Symbolic Arithmetical Reasoning with Qualified Number Restrictions. Ohlbach, Jürgen, H., Schmidt, R. A., & Hustadt, U. In Borgida, A., Lenzerini, M., Nardi, D., & Nebel, B., editors, International Workshop on Description Logics, pages 89--95. Appeared as Technical Report RAP.07.95, Dipartimento di Informatica e Sistemistica, Univ. degli studia di Roma, 1995
abstract   bibtex   
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 (atleast 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 (May 1995) for reasoning with graded modalities. We exploit the exact correspondence between the concept description language ALCN and the multi-modal version of the graded modal logic K and show how the method can be applied to ALCN as well. This paper is a condensed version of Ohlbach et al. (May 1995). We omit proofs and much of the technical details, but we include some examples.
@inproceedings{ OhlbachSchmidtHustadt95,
  author = {Ohlbach, Hans Jürgen and Schmidt, Renate A. and 
              Hustadt, Ullrich},
  title = {Symbolic Arithmetical Reasoning with Qualified Number 
              Restrictions},
  booktitle = {International Workshop on Description Logics},
  pmonth = {May},
  pyear = {1995},
  editor = {Borgida, A. and Lenzerini, M. and Nardi, D. and Nebel, B.},
  pages = {89--95},
  caddress = {Rome, Italy},
  cmonth = {June~2--3},
  cyear = {1995},
  note = {Appeared as Technical Report RAP.07.95, Dipartimento di 
              Informatica e Sistemistica, Univ. degli studia di Roma, 
              1995},
  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 (atleast 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 (May 1995) for reasoning with graded modalities. We exploit 
     the exact correspondence between the concept description language 
     ALCN and the multi-modal version of the graded modal logic K and 
     show how the method can be applied to ALCN as well. 
     This paper is a condensed version of Ohlbach et al. (May 1995). We 
     omit proofs and much of the technical details, but we include some 
     examples.}
}
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