Image Schemas and Conceptual Blending in Diagrammatic Reasoning: The Case of Hasse Diagrams

In this work, we propose a formal, computational model of the sense-making of diagrams by using the theories of image schemas and conceptual blending, stemming from cognitive linguistics. We illustrate our model here for the case of a Hasse diagram, using typed first-order logic to formalise the image schemas and to represent the geometry of a diagram. The latter additionally requires the use of some qualitative spatial reasoning formalisms. We show that, by blending image schemas with the geometrical configuration of a diagram, we can formally describe the way our cognition structures the understanding of, and the reasoning with, diagrams. In addition to a theoretical interest for diagrammatic reasoning, we also briefly discuss the cognitive underpinnings of good practice in diagram design, which are important for fields such as human-computer interaction and data visualization.