Reasoning mechanism for cardinal direction relations

In the classical Projection-based Model for cardinal directions [6], a two-dimensional Euclidean space relative to an arbitrary single-piece region, a, is partitioned into the following nine tiles: North-West, NW(a); North, N(a); North-East, NE(a); West, W(a); Neutral Zone, O(a);East, E(a); South-West, SW(a); South, S(a); and South-East,SE(a). In our Horizontal and Vertical Constraints Model [9], [10] these cardinal directions are decomposed into sets corresponding to horizontal and vertical constraints. Composition is computed for these sets instead of the typical individual cardinal directions. In this paper, we define several whole and part direction relations followed by showing how to compose such relations using a formula introduced in our previous paper [10]. In order to develop a more versatile reasoning system for direction relations, we shall integrate mereology, topology, cardinal directions and include their negations as well. © 2010 Springer-Verlag

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

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