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Description Logics with Concrete Domains and General Concept Inclusions Revisited
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), whi...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7324241/ http://dx.doi.org/10.1007/978-3-030-51074-9_24 |
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author | Baader, Franz Rydval, Jakub |
author_facet | Baader, Franz Rydval, Jakub |
author_sort | Baader, Franz |
collection | PubMed |
description | 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. One contribution of this paper is to strengthen the existing undecidability results further by showing that concrete domains even weaker than the ones considered in the previous proofs may cause undecidability. To regain decidability in the presence of GCIs, quite strong restrictions, in sum called [Formula: see text]-admissibility, need to be imposed on the concrete domain. On the one hand, we generalize the notion of [Formula: see text]-admissibility from concrete domains with only binary predicates to concrete domains with predicates of arbitrary arity. On the other hand, we relate [Formula: see text]-admissibility to well-known notions from model theory. In particular, we show that finitely bounded, homogeneous structures yield [Formula: see text]-admissible concrete domains. This allows us to show [Formula: see text]-admissibility of concrete domains using existing results from model theory. |
format | Online Article Text |
id | pubmed-7324241 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
record_format | MEDLINE/PubMed |
spelling | pubmed-73242412020-06-30 Description Logics with Concrete Domains and General Concept Inclusions Revisited Baader, Franz Rydval, Jakub Automated Reasoning Article 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. One contribution of this paper is to strengthen the existing undecidability results further by showing that concrete domains even weaker than the ones considered in the previous proofs may cause undecidability. To regain decidability in the presence of GCIs, quite strong restrictions, in sum called [Formula: see text]-admissibility, need to be imposed on the concrete domain. On the one hand, we generalize the notion of [Formula: see text]-admissibility from concrete domains with only binary predicates to concrete domains with predicates of arbitrary arity. On the other hand, we relate [Formula: see text]-admissibility to well-known notions from model theory. In particular, we show that finitely bounded, homogeneous structures yield [Formula: see text]-admissible concrete domains. This allows us to show [Formula: see text]-admissibility of concrete domains using existing results from model theory. 2020-05-30 /pmc/articles/PMC7324241/ http://dx.doi.org/10.1007/978-3-030-51074-9_24 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic. |
spellingShingle | Article Baader, Franz Rydval, Jakub Description Logics with Concrete Domains and General Concept Inclusions Revisited |
title | Description Logics with Concrete Domains and General Concept Inclusions Revisited |
title_full | Description Logics with Concrete Domains and General Concept Inclusions Revisited |
title_fullStr | Description Logics with Concrete Domains and General Concept Inclusions Revisited |
title_full_unstemmed | Description Logics with Concrete Domains and General Concept Inclusions Revisited |
title_short | Description Logics with Concrete Domains and General Concept Inclusions Revisited |
title_sort | description logics with concrete domains and general concept inclusions revisited |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7324241/ http://dx.doi.org/10.1007/978-3-030-51074-9_24 |
work_keys_str_mv | AT baaderfranz descriptionlogicswithconcretedomainsandgeneralconceptinclusionsrevisited AT rydvaljakub descriptionlogicswithconcretedomainsandgeneralconceptinclusionsrevisited |