Diagrammatic Inference and Graphical Proof

In this paper we present a diagrammatic inference scheme that can be used in the proof and discovery of diagrammatic theorems. First, we present the theory of abstraction markers and notational keys for explaining how abstraction can be incorporated in the interpretation of graphics through both syntactic and semantic means. We also explore how the process of reinterpretation of graphics is essential for learning and proving graphical theorems. Then, we present the diagrammatic inference scheme; it is illustrated with the proof of the theorem of the sum of the odd numbers. The paper concludes with a discussion on the relation between abstraction, visualization, interpretation change and learning, applied to understand a purely diagrammatic proof of the Theorem of Pythagoras.