Reformulation of the theory of conceptual spaces

This paper presents a conceptual system based on two independently developed extensions of Gardenförs’ formulation of conceptual spaces. The new approach continues to emphasize the role of properties and their associations in conceptual representation, and to recognize the importance of similarity judgments in reasoning tasks. In the new theory, domains are sets equipped with a measure, and a property is a measurable membership function on a domain. Concepts are sets of properties and their binary associations. A new notion of the degree of ambiguity of properties for a given reasoning task is used to focus attention upon properties having the greatest discrimination power. The theory is demonstrated on a maritime application involving the categorization of vessel routes.