A Mathematical Framework for Studying Representation

The ultimate goal of our research is a set of tools that will automate, or at least aid, the process of discovering a representation that is well-suited to a given task. An early step in this direction is a mathematical analysis of the nature of representation and representation change. The framework in which we propose to carry out this analysis is based on the flexible notion of logical semantics afforded by category theory. This paper motivates this line of research and describes the intuitions underlying the mathematical framework we are developing.