  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.
