Foundations for a formalism of nearness

Abstract

Reasoning about your spatial environment can be a challenging task, especially when you are a robot trying to rely solely on quantitative measures. With nearness being such a vague concept, a qualitative representation is an obvious choice offering a wider range of possible values. This paper introduces a qualitative representation for spatial proximity that accounts for absolute binary nearness relations. The formalism is based on the notion of perceived points, called sites, in a point based universe. Proximity concepts are determined by the parameters of distance between two sites and weight of each of those sites. These parameters were drawn from the concept of Generalised Voronoi Diagrams. Cognitively useful models and interpretations of our formalism are shown in both a navigation and a natural language context.