Introduction

According to Mervis and Rosch [MeRo1981] dimensions are usually employed to describe quantative properties (e.g. size) of objects where in a given domain every object is assigned some value on each of the dimensions. “An ideal dimensional representation includes only a small number fo dimensions”. The authors distinguish metric and nonmetric dimensions and state “It can be shown that features may be extended to handle quantative properties, and dimensions may be extended to handle most (perhaps not all) qualative properties”.

“A Conceptual Space (CS) is a geometric structure that represents a number of quality dimensions, which denote basic features by which concepts and objects can be compared, such as weight, color, taste, temperature, pitch, and the three ordinary spatial dimensions. In a conceptual space, points denote objects, and regions denote concepts. The theory of conceptual spaces is a theory about concept learning first proposed by Peter Gärdenfors[Gaer2004]. It is motivated by notions such as conceptual similarity and prototype theory. The theory also puts forward the notion that natural categories are convex regions in conceptual spaces.  In that if x and y are elements of a category, and if z is between x and y  then z is also likely to belong to the category. The notion of concept convexity allows the interpretation of the focal points of regions as category prototypes. In the more general formulations of the theory, concepts are defined in terms conceptual similarity to their prototypes. Conceptual spaces have found applications in both cognitive modelling and artificial intelligence.”