Construction and repair of description-logic knowledge bases

• Applicant: Dr.-Ing. Francesco Kriegel
• Subject Area: Theoretical Computer Science
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 558917076

Knowledge-based systems represent complex domains explicitly and use an inference engine to draw conclusions and answer queries, aiding decision-making based on encoded knowledge. A modern foundation of these systems is description logics, which represent an application domain as a knowledge base consisting of data and an ontology. Building an ontology is challenging, especially for large domains, as the included terminology must be diverse enough to describe all domain objects and, moreover, all objects are governed by the ontology's statements. Typically, domain experts and knowledge engineers manually create these ontologies, but leveraging existing ones or using automated and interactive methods can reduce their workload. Formal concept analysis (FCA), for instance, helps construct ontologies---namely by its key application of computing the canonical implication base (a minimal complete set of implications valid in the data), which has been extended to the description-logic setting by supporting relations between objects. In a recent conference article, I revised and extended this method, implemented efficiency improvements, and tested a prototype on real-world datasets. Moving forward, I aim to further enhance efficiency, support a more expressive description logic, and combine this method with others for new applications and wider adoption. Despite the logical correctness and explainability of inferences in knowledge-based systems, errors in the knowledge base can lead to faulty conclusions, necessitating repairs. In a previous project, we started to develop the optimal-repair framework to address such issues, focusing on cases where only the data might contain errors, while the ontology remains static. Traditional repair methods either delete too much knowledge or rely on expensive searches for weaker statements, but our method efficiently computes optimal repairs by directly subtracting unwanted consequences from the knowledge base, minimizing the removal of unrelated knowledge. I am keen to continue this research, aiming to support more expressive logics and incorporate abduction methods to include wanted consequences in the repair process. As further directions, I plan to relax the assumption of a static, error-free ontology, explore more ways to compare repairs and so facilitate selection of relevant ones, and identify weaker conditions that still guarantee existence and coverage of optimal repairs. With lower priority, I want to investigate further applications of the repair method, such as in privacy-preserving knowledge publishing, error-tolerant reasoning, or defeasible reasoning.

• DFG Programme: Research Grants