A Thorough Formalization of Conceptual Spaces
  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.
