Formalized Conceptual Spaces with a Geometric Representation of
  Correlations
  The highly influential framework of conceptual spaces provides a geometric
way of representing knowledge. Instances are represented by points in a
similarity 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 various operations for our
formalization, both for creating new concepts from old ones and for measuring
relations between concepts. We present an illustrative toy-example and sketch a
research project on concept formation that is based on both our formalization
and its implementation.
