Diagrammatic Reasoning for ALC Visualization with Logic Graphs

User studies show the demand for diagrammatic reasoning techniques for knowledge representation formats. OWL ontologies are highly relevant for Web 3.0, however, existing ontology visualization tools do not support diagrammatic reasoning, while existing diagrammatic reasoning systems utilize suboptimal visual languages. The purpose of this research is to facilitate the usage of OWL ontologies by providing a diagrammatic reasoning system over their visual representations. We focus on the ALC description logic, which covers most of the expressivity of the ontologies. As a visual language to reason about, we utilize Logic Graphs, which provide the simplest visualizations regarding graph- and information-theoretic properties. We adapt the tableau algorithm to LGs to reason about concept satisfiability, prove the correctness of the proposed system and illustrate it with examples. The proposed diagrammatic reasoning system allows reasoning over ontologies, reducing complex concepts step by step, and identifying elements that produce a contradiction.