Reasoning with Concept Diagrams about Antipatterns in Ontologies

Ontologies are notoriously hard to de ne, express and reason about. Many tools have been developed to ease the ontology debugging and reasoning, however they often lack accessibility and formalisation. A visual representation language, concept diagrams, was developed for expressing ontologies, which has been empirically proven to be cognitively more accessible to ontology users. In this paper we answer the question of \How can concept diagrams be used to reason about inconsistencies and incoherence of ontologies?". We do so by formalising a set of inference rules for concept diagrams that enables stepwise veri cation of the inconsistency and incoherence of a set of ontology axioms. The design of inference rules is driven by empirical evidence that concise (merged) diagrams are easier to comprehend for users than a set of lower level diagrams that are a one-to-one translation from OWL ontology axioms. We prove that our inference rules are sound, and exemplify how they can be used to reason about inconsistencies and incoherence.