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Fitting Description Logic Ontologies to ABox and Query Examples

Created by
  • Haebom

Author

Maurice Funk, Marvin Grosser, Carsten Lutz

Outline

This paper studies the fitting problem inspired by ontology-mediated queries. Given a set of positive and negative examples $(\mathcal{A},q)$ (where $\mathcal{A}$ is an ABox and $q$ is a Boolean query), the problem is to find an ontology $\mathcal{O}$ such that $\mathcal{A} \cup \mathcal{O} \vDash q$ for all positive examples and $\mathcal{A} \cup \mathcal{O}\not\vDash q$ for all negative examples. We consider $\mathcal{ALC}$ and $\mathcal{ALCI}$ as ontology languages, and atomic queries (AQs), conjunction queries (CQs), and their unions (UCQs) as query languages. Consequently, we provide an effective characterization of all the resulting fitting problems and determine the computational complexity of determining whether a fitting ontology exists. This problem is shown to be ${\scriptsize CO}NP$ for AQs and all CQs, and $2E{\scriptsize XP}T{\scriptsize IME}$-complete for CQs and UCQs. These results hold for both $\mathcal{ALC}$ and $\mathcal{ALCI}$.

Takeaways, Limitations

Takeaways: We clearly elucidate the computational complexity of the ontology fitting problem under the $\mathcal{ALC}$ and $\mathcal{ALCI}$ ontology languages and various query languages (AQs, CQs, UCQs). This makes important theoretical contributions to the fields of ontology engineering and knowledge representation.
Limitations: There is a lack of discussion on developing efficient algorithms applicable to real-world applications. The $2E{\scriptsize XP}T{\scriptsize IME}$-completeness result suggests difficulties in solving real-world problems. Further research is needed on other ontology languages and query languages.
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