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.