An algebra for the manipulation of conceptual spaces in cognitive agents

According to Gärdenfors, the theory of conceptual spaces describes a level of representation present in some cognitive agents between a sub-conceptual and a symbolic level of representation. In contrast to a large part of contemporary philosophical speculation on these matters for which concepts and conceptual content are propositional, conceptual spaces provide a geometric framework for the representation of concepts. In this paper we introduce an algebra for the manipulation of different conceptual spaces in order to formalise the process whereby an artificial agent rearranges its internal conceptual representations as a consequence of its perceptions, which are here rendered in terms of measurement processes.