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Advances in Artificial Intelligence
Volume 2013 (2013), Article ID 205261, 20 pages
Research Article

A Hybrid Reasoning Model for “Whole and Part” Cardinal Direction Relations

1Arts Environment and Technology Faculty, Leeds Metropolitan University, Headingley Campus, Leeds LS6 3QS, UK
2School of Computing, University of Leeds, Leeds LS2 9JT, UK

Received 8 May 2012; Accepted 24 September 2012

Academic Editor: Ian Mitchell

Copyright © 2013 Ah-Lian Kor and Brandon Bennett. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We have shown how the nine tiles in the projection-based model for cardinal directions can be partitioned into sets based on horizontal and vertical constraints (called Horizontal and Vertical Constraints Model) in our previous papers (Kor and Bennett, 2003 and 2010). In order to come up with an expressive hybrid model for direction relations between two-dimensional single-piece regions (without holes), we integrate the well-known RCC-8 model with the above-mentioned model. From this expressive hybrid model, we derive 8 basic binary relations and 13 feasible as well as jointly exhaustive relations for the x- and y-directions, respectively. Based on these basic binary relations, we derive two separate composition tables for both the expressive and weak direction relations. We introduce a formula that can be used for the computation of the composition of expressive and weak direction relations between “whole or part” regions. Lastly, we also show how the expressive hybrid model can be used to make several existential inferences that are not possible for existing models.