The Expressive Power of Description Logics with Numerical Constraints over Restricted Classes of Models

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Abstract

Standard Description Logics (DLs) can encode quantitative aspects of an application domain through either number restrictions, which constrain the number of individuals that are in a certain relationship with an individual, or concrete domains, which can be used to assign concrete values to individuals using so-called features. These two mechanisms have been extended towards very expressive DLs, for which reasoning nevertheless remains decidable. Number restrictions have been generalized to more powerful comparisons of sets of role successors in ALCSCC, while the comparison of feature values of different individuals in ALC(D) has been studied in the context of ω-admissible concrete domains D. In this paper, we combine both formalisms and investigate the complexity of reasoning in the thus obtained DL ALCOSCC(D), which additionally includes the ability to refer to specific individuals by name. We show that, in spite of its high expressivity, the consistency problem for this DL is ExpTime-complete, assuming that the constraint satisfaction problem of D is also decidable in exponential time. It is thus not higher than the complexity of the basic DL ALC. At the same time, we show that many natural extensions to this DL, including a tighter integration of the concrete domain and number restrictions, lead to undecidability.

Details

Original languageEnglish
Title of host publicationFrontiers of Combining Systems
Editors René Thiemann, Christoph Weidenbach
PublisherSpringer, Cham
Pages22-39
Number of pages18
Edition1
ISBN (electronic)978-3-032-04167-8
ISBN (print)978-3-032-04166-1
Publication statusE-pub ahead of print - 15 Sept 2025
Peer-reviewedYes

Publication series

SeriesLecture Notes in Artificial Intelligence (LNAI)
Volume15979
ISSN0302-9743

External IDs

ORCID /0000-0002-4049-221X/work/192040065
Scopus 105017118131

Keywords