A potential theory approach to an algorithm of conceptual space partitioning

This paper proposes a new classification algorithm for the partitioning of a conceptual space. All the algorithms which have been used until now have mostly been based on the theory of Voronoi diagrams. This paper proposes an approach based on potential theory, with the criteria for measuring simila...

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Bibliographic Details
Published in:Cognitive studies (Warsaw) 2017-01, Vol.17 (17), p.1-10
Main Authors: Urban, Roman, Grzelińska, Magdalena
Format: Article
Language:English
Subjects:
Algorithms
Cognitive Psychology
concept
conceptual space
Euclidean space
geodesics
natural concept
potential theory
Prototypes
Riemannian manifolds
Space
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Summary:This paper proposes a new classification algorithm for the partitioning of a conceptual space. All the algorithms which have been used until now have mostly been based on the theory of Voronoi diagrams. This paper proposes an approach based on potential theory, with the criteria for measuring similarities between objects in the conceptual space being based on the Newtonian potential function. The notion of a fuzzy prototype, which generalizes the previous definition of a prototype, is introduced. Furthermore, the necessary conditions that a natural concept must meet are discussed. Instead of convexity, as proposed by Gärdenfors, the notion of geodesically convex sets is used. Thus, if a concept corresponds to a set which is geodesically convex, it is a natural concept. This definition applies, for example, if the conceptual space is an Euclidean space. As a by-product of the construction of the algorithm, an extension of the conceptual space to d-dimensional Riemannian manifolds is obtained.
ISSN:2080-7147
2392-2397
2392-2397
DOI:10.11649/cs.1310