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Neighbourhood Logic and Interval Algebra
, 1997
"... A complete first order logic called Neighbourhood Logic to model hybrid systems is first proposed by Zhou and Hansen. Two neighbourhood modalities are introduced and it is shown that the logic is complete, adequate and suitable for modelling hybridsystems. In AI literature, reasoning and representi ..."
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Cited by 3 (1 self)
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and representing indefinite temporal information of qualitative nature have been elaborately studied and this study originates from Allen's proposal of Interval Algebra. Since the satisfiability problem for Interval Algebra is established to be NPcomplete, the main research has been to determine maximal
An interval algebra for indeterminate time
 In Proceedings of the Seventeenth National Conference on Artificial Intelligence (AAAI 2000
"... Temporal indeterminacy is an inherent problem which arises when capturing and manipulating temporal data in many application areas. As such, representation and manipulation of timestamps with indeterminacy is a requirement for these applications. We present an extension of Allen’s thirteen interv ..."
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Cited by 1 (0 self)
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Temporal indeterminacy is an inherent problem which arises when capturing and manipulating temporal data in many application areas. As such, representation and manipulation of timestamps with indeterminacy is a requirement for these applications. We present an extension of Allen’s thirteen interval
An Interval Algebra for Indeterminate Time
 In Proceedings of the Seventeenth National Conference on Artificial Intelligence (AAAI 2000
, 2000
"... Temporal indeterminacy is an inherent problem which arises when capturing and manipulating temporal data in many application areas. As such, representation and manipulation of timestamps with indeterminacy is a requirement for these applications. ..."
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Temporal indeterminacy is an inherent problem which arises when capturing and manipulating temporal data in many application areas. As such, representation and manipulation of timestamps with indeterminacy is a requirement for these applications.
Tractable Sets of the Generalized Interval Algebra
, 2000
"... To offer a generic frame which groups together several interval algebra generalizations, we simply define a generalized interval as a tuple of intervals. After introducing the generalized relations we focus on the consistency problem of generalized constraint networks and we present sets of generali ..."
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To offer a generic frame which groups together several interval algebra generalizations, we simply define a generalized interval as a tuple of intervals. After introducing the generalized relations we focus on the consistency problem of generalized constraint networks and we present sets
Software support for calculations in Allen’s Interval Algebra
, 2005
"... Allen’s interval algebra formally expresses temporal relations between intervals, operations on them, and reasoning about them. Many of its most interesting operations are tedious or difficult to perform by hand. This report gives a compact introduction to interval algebra and describes a software t ..."
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Cited by 4 (2 self)
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Allen’s interval algebra formally expresses temporal relations between intervals, operations on them, and reasoning about them. Many of its most interesting operations are tedious or difficult to perform by hand. This report gives a compact introduction to interval algebra and describes a software
© Hindawi Publishing Corp. ON HEREDITARY INTERVAL ALGEBRAS
, 2003
"... We show that each hereditary interval algebra has a countable density and not conversely. Moreover, we show that, for an interval algebra, having countable density and being subalgebra of the interval algebra over the real line are equivalent statements. 2000 Mathematics Subject Classification: 06E ..."
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We show that each hereditary interval algebra has a countable density and not conversely. Moreover, we show that, for an interval algebra, having countable density and being subalgebra of the interval algebra over the real line are equivalent statements. 2000 Mathematics Subject Classification: 06
Ktheory for operator algebras
 Mathematical Sciences Research Institute Publications
, 1998
"... p. XII line5: since p. 12: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The RieszFischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e int}. If [a, b] is a ..."
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Cited by 558 (0 self)
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] is a bounded interval in R, in modern language the original statement of the theorem was that L 2 ([a, b]) is complete and abstractly isomorphic to l 2. According to [Jah03, p. 385], the name “Hilbert space ” was first used in 1908 by A. Schönflies, apparently to refer to what we today call l 2. Von
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 ..."
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Cited by 199 (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
Using interval algebras to model order of magnitude reasoning
 Arti Intelligence in Engineering
, 1993
"... Qualitative reasoning, introduced as a means of simulating human commonsense reasoning, has been extended by several authors to encompass reasoning about the order of magnitude of quantities. This paper discusses how interval algebras may form a basis for modelling three schemes for order of magnitu ..."
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Cited by 3 (2 self)
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Qualitative reasoning, introduced as a means of simulating human commonsense reasoning, has been extended by several authors to encompass reasoning about the order of magnitude of quantities. This paper discusses how interval algebras may form a basis for modelling three schemes for order
Global Consistency in Interval Algebra Networks: Tractable Subclasses
 In Proc. ECAI'96
, 1996
"... . Global consistency is an important property in binary constraint satisfaction problems. It implies minimality in the sense that the edges contain all and only the labels that can participate in a global solution, which, for instance, is an important property in querying temporal knowledge bases. A ..."
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Cited by 11 (0 self)
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. Another, computational, advantage of a globally consistent network is that finding a solution can be done in a backtrackfree manner. In this paper, we propose two new subclasses of the interval algebra for which pathconsistency is sufficient to ensure global consistency, i.e. pathconsistency applied
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