In the last two blog posts (see here and here), I have described the problem I address in my paper “A Thorough Formalization of Conceptual Spaces” [1]: Convex regions in a conceptual space are unable to encode correlations between domains. I have furthermore argued that star-shaped regions are a possible solution to this problem.

In this blog post, I would like to illustrate the basic idea of my formalization. I won’t address the underlying math too much (whoever is interested can check out the paper), because my main goal is to give you some intuitive understanding of what’s going on.

The question that was still left open last time is the following one: How exactly can we represent star-shaped regions in a conceptual space?

Continue reading “Formalizing Conceptual Spaces With Simple Star-Shaped Sets”