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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 of knowledg ..."
Abstract

Cited by 234 (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.
An Algebraic Approach to Granularity in Qualitative Time and Space
 Representation, Proceedings of IJCAI95
"... Any phenomenon can be seen under a more or less precise granularity, depending on the kind of details which are perceivable. This can be applied to time and space. A characteristic of abstract spaces such as the one used for representing time is their granularity independence, i.e. the fact that the ..."
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Cited by 11 (2 self)
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Any phenomenon can be seen under a more or less precise granularity, depending on the kind of details which are perceivable. This can be applied to time and space. A characteristic of abstract spaces such as the one used for representing time is their granularity independence, i.e. the fact that they have the same structure under different granularities. So, time "places " and their relationships can be seen under different granularities and they still behave like time places and relationships under each granularity. However, they do not remain exactly the same time places and relationships. Here is presented a pair of operators for converting (upward and downward) qualitative time relationships from one granularity to another. These operators are the only ones to satisfy a set of six constraints which characterize granularity changes. They are also shown to be useful for spatial relationships. 1.
A Computational Account of Preferences in Mental Model Construction
 In
, 1996
"... Experiments on spatialrelational inferences conducted by Knauff, Rauh & Schlieder (1995) showed clear answer preferences for the reasoning problems having several solutions. The preferences can be explained by a specific process that constructs the mental model used by the reasoner. Schlieder ..."
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Cited by 1 (0 self)
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Experiments on spatialrelational inferences conducted by Knauff, Rauh & Schlieder (1995) showed clear answer preferences for the reasoning problems having several solutions. The preferences can be explained by a specific process that constructs the mental model used by the reasoner. Schlieder (in press) has proposed an algorithmic description of this model construction process which is able to reproduce most of the preferences found. This paper addresses the issue of whether from a computational point of view there is an advantage in preferring some models over others. It is conjectured that the empirical model construction process follows a general spatial layout strategy, the linearization principle. An analysis of this principle reveals that mental models which are constructed in accordance with the principle allow an efficient inspection process. All together, a simple computational explanation results: those models are preferred which are easiest to inspect. ...
A Categorical Approach to Time Representation First Study on Qualitative Aspects
"... : The qualitative time representation formalisms are considered from the viewpoint of category theory. The representation of a temporal situation can be expressed as a graph and the relationship holding between that graph and others (imprecise or coarser) views of the same situation are expressed as ..."
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Cited by 1 (0 self)
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: The qualitative time representation formalisms are considered from the viewpoint of category theory. The representation of a temporal situation can be expressed as a graph and the relationship holding between that graph and others (imprecise or coarser) views of the same situation are expressed as morphisms. These categorical structures are expected to be combinable with other aspects of knowledge representation providing a framework for the integration of temporal representation tools and formalisms with other areas of knowledge representation. KEYWORDS: Category theory, time representation, temporal granularity, interval algebra. Time and space representation are only one aspect of knowledge representation. It is thus useful to place them in a wider context. Category theory which is widely used in programming language semantics has been introduced in knowledge representation [AÏTK93] in order to account for the relation of approximation between, on the one hand, a knowledge base ...
On The Qualitative Representation of . . .
 VLDB JOURNAL
, 1994
"... Various relationbased systems, concerned with the qualitative representation and processing of spatial knowledge, have been developed in numerous application domains. In this paper we identify the common concepts underlying qualitative spatial knowledge representation, we compare the representati ..."
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Various relationbased systems, concerned with the qualitative representation and processing of spatial knowledge, have been developed in numerous application domains. In this paper we identify the common concepts underlying qualitative spatial knowledge representation, we compare the representational properties of the different systems and we outline the computational tasks involved in relationbased spatial information processing. The paper also describes symbolic spatial indexes, relationbased structures which combine several ideas in spatial knowledge representation. A symbolic spatial index is an array that preserves only a set of spatial relations among distinct objects in an image, called the modelling space; the index array discards information, such as shape and size of objects, and irrelevant spatial relations. The construction of a symbolic spatial index from an input image can be thought of as a transformation that keeps only a set of representative points needed for the...