A Logical Investigation on Global Reading of Diagrams

In graphical or diagrammatic representations, not only a basic component of a diagram, but also a collection of multiple components can form a semantic unit, and it often helps reasoning with that diagram. For example, a row and a column in a table, or transitively closed nodes in a directed graph can be regarded as a semantic unit on its own. Designers have long noticed the importance of information conveyed by these global objects [1, 2, 21, 3], and considerable psychological research has also been done on their interpretation process [12, 22, 4, 13]. In this paper, we investigate the global reading of diagrams from the viewpoint of logic. We call those abstract global objects that are invariant under any representation in the given diagrammatic system as “units,” and we define units in a table, a directed graph, and an Euler diagram, respectively. We give a mathematical characterization of them, and study relationships between them. We further investigate how units in a diagram help logical reasoning with that diagram.