Aligning logical and psychological perspectives on diagrammatic reasoning

Abstract

We advance a theoretical framework which combines recent insights of research in logic, psychology, and formal semantics, on the nature of diagrammatic representation and reasoning. In particular, we wish to explain the varied efficacy of reasoning and representing with diagrams. In general we consider diagrammatic representations to be restricted in expressive power, and we wish to explain efficacy of reasoning with diagrams via the semantical and computational properties of such restricted `languages'. Connecting these foundational insights (from semantics and complexity theory) to the psychology of reasoning with diagrams requires us to develop the notion of the {\it availability} (to an agent) of {\it constraints} operating within representation systems, as a consequence of their direct semantic interpretation. Thus we offer a number of fundamental definitions as well as a research programme which aligns current efforts in the logical and psychological analysis of diagrammatic representation systems.