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14
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 ..."
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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.
Using Orientation Information for Qualitative Spatial Reasoning
 Theories and Methods of SpatioTemporal Reasoning in Geographic Space, LNCS 639, SpringerVerlag
, 1992
"... Abstract. A new approach to representing qualitative spatial knowledge and to spatial reasoning is presented. This approach is motivated by cognitive considerations and is based on relative orientation information about spatial environments. The approach aims at exploiting properties of physical spa ..."
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Cited by 163 (8 self)
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Abstract. A new approach to representing qualitative spatial knowledge and to spatial reasoning is presented. This approach is motivated by cognitive considerations and is based on relative orientation information about spatial environments. The approach aims at exploiting properties of physical space which surface when the spatial knowledge is structured according to conceptual neighborhood of spatial relations. The paper introduces the notion of conceptual neighborhood and its relevance for qualitative temporal reasoning. The extension of the benefits to spatial reasoning is suggested. Several approaches to qualitative spatial reasoning are briefly reviewed. Differences between the temporal and the spatial domain are outlined. A way of transferring a qualitative temporal reasoning method to the spatial domain is proposed. The resulting neighborhoodoriented representation and reasoning approach is presented and illustrated. An example for an application of the approach is discussed. 1
Preferred mental models in qualitative spatial reasoning: A cognitive assessment of Allen's calculus
 In Proceedings of the Seventeenth Annual Conference of the Cognitive Science Society
, 1995
"... An experiment based on Allen's calculus and its transfer to qualitative spatial reasoning, was conducted. Subjects had to find a conclusion X r 3 Z that was consistent with the given premises X r 1 Y and Y r 2 Z. Implications of the obtained results are discussed with respect to the mental model the ..."
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Cited by 49 (17 self)
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An experiment based on Allen's calculus and its transfer to qualitative spatial reasoning, was conducted. Subjects had to find a conclusion X r 3 Z that was consistent with the given premises X r 1 Y and Y r 2 Z. Implications of the obtained results are discussed with respect to the mental model theory of spatial inference. The results support the assumption that there are preferred models when people solve spatial threeterm series problems. Although the subjects performed the task surprisingly well overall, there were significant differences in error rates between some of the tasks. They are discussed with respect to the subprocesses of model construction, model inspection, validation of the answer, and the interaction of these subprocesses.
Conceptual Neighborhood and its role in temporal and spatial reasoning
, 1991
"... this paper was supported by the Deutsche Forschungsgemeinschaft and by Siemens AG. I also acknowledge discussions with Wilfried Brauer, Jerry Feldman, Daniel Hernndez, Kerstin Schill, and Kai Zimmermann ..."
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Cited by 38 (4 self)
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this paper was supported by the Deutsche Forschungsgemeinschaft and by Siemens AG. I also acknowledge discussions with Wilfried Brauer, Jerry Feldman, Daniel Hernndez, Kerstin Schill, and Kai Zimmermann
Qualitative Spatial Reasoning Using Orientation, Distance, and Path Knowledge
 Applied Intelligence
, 1996
"... We give an overview of an approach to qualitative spatial reasoning based on directional orientation information as available through perception processes or natural language descriptions. Qualitative orientations in 2dimensional space are given by the relation between a point and a vector. The ..."
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Cited by 32 (0 self)
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We give an overview of an approach to qualitative spatial reasoning based on directional orientation information as available through perception processes or natural language descriptions. Qualitative orientations in 2dimensional space are given by the relation between a point and a vector. The paper presents our basic iconic notation for spatial orientation relations that exploits the spatial structure of the domain and explores a variety of ways in which these relations can be manipulated and combined for spatial reasoning. Using this notation, we explore a method for exploiting interactions between space and movement in this space for enhancing the inferential power. Finally, the orientationbased approach is augmented by distance information, which can be mapped into position constraints and vice versa.
The Cognitive Adequacy of Allen's Interval Calculus for . . .
 SPATIAL COGNITION AND COMPUTATION
, 1999
"... Qualitative spatial reasoning (QSR) is often claimed to be cognitively more plausible than conventional numerical approaches to spatial reasoning, because it copes with the indeterminacy of spatial data and allows inferences based on incomplete spatial knowledge. The paper reports experimental resul ..."
