A general formulation of conceptual spaces as a meso level representation

Representing cognitive processes remains one of the great research challenges. Many important application areas, such as clinical diagnosis, operate in an environment of relative magnitudes, counts, shapes, colours, etc. which are not well captured by current representational approaches. This paper presents conceptual spaces as a meso level representation for cognitive systems, between the high level symbolic representations and the subconceptual connectionist representations which have dominated AI. Conceptual spaces emphasize orders and measures and therefore naturally represent counts, magnitudes, and volumes. Taking Grdenfors' decade-long investigation of conceptual spaces [Grdenfors, Conceptual Spaces: The Geometry of Thought, MIT Press, 2000] as start point, the paper presents a formal foundation for conceptual spaces, shows how they are theoretically and practically linked to higher and lower representational levels, and develops dynamics which allow the orbits of states in the space to solve appropriate meso level reasoning tasks. Interpretations of conceptual spaces are given to illustrate the formal definitions and show the flexibility of the representation.

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