Composing Cardinal Direction Relations
In Artificial Intelligence, 152(2):143--171, 2004
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.
Note: This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.