A Thorough Formalization of Conceptual Spaces

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10505)

Abstract

The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by convex regions in this space. After pointing out a problem with the convexity requirement, we propose a formalization of conceptual spaces based on fuzzy star-shaped sets. Our formalization uses a parametric definition of concepts and extends the original framework by adding means to represent correlations between different domains in a geometric way. Moreover, we define computationally efficient operations on concepts (intersection, union, and projection onto a subspace) and show that these operations can support both learning and reasoning processes.

Keywords

Conceptual spaces Star-shaped sets Fuzzy sets 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Cognitive ScienceOsnabrück UniversityOsnabrückGermany

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