Fitting Description Logic Ontologies to ABox and Query Examples
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| author | Funk, Maurice Grosser, Marvin Lutz, Carsten |
| author_facet | Funk, Maurice Grosser, Marvin Lutz, Carsten |
| contents | We study a fitting problem inspired by ontology-mediated querying: given a collection of positive and negative examples of the form $(\mathcal{A},q)$ with $\mathcal{A}$ an ABox and $q$ a Boolean query, we seek an ontology $\mathcal{O}$ that satisfies $\mathcal{A} \cup \mathcal{O} \vDash q$ for all positive examples and $\mathcal{A} \cup \mathcal{O}\not\vDash q$ for all negative examples. We consider the description logics $\mathcal{ALC}$ and $\mathcal{ALCI}$ as ontology languages and a range of query languages that includes atomic queries (AQs), conjunctive queries (CQs), and unions thereof (UCQs). For all of the resulting fitting problems, we provide effective characterizations and determine the computational complexity of deciding whether a fitting ontology exists. This problem turns out to be ${\scriptsize CO}NP$ for AQs and full CQs and $2E{\scriptsize XP}T{\scriptsize IME}$-complete for CQs and UCQs. These results hold for both $\mathcal{ALC}$ and $\mathcal{ALCI}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fitting Description Logic Ontologies to ABox and Query Examples Funk, Maurice Grosser, Marvin Lutz, Carsten Artificial Intelligence Logic in Computer Science Computing methodologies~Description logics, Computing methodologies~Ontology engineering We study a fitting problem inspired by ontology-mediated querying: given a collection of positive and negative examples of the form $(\mathcal{A},q)$ with $\mathcal{A}$ an ABox and $q$ a Boolean query, we seek an ontology $\mathcal{O}$ that satisfies $\mathcal{A} \cup \mathcal{O} \vDash q$ for all positive examples and $\mathcal{A} \cup \mathcal{O}\not\vDash q$ for all negative examples. We consider the description logics $\mathcal{ALC}$ and $\mathcal{ALCI}$ as ontology languages and a range of query languages that includes atomic queries (AQs), conjunctive queries (CQs), and unions thereof (UCQs). For all of the resulting fitting problems, we provide effective characterizations and determine the computational complexity of deciding whether a fitting ontology exists. This problem turns out to be ${\scriptsize CO}NP$ for AQs and full CQs and $2E{\scriptsize XP}T{\scriptsize IME}$-complete for CQs and UCQs. These results hold for both $\mathcal{ALC}$ and $\mathcal{ALCI}$. |
| title | Fitting Description Logic Ontologies to ABox and Query Examples |
| topic | Artificial Intelligence Logic in Computer Science Computing methodologies~Description logics, Computing methodologies~Ontology engineering |
| url | https://arxiv.org/abs/2508.08007 |