Visualizing ALC Using Concept Diagrams

This paper addresses the problem of how to visualize axioms from \(\mathcal {ALC}\) using concept diagrams. We establish that 66.4% of OWL axioms defined for ontologies in the Manchester corpus are formulated over \(\mathcal {ALC}\), demonstrating the significance of considering how to visualize this relatively simple description logic. Our solution to the problem involves providing a general translation from \(\mathcal {ALC}\) axioms into concept diagrams, which is sufficient to establish that all of \(\mathcal {ALC}\) can be expressed. However, the translation itself is not designed to give optimally readable diagrams, which is particularly challenging to achieve in the general case. As such, we also improve the translations for a selected category of \(\mathcal {ALC}\) axioms, to illustrate that more effective diagrams can be produced.