On Representing Concepts in High-dimensional Linear Spaces

Producing a mathematical model of concepts is a very important issue in artificial intelligence, because if such a model were found this, besides being a very interesting result in its own right, would also contribute to the emergence of what we could call the ‘mathematics of thought.’ One of the most interesting attempts made in this direction is P. Gärdenfors’ theory of conceptual spaces, a theory which is mostly presented by its author in an informal way. The main aim of the present article is contributing to Gärdenfors’ theory of conceptual spaces by discussing some of the advantages which derive from the possibility of representing concepts in high-dimensional linear spaces.