Relative Representation of Spatial Knowledge: The 2-D Case

Abstract

There have been some straightforward efforts to extend Allen’s interval-based temporal logic to spatial dimensions by using Cartesian tuples of relations (Guesgen, 1989). We take a different approach based on a study of the kind of information that best relates two entities in 2-dimensional space qualitatively. The relevant spatial categories turn out to be “projection” and “orientation.” We define a small set of spatial relations and stress the importance of making their reference frames explicit. Furthermore, we introduce “abstract maps,” an analogical representation that inherently reflects the structure of the represented domain, and demonstrate their use in spatial reasoning. This scheme also facilitates “coarse” reasoning and the hierarchical organization of knowledge. These representational issues form the basis for an experimental system to develop “cognitive maps” from 2-D scanned layout plans of buildings.