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.
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