© 2017 ACM. Ontologies describe complex world knowledge in that they consist of hierarchical relations, such as is-a, which can be expressed by quantifiers or sets, and various binary relations, which can be expressed by links or networks. Should hierarchical relations be distinguished from other binary relations as essentially different ones in building cognitively accessible systems of ontologies? In this study, two kinds of ontology visualizations, a network-based visualization (SOVA) and a set-based visualization (concept diagrams), are empirically compared in the case of consistency checking. Participants were presented with one diagram and then asked to answer the question of whether the meaning of the diagram was contradictory. Our results showed that SOVA is more effective than concept diagrams, suggesting that to represent hierarchical and binary relations of ontologies in a way based on networks suits human cognition when checking ontologies' consistencies.