Evaluating Diagrammatic Patterns for Ontology Engineering

Diagrammatic logics have been widely studied since Shin'sseminal work on Venn diagrams in the 1990s. There have been significant theoretical advances alongside empirical work investigating their efficacy with respect to symbolic notations. However, we have little understanding about how to choose between syntactically different diagrams whenformulating logical axioms. This paper sets out to provide insight into such choices. By appealing to ontology engineering, we identify commonly required semantic properties that require axiomatization. We systematically identify three different ways of axiomatizing these properties using diagrammatic patterns. One way does not use explicit quantification.The other ways both use explicit quantification but employ different diagrammatic devices to capture the required semantics. We evaluated these competing patterns by conducting an empirical study, collectingperformance data.We conclude that avoiding explicit quantification, and representing the information purely diagrammatically, best supports task performance. As a result, users and designers of diagrammatic logics are guided towards avoiding explicit quantification where possible.