Conceptual Spaces as Voltage Maps

Abstract

Conceptual spaces have been proposed as a meso level representation, intermediate between symbolic and connectionist representations. We define a conceptual space to be a set of images or “voltage maps” on a compact sub plane, and equip it with pseudo-physiological notions of distance and betweenness. While our meso level representation is easily linked to higher and lower representations, we argue that its natural notion of geometry provides powerful additional tools for knowledge modelling and reasoning. As illustration, we offer an explanation of multi-dimensional experimental results which suggets distances follow different order Minkowski measures according to whether the dimentions are integral or separable.