Concrete domains have been introduced in Description Logic (DL) to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. The primary research goal in this context was to find restrictions on the concrete domain such that its integration into certain DLs preserves decidability or tractability. In this paper, we investigate the abstract expressive power of logics extended with concrete domains, namely which classes of first-order interpretations can be expressed using these logics. In the first part of the paper, we show that, under natural conditions on the concrete domain D (which also play a role for decidability), extensions of first-order logic (FOL) or 𝒜ℒ𝒞 with D share important formal properties with FOL, such as the compactness and the Löwenheim-Skolem property. Nevertheless, their abstract expressive power need not be contained in that of FOL. In the second part of the paper, we investigate whether finitely bounded homogeneous structures, which preserve decidability if employed as concrete domains, can be used to express certain universal first-order sentences, which then could be added to DL knowledge bases without destroying decidability. We show that this requires rather strong conditions on said sentences or an extended scheme for integrating the concrete domain that leads to undecidability.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:93538 |
| Date | 02 September 2024 |
| Creators | Baader, Franz, De Bortoli, Filippo |
| Contributors | Technische Universität Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/acceptedVersion, doc-type:report, info:eu-repo/semantics/report, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | urn:nbn:de:bsz:14-qucosa2-785040, qucosa:78504 |
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