Towards a Formal Approach to Information Systems Design Theory Using Category Theory

This paper reports research in progress for the formalization of the notion of information systems design theory within the framework of formal logic and category theory. The formalization starts with the concept of four relational systems (empirical, subjective, conceptual and formal) that are linked by the four activities for design science research proposed by Venable (2006). Category theory is used as the basis of representing the concept of an information systems design theory as a formal framework by representing each of the four relational systems as either types (theories) or tokens (models). The arrows (morphisms) between the four concepts are explained using Barwise and Seligman’s (1997) definition of “infomorphisms”. The contributions of this research are that it explicates the role of kernel theory (background theory) in information systems design theory and it links this design theory to information fusion and information flow research efforts. It thus provides structures that represent a formalization of the design of information systems.