artificial Intelligence
, 1996
"... This paper presents a general model for temporal reasoning that is capable of handling both qualitative and quantitative information. This model allows the representation and processing of many types of constraints discussed in the literature to date, including metric constraints (restricting the ..."
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Cited by 139 (0 self)
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This paper presents a general model for temporal reasoning that is capable of handling both qualitative and quantitative information. This model allows the representation and processing of many types of constraints discussed in the literature to date, including metric constraints (restricting the distance between time points) and qualitative, disjunctive constraints (specifying the relative position of temporal objects). Reasoning tasks in this unified framework are formulated as constraint satisfaction problems and are solved by traditional constraint satisfaction techniques, such as backtracking and path consistency. New classes of tractable problems are characterized, involving qualitative networks augmented by quantitative domain constraints, some of which can be solved in polynomial time using arc and path consistency. This work was supported in part by grants from the Air Force Office of Scientific Research, AFOSR 900136, and the National Science Foundation, IRI 8815522...
A Survey on Temporal Reasoning in Artificial Intelligence
, 1994
"... The notion of time is ubiquitous in any activity that requires intelligence. In particular, several important notions like change, causality, action are described in terms of time. Therefore, the representation of time and reasoning about time is of crucial importance for many Artificial Intelligenc ..."
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Cited by 42 (4 self)
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The notion of time is ubiquitous in any activity that requires intelligence. In particular, several important notions like change, causality, action are described in terms of time. Therefore, the representation of time and reasoning about time is of crucial importance for many Artificial Intelligence systems. Specifically during the last 10 years, it has been attracting the attention of many AI researchers. In this survey, the results of this work are analysed. Firstly, Temporal Reasoning is defined. Then, the most important representational issues which determine a Temporal Reasoning approach are introduced: the logical form on which the approach is based, the ontology (the units taken as primitives, the temporal relations, the algorithms that have been developed,. . . ) and the concepts related with reasoning about action (the representation of change, causality, action,. . . ). For each issue the different choices in the literature are discussed. 1 Introduction The notion of time i...
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...
A Spectrum of Definitions for Temporal ModelBased Diagnosis
 Artificial Intelligence
, 1998
"... Modelbased diagnosis (MBD) tackles the problem of troubleshooting systems starting from a description of their structure and function (or behavior). Time is a fundamental dimension in MBD: the behavior of most systems is timedependent in one way or another. Temporal MBD, however, is a difficult ta ..."
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Cited by 21 (6 self)
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Modelbased diagnosis (MBD) tackles the problem of troubleshooting systems starting from a description of their structure and function (or behavior). Time is a fundamental dimension in MBD: the behavior of most systems is timedependent in one way or another. Temporal MBD, however, is a difficult task and indeed many simplifying assumptions have been adopted in the various approaches in the literature. These assumptions concern different aspects such as the type and granularity of the temporal phenomena being modeled, the definition of diagnosis, the ontology for time being adopted. Unlike the atemporal case, moreover, there is no general "theory" of temporal MBD which can be used as a knowledgelevel characterization of the problem. In this paper we present a general characterization of temporal modelbased diagnosis. We distinguish between different temporal phenomena that can be taken into account in diagnosis and we introduce a modeling language which can capture all such phenomena...
Temporal Constraints: A Survey
, 1998
"... . Temporal Constraint Satisfaction is an information technology useful for representing and answering queries about the times of events and the temporal relations between them. Information is represented as a Constraint Satisfaction Problem (CSP) where variables denote event times and constraints re ..."
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Cited by 20 (1 self)
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. Temporal Constraint Satisfaction is an information technology useful for representing and answering queries about the times of events and the temporal relations between them. Information is represented as a Constraint Satisfaction Problem (CSP) where variables denote event times and constraints represent the possible temporal relations between them. The main tasks are two: (i) deciding consistency, and (ii) answering queries about scenarios that satisfy all constraints. This paper overviews results on several classes of Temporal CSPs: qualitative interval, qualitative point, metric point, and some of their combinations. Research has progressed along three lines: (i) identifying tractable subclasses, (ii) developing exact search algorithms, and (iii) developing polynomialtime approximation algorithms. Most available techniques are based on two principles: (i) enforcing local consistency (e.g. pathconsistency), and (ii) enhancing naive backtracking search. Keywords: Temporal Constra...
Intervalbased Temporal Reasoning with General TBoxes
 LUFG THEORETICAL COMPUTER SCIENCE, RWTH
, 2000
"... Until now, intervalbased temporal Description Logics (DLs) didif at allonly admit TBoxes of a very restricted form, namely acyclic macro definitions. In this paper, we present a temporal DL that overcomes this deficieny and combines intervalbased temporal reasoning with general TBoxes. W ..."
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Cited by 19 (9 self)
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Until now, intervalbased temporal Description Logics (DLs) didif at allonly admit TBoxes of a very restricted form, namely acyclic macro definitions. In this paper, we present a temporal DL that overcomes this deficieny and combines intervalbased temporal reasoning with general TBoxes. We argue that this combination is very interesting for many application domains. An automatabased decision procedure is devised and a tight EXPTIMEcomplexity bound is obtained. Since the presented logic can be viewed as being equipped with a concrete domain, our results can be seen from a different perspective: we show that there exist interesting concrete domains for which reasoning with general TBoxes is decidable.