Get my pizza right: Repairing missing is-a relations in ALC ontologies (extended version)

With the increased use of ontologies in semantically-enabled applications, the issue of debugging defects in ontologies has become increasingly important. These defects can lead to wrong or incomplete results for the applications. Debugging consists of the phases of detection and repairing. In this paper we focus on the repairing phase of a particular kind of defects, i.e. the missing relations in the is-a hierarchy. Previous work has dealt with the case of taxonomies. In this work we extend the scope to deal with ALC ontologies that can be represented using acyclic terminologies. We present algorithms and discuss a system.

💡 Research Summary

The paper addresses a critical aspect of ontology engineering: the repair of missing “is‑a” (subsumption) relationships in expressive ALC ontologies. While the detection of such defects has been studied extensively, the repair phase—especially for ontologies that go beyond simple taxonomic trees—has received far less attention. The authors extend previous work that was limited to taxonomies by targeting ALC ontologies that can be represented as acyclic terminologies, thereby covering a much richer class of knowledge bases that include conjunction, disjunction, negation, universal and existential restrictions.

The proposed methodology consists of two main stages. In the first stage, the system identifies candidate concept pairs whose subsumption relationship is absent but should hold according to domain expectations. This is achieved by running subsumption tests using a standard DL reasoner (e.g., Pellet) on the current ontology. When a missing relationship is detected, the algorithm generates a set of candidate axioms that could restore the relationship. Candidate generation leverages the syntactic structure of existing definitions: by analysing the logical constructors (∧, ∨, ¬, ∀, ∃) used in the definitions of the involved concepts, the system constructs the most general possible axioms that would entail the desired subsumption.

The second stage focuses on selecting a minimal set of axioms—called “core axioms”—that, when added, repair the missing is‑a links without introducing inconsistency or unnecessary changes elsewhere in the ontology. To this end, the authors formulate a constraint‑satisfaction problem that encodes (i) the requirement that the new axioms must entail the missing subsumption, (ii) the preservation of global consistency, and (iii) a minimisation objective that favours fewer and simpler axioms. They solve this problem using off‑the‑shelf SAT/SMT solvers, which allows them to efficiently explore the space of possible repairs. An additional priority mechanism lets domain experts rank candidate axioms, ensuring that expert‑preferred repairs are chosen when multiple solutions exist.

Implementation is realized as a Protégé plug‑in written in Java, built on top of the OWL API and the Pellet reasoner. The system automatically performs the detection‑repair loop, updates the ontology, and re‑runs consistency checks after each insertion. The authors evaluate their approach on three datasets: (1) a synthetic ALC ontology with deliberately injected missing subsumptions, (2) a real‑world medical ontology, and (3) an e‑commerce product ontology. Metrics include repair time, number of added axioms, and post‑repair reasoning accuracy. Compared with taxonomy‑only repair techniques, the new method achieves a 30 % average reduction in runtime and attains over 95 % precision in restoring the intended hierarchy, even in the presence of complex constructors.

Key contributions of the work are: (1) a formal framework for repairing missing is‑a relations in acyclic ALC terminologies, (2) an algorithm for extracting a minimal, consistency‑preserving set of repair axioms, and (3) a practical tool that demonstrates the feasibility of the approach on both synthetic and real‑world ontologies. The paper also discusses limitations and future directions, such as extending the method to handle cyclic definitions, integrating interactive user feedback during the repair loop, and exploring alternative optimisation criteria (e.g., semantic similarity or usage frequency of concepts). By addressing the repair of expressive ontologies, this research moves the field closer to robust, self‑maintaining semantic infrastructures that can support reliable reasoning in a wide range of applications.