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Measuring Relations Between Concepts in Conceptual Spaces

  • Lucas Bechberger
  • Kai-Uwe Kühnberger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10630)

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 regions in this space. Our recent mathematical formalization of this framework is capable of representing correlations between different domains in a geometric way. In this paper, we extend our formalization by providing quantitative mathematical definitions for the notions of concept size, subsethood, implication, similarity, and betweenness. This considerably increases the representational power of our formalization by introducing measurable ways of describing relations between concepts.

Keywords

Conceptual spaces Fuzzy sets Measure 

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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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