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Cited by 15 (6 self)
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Qualitative spatial reasoning (QSR) is often claimed to be cognitively more plausible than conventional numerical approaches to spatial reasoning, because it copes with the indeterminacy of spatial data and allows inferences based on incomplete spatial knowledge. The paper reports experimental results concerning the cognitive adequacy of an important approach used in QSR, namely the spatial interpretation of the interval calculus introduced by Allen (1983). Knauff, Rauh and Schlieder (1995) distinguished between the conceptual and inferential cognitive adequacy of Allen's interval calculus. The former refers to the thirteen base relations as a representational system and the latter to the compositions of these relations as a tool for reasoning. The results of two memory experiments on conceptual adequacy show that people use ordinal information similar to the interval relations when representing and remembering spatial arrangements. Furthermore, symmetry transformations on the interval relations were found to be responsible for most of the errors, whereas conceptual neighborhood theory did not appear to correspond to cognitively relevant concepts. Inferential adequacy was investigated by two reasoning experiments and the results show that in inference tasks where the number of possible interval relations for the composition is more than one, subjects ignore numerous possibilities and interindividually prefer the same relations. Reorientations and transpositions operating on the relations seem to be important for reasoning performance as well, whereas conceptual neighborhood did not appear to affect the difficulty of reasoning tasks based on the interval relations.
A New Tractable Subclass of the Rectangle Algebra
 PROCEEDINGS OF THE 16TH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 1999
"... This paper presents the 169 permitted relations between two rectangles whose sides are parallel to the axes of some orthogonal basis in a 2dimensional Euclidean space. Elaborating rectangle algebra just like interval algebra, it defines the concept of convexity as well as the ones of weak pre ..."
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Cited by 11 (1 self)
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This paper presents the 169 permitted relations between two rectangles whose sides are parallel to the axes of some orthogonal basis in a 2dimensional Euclidean space. Elaborating rectangle algebra just like interval algebra, it defines the concept of convexity as well as the ones of weak preconvexity and strong preconvexity. It introduces afterwards the fundamental operations of intersection, composition and inversion and demonstrates that the concept of weak preconvexity is preserved by the operation of composition whereas the concept of strong preconvexity is preserved by the operation of intersection. Finally, fitting the propagation techniques conceived to solve interval networks, it shows that the polynomial pathconsistency algorithm is a decision method for the problem of proving the consistency of strongly preconvex rectangle networks.
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 Method of Spatial Reasoning Based on Qualitative Trigonometry
 Artificial Intelligence
, 1997
"... Due to the lack of exact quantitative information or the difficulty associated with obtaining or processing such information, qualitative spatial knowledge representation and reasoning often become an essential means for solving spatial constraint problems as found in science and engineering. This p ..."
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Cited by 10 (0 self)
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Due to the lack of exact quantitative information or the difficulty associated with obtaining or processing such information, qualitative spatial knowledge representation and reasoning often become an essential means for solving spatial constraint problems as found in science and engineering. This paper presents a computational approach to representing and reasoning about spatial constraints in twodimensional Euclidean space, where the a priori spatial information is not precisely expressed in quantitative terms. The spatial quantities considered in this work are qualitative distances and qualitative orientation angles. Here, we explicitly define the semantics of these quantities and thereafter formulate a representation of qualitative trigonometry (QTRIG). The resulting QTRIG formalism provides the necessary inference rules for qualitative spatial reasoning. In the paper, we illustrate how the QTRIG relationships can be employed in generating qualitative spatial descriptions in two...
The Augmented Interval and Rectangle Networks
"... We augment Allen's Interval Algebra networks and Rectangle Algebra networks by quantitative constraints represented by ST Ps. With the help of polynomial algorithms based on the traditional and weak pathconsistency methods, we prove the tractability of the consistency problem of preconvex au ..."
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Cited by 4 (0 self)
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We augment Allen's Interval Algebra networks and Rectangle Algebra networks by quantitative constraints represented by ST Ps. With the help of polynomial algorithms based on the traditional and weak pathconsistency methods, we prove the tractability of the consistency problem of preconvex augmented interval networks and stronglypreconvex augmented rectangle networks. Keywords: Temporal and spatial reasoning, Interval Algebra and Rectangle Algebra, constraint networks, complexity. 1 Introduction Temporal and spatial reasoning with constraints is a relevant activity in artificial intelligence. Concerning qualitative temporal reasoning, Allen's Interval Algebra [1] (IA) is one of the most known and used formalisms. Allen takes intervals as primitive temporal entities and considers 13 atomic relations between these intervals (fig. 1). These relations represent all the possible relative positions between two intervals on the rational line. With this formalism we can represent qu...