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Composing cardinal direction relations
Authors:Spiros Skiadopoulos  Manolis Koubarakis
Institution:a Knowledge and Database Systems Laboratory, Department of Electrical and Computer Engineering, National Technical University of Athens, Zographou, 15773 Athens, Greece
b Intelligent Systems Laboratory, Department of Electronic and Computer Engineering, Technical University of Crete, Chania, 73100 Crete, Greece
Abstract:We study the recent proposal of Goyal and Egenhofer who presented a model for qualitative spatial reasoning about cardinal directions. Our approach is formal and complements the presentation of Goyal and Egenhofer. We focus our efforts on the composition operator for two cardinal direction relations. We consider two interpretations of the composition operator: consistency-based and existential composition. We point out that the only published method to compute the consistency-based composition does not always work correctly. Then, we consider progressively more expressive classes of cardinal direction relations and give consistency-based composition algorithms for these classes. Our theoretical framework allows us to prove formally that our algorithms are correct. When we consider existential composition, we demonstrate that the binary relation resulting from the composition of two cardinal direction relations cannot be expressed using the relations defined by Goyal and Egenhofer. Finally, we discuss some extensions to the basic model and consider the composition problem for these extensions.
Keywords:Cardinal direction relations  Spatial constraints  Consistency-based composition  Existential composition  Qualitative spatial reasoning  Composition table
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