On Representing Concepts in High-dimensional Linear Spaces

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