Debugging Classical Ontologies Using Defeasible Reasoning Tools

A successful application of ontologies relies on representing as much accurate and relevant domain knowledge as possible, while maintaining logical consistency. As the successful implementation of a real-world ontology is likely to contain many concepts and intricate relationships between the concepts, it is necessary to follow a methodology for debugging and refining the ontology. Many ontology debugging approaches have been developed to help the knowledge engineer pinpoint the cause of logical inconsistencies and rectify them in a strategic way. We show that existing debugging approaches can lead to unintuitive results, which may lead the knowledge engineer to opt for deleting potentially crucial and nuanced knowledge. We provide a methodological and design foundation for weakening faulty axioms in a strategic way using defeasible reasoning tools. Our methodology draws from Rodler’s interactive ontology debugging approach and extends this approach by creating a methodology to systematically find conflict resolution recommendations. Importantly, our goal is not to convert a classical ontology to a defeasible ontology. Rather, we use the definition of exceptionality of a concept, which is central to the semantics of defeasible description logics, and the associated algorithm to determine the extent of a concept’s exceptionality (their ranking); then, starting with the statements containing the most general concepts (the least exceptional concepts) weakened versions of the original statements are constructed; this is done until all inconsistencies have been resolved.

Properties of Module Notions and Atomic Decomposition

Various properties of ontology modules have been studied, such as coverage, self-containment, depletingness, monotonicity, preservation of justifications. These properties are important from a theoretical and practical point of view because they ensure, e.g., that modules have meaningful interfaces, can be used for ontology debugging, or are suitable for computing a meaningful modular structure of an ontology, such as via atomic decomposition (AD). Given one of the many existing module notions, it is not always obvious whether it satisfies a given property, particularly when the module extraction procedure is based on normalization. We investigate several module properties from an abstract point of view with an emphasis on properties relevant for AD. We examine their interrelations, their relation with iterated module extraction, their preservation in normalization-based module notions, and the adjustment of the latter to the requirements of AD. As a case study, we apply our results to modules based on Datalog reasoning (DBMs), which comprise a large family of normalization-based module notions that provide logical guarantees of varying strengths and are thus suitable to a wide range of use cases. This makes DBMs ready to be used for AD and thereby opens AD to new applications.

Reasoning with Concept Diagrams about Antipatterns

Ontologies are notoriously hard to define, express and reason about. Many tools have been developed to ease the debugging and the reasoning process with ontologies, however they often lack accessibility and formalisation. A visual representation language, concept diagrams, was developed for expressing and reasoning about ontologies in an accessible way. Indeed, empirical studies show that concept diagrams are cognitively more accessible to users in ontology debugging tasks. 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 verification of the inconsistency and/or 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 offer a one-to-one translation of OWL ontology axioms into concept diagrams. We prove that our inference rules are sound, and exemplify how they can be used to reason about inconsistencies and incoherence. Finally, we indicate how our rules can serve as a foundation for new rules required when representing ontologies in diverse new domains.