- Titel
- Using Model Theory to Find Decidable and Tractable Description Logics with Concrete Domains
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:14-qucosa2-887205
- Quellenangabe
- Journal of automated reasoning
Erscheinungsjahr: 2022
Jahrgang: 66
Seiten: 357-407
ISSN: 0168-7433
E-ISSN: 1573-0670 - Erstveröffentlichung
- 2022
- Abstract (EN)
- Concrete domains have been introduced in the area of Description Logic to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. Unfortunately, in the presence of general concept inclusions (GCIs), which are supported by all modern DL systems, adding concrete domains may easily lead to undecidability. To regain decidability of the DL ALC in the presence of GCIs, quite strong restrictions, in sum called ω-admissibility, were imposed on the concrete domain. On the one hand, we generalize the notion of ω-admissibility from concrete domains with only binary predicates to concrete domains with predicates of arbitrary arity. On the other hand, we relate ω-admissibility to well-known notions from model theory. In particular, we show that finitely bounded homogeneous structures yield ω-admissible concrete domains. This allows us to show ω-admissibility of concrete domains using existing results from model theory. When integrating concrete domains into lightweight DLs of the E L family, achieving decidability is not enough. One wants reasoning in the resulting DL to be tractable. This can be achieved by using so-called p-admissible concrete domains and restricting the interaction between the DL and the concrete domain. We investigate padmissibility from an algebraic point of view. Again, this yields strong algebraic tools for demonstrating p-admissibility. In particular, we obtain an expressive numerical p-admissible concrete domain based on the rational numbers. Althoughω-admissibility and p-admissibility are orthogonal conditions that are almost exclusive, our algebraic characterizations of these two properties allow us to locate an infinite class of p-admissible concrete domains whose integration into ALC yields decidable DLs.
- Andere Ausgabe
- Link zum Artikel, der zuerst in der Zeitschrift „Journal of automated reasoning” erschienen ist.
DOI: 10.1007/s10817-022-09626-2 - Freie Schlagwörter (DE)
- Beschreibungslogik, Konkrete Domänen, GCIs, ω-Zulässigkeit, Homogenität, endliche Begrenztheit
- Freie Schlagwörter (EN)
- Description logic, Concrete domains, GCIs, ω-Admissibility, Homogeneity, Finite boundedness
- Klassifikation (DDC)
- 004
- Verlag
- Springer Science + Business Media B.V., Dordrecht [u.a.]
- Förder- / Projektangaben
- Deutsche Forschungsgemeinschaft (DFG)
Transregios
TRR 248: Grundlagen verständlicher Software-Systeme - für eine nachvollziehbare cyber-physische Welt
ID: 389792660 - Deutsche Forschungsgemeinschaft (DFG)
Graduiertenkollegs
GRK 1763: Quantitative Logiken und Automaten
(QuantLA)
ID: 9782547 - Version / Begutachtungsstatus
- publizierte Version / Verlagsversion
- URN Qucosa
- urn:nbn:de:bsz:14-qucosa2-887205
- Veröffentlichungsdatum Qucosa
- 22.02.2024
- Dokumenttyp
- Artikel
- Sprache des Dokumentes
- Englisch
- Lizenz / Rechtehinweis
CC BY 4.0