On the Expressive Power of Description Logics with Cardinality Constraints on Finite and Infinite Sets

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In recent work we have extended the description logic (DL) ALCQ by means of more expressive number restrictions using numerical and set constraints stated in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA). It has been shown that reasoning in the resulting DL, called ALCSCC, is PSpace-complete without a TBox and ExpTime-complete w.r.t. a general TBox. The semantics of ALCSCC is defined in terms of finitely branching interpretations, that is, interpretations where every element has only finitely many role successors. This condition was needed since QFBAPA considers only finite sets. In this paper, we first introduce a variant of ALCSCC, called ALCSCC, in which we lift this requirement (inexpressible in first-order logic) and show that the complexity results for ALCSCC mentioned above are preserved. Nevertheless, like ALCSCC, ALCSCC is not a fragment of first-order logic. The main contribution of this paper is to give a characterization of the first-order fragment of ALCSCC. The most important tool used in the proof of this result is a notion of bisimulation that characterizes this fragment.


Original languageEnglish
Title of host publicationFrontiers of Combining Systems - 12th International Symposium, FroCoS 2019, Proceedings
EditorsAndreas Herzig, Andrei Popescu
PublisherSpringer, Berlin [u. a.]
Number of pages17
ISBN (print)9783030290061
Publication statusPublished - 2019

Publication series

SeriesLecture Notes in Computer Science, Volume 11715


Title12th International Symposium on Frontiers of Combining Systems, FroCoS 2019
Duration4 - 6 September 2019
CountryUnited Kingdom

External IDs

Scopus 85071934839
ORCID /0000-0002-4049-221X/work/142247949
ORCID /0000-0002-8623-6465/work/142251902


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