Diagrams as physical models

Abstract

We discuss a variety of roles for diagrams in helping with reasoning, focusing in particular on their role as physical models of states of affairs, much like an architectural model of a building or a 3-D molecular model of a chemical compound. We discuss the concept of a physical model for a logical sentence, and the role played by the causal structure of the physical medium in making the given sentence as well as a set of implied sentences true. This role of a diagram is consistent with a widely-held intuition that diagrams exploit the fact that 2-D space is an analog of the domain of discourse. One line of research in diagrammatic reasoning is that diagrams, rather then being models, are formal representations with specialized rules of inference that generate new diagrams. We reconcile these contrasting views by relating the usefulness of diagrammatic systems as formal representations to the fact that their rewrite rules take advantage of the diagrams' model-like character. When the physical model is prototypical, it supports the inference of certain other sentences for which it provides a model as well. We also informally discuss a proposal that diagrams and similar physical models help to explicate a certain sense of relevance in inference, an intuition that so-called Relevance Logics attempt to capture. © Springer-Verlag Berlin Heidelberg 2006.