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 Author, Editor
 Editor(s): Borgida, A. Lenzerini, M. Nardi, D. Nebel, B. dblp dblp dblp dblp

 Title, Booktitle
 Title*: Symbolic Arithmetical Reasoning with Qualified Number Restrictions Booktitle*: Proceedings of International Workshop on Description Logics'95

 Event, URLs
 URL of the conference: URL for downloading the paper: Event Address*: Rome, Italy Language: English Event Date* (no longer used): June 2-3, 1995 Organization: Event Start Date: 18 September 2019 Event End Date: 18 September 2019

 Publisher
 Name*: Dipartimento di Informatica e Sistemistica, Univ. degli studia di Roma URL: Address*: Rome Type:

 Vol, No, Year, pp.
 Series: Rap.
 Volume: Number: 07.95 Month: May Pages: 89-95 Year*: 1995 VG Wort Pages: ISBN/ISSN: Sequence Number: DOI:

 (LaTeX) Abstract: Many inference systems used for concept description logics are constraint systems that employ tableaux methods. These have the disadvantage that for reasoning with qualified number restrictions $n$ new constant symbols are generated for each concept of the form $(\geq n \ R \ C)$. In this paper we present an alternative method that avoids the generation of constants and uses a restricted form of symbolic arithmetic considerably different from the tableaux method. The method we use is introduced in Ohlbach, Schmidt and Hustadt (1995) for reasoning with graded modalities. We exploit the exact correspondence between the concept description language $\cal ALCN$ and the multi-modal version of the graded modal logic $\overline{\mbox{\bf K}}$ and show how the method can be applied to $\cal ALCN$ as well. This paper is a condensed version of Ohlbach et al.\ (1995). We omit proofs and much of the technical details, but we include some examples. Keywords: KL-ONE-type knowledge representation, correspondence problem, functional semantics, symbolic arithmetical reasoning, theorem proving, graded modal logic, non-classical logics, theory resolution, transformation to many-sorted logic, quantifier elimination, ALCN HyperLinks / References / URLs: This paper is a condensed version of Ohlbach et al.\ (1995), Translating Graded Modalities into Predicate Logic, MPII Research Report 95-2-008 Download Access Level:

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 MPG Unit: Max-Planck-Institut für Informatik MPG Subunit: Programming Logics Group Audience: experts only Appearance: MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat

BibTeX Entry:

AUTHOR = {Ohlbach, Hans J{\"u}rgen and Schmidt, Renate A. and Hustadt, Ullrich},
EDITOR = {Borgida, A. and Lenzerini, M. and Nardi, D. and Nebel, B.},
TITLE = {Symbolic Arithmetical Reasoning with Qualified Number Restrictions},
BOOKTITLE = {Proceedings of International Workshop on Description Logics'95},
PUBLISHER = {Dipartimento di Informatica e Sistemistica, Univ. degli studia di Roma},
YEAR = {1995},
NUMBER = {07.95},
PAGES = {89--95},
SERIES = {Rap.},