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Accessible Reasoning with Diagrams: Ontology Debugging

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BPRW01 - Computer-aided mathematical proof

Co-authors: Gem Stapleton (University of Brighton, UK), Zohreh Shams (University of Cambridge, UK), Yuri Sato (University of Brighton, UK)

Ontologies are notoriously hard to define, 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 ex- pressing 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 infer- ence rules for concept diagrams that enables stepwise verification 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.

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