We propose a formal framework to represent types intended as (intentional) complex properties characterised in terms of (i) simple qualities, e.g., colors or weights; (ii) structural properties, i.e., properties concerning the spatial distribution of qualities, e.g., being polka-dotted or being uniformly dense; and (iii) structured properties, i.e., properties concerning the topological arrangement of the components of assemblies. Our framework is inspired by work done in cognitive science, in particular by Ggrdenfors' theory of conceptual spaces, as well as by the notion of image schema, the latter being a theoretical construct to represent general patterns and the way they apply to heterogeneous cases. Hopefully, our approach can also contribute to the understanding of the notions of image schema and conceptual space.
