Syllogistic Reasoning for Cardinal Direction Relations

Syllogistics is a type of logical reasoning which involves quantifiers such as All, and Some. Here, we explore the use of syllogisms to formalize quantified direction relations by incorporated them into the classical Projection-based Model for cardinal directions [Frank,1992], 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). Typically, only these tiles are employed for reasoning about cardinal direction relations [Ligozat,1988; Goyal and Egenhofer, 2000;.Skiadopoulos and Koubarakis, 2001,2004]. Chen et. al (2007) have integrated cardinal direction relations and RCC-5 and RCC-8 to represent directional and topological information. They have investigated the mutual dependencies them, and discussed the composition of the hybrid relations. However, in this paper, we have developed formalisms to facilitate an expressive reasoning mechanism for spatial databases. These formalisms is the outcome of the integration of RCC-5 [Cohn, et.al,1997] for topological relations, the Project-based Model for cardinal direction relations and syllogisms. In the latter part of the paper, we demonstrate how to compute the composition of such hybridized cardinal direction relations.

http://world-comp.org/p2013/ICA2816.pdf