Abstract

The development of diagrammatic logics is strongly motivated by the desire to make formal reasoning accessible to broad audiences. One major research problem, for which surprisingly little progress has been made, is to understand how to choose between semantically equivalent diagrams from the perspective of human cognition. The particular focus of this paper is on choosing between diagrams that represent either the presence or absence of individuals. To understand how to best make this choice, we conducted an empirical study. We found that representing the presence of individuals supported task performance either significantly better than, or no worse than, representing the absence of individuals. The particularly striking feature of our results was that representing the absence of individuals in a way that makes the diagram highly cluttered is detrimental to human cognition. As a result, diagrams with this feature should be avoided, but diagrams using presence or low-cluttered absence can be used to support cognition in the context of the tasks performed in our study.