- Titel
- An Order-Theoretic View on Optimal Repairs and Complete Sets of Unifiers
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:14-qucosa2-981523
- Schriftenreihe
- LTCS-Report
- Bandnummer
- 25-02
- Erstveröffentlichung
- 2025
- DOI
- https://doi.org/10.25368/2025.143
- Abstract (EN)
- The optimal repair property, which says that there is a finite set of optimal (i.e., entailment-maximal) repairs that covers all repairs, has turned out to be useful both in the context of ontology engineering and in belief change. We provide abstract order-theoretic conditions that guarantee the existence of finite sets of optimal repairs covering all repairs, and illustrate their use with abstract examples as well as with more practical examples from the realm of Description Logic (DL). The order-theoretic view on optimal repairs also reveals that there is a strong similarity between the optimal repair property and the existence of a finite complete set of unifiers for unification modulo equational theories. Applying Siekmann’s proposal to divide unification problems into the unification types unitary, finitary, infinitary, and zero to repair problems, we obtain a more fine-grained classification of repair problems. For the DL examples introduced in this paper, we observe that types unitary, finitary and zero can occur, but none of these examples provides us with an infinitary repair problem. However, we also show that unification problems can actually be viewed as repair problems in the abstract framework introduced in our previous work on contractions based on optimal repairs. Thus, within this framework, known results on unification types of certain equational theories provide us with examples of repair problems of these types.
- Zitiert in
- The 18th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2025)
- Freie Schlagwörter (DE)
- Revision, Beschreibungslogik, Unifikation, Ontologiereperatur
- Freie Schlagwörter (EN)
- Belief Revision, Description Logic, Unification, Ontology Repair
- Klassifikation (DDC)
- 004
- Klassifikation (RVK)
- ST 136
- Herausgeber (Institution)
- Technische Universität Dresden
- Förder- / Projektangaben
- Center for Scalable Data Analytics and Artificial Intelligence Dresden/Leipzig (ScaDS.AI)
- Deutsche Forschungsgemeinschaft (DFG)
TRR 248: Grundlagen verständlicher Software-Systeme - für eine nachvollziehbare cyber-physische Welt
ID: 389792660 - Version / Begutachtungsstatus
- angenommene Version / Postprint / Autorenversion
- URN Qucosa
- urn:nbn:de:bsz:14-qucosa2-981523
- Veröffentlichungsdatum Qucosa
- 04.08.2025
- Dokumenttyp
- Bericht
- Sprache des Dokumentes
- Englisch
- Lizenz / Rechtehinweis
CC BY 4.0