On the Admissibility of Concrete Domains for CBR
Based on Description Logics

Gerd Kamp

Universitt Hamburg, Vogt-Klln-Str.30, 22527 Hamburg
kamp@informatik.uni-hamburg.de


Abstract. In order to use descriptions logics for case-based reasoning it must
be possible to use primitive datatypes such as numbers and strings within the
representation and inference mechanisms of the logic. The best way to do so is
via so called admissible concrete domains. In this paper we address the general
problem of the admissibility of concrete domains, using the application area of
the retrieval of bibliographic data as an example. We investigate the theoretical
limitations on admissible concrete domains over numbers and strings imposed by
decidability results known from mathematical logic and automata theory, as well
as the prospects of potential implementations in our description logic CTL.
References

1.	F. Baader and P. Hanschke. A Scheme for Integrating Concrete Domains into Concept Languages. 
Research Report RR-91-1O, DFKI, Kaiserslautern, Germany, April 1991.
2.	Stanley Bums and H.P. Sankappanavar. A Course in Universal Algebra. Springer Verlag,
New York, 1981.
3.	G. E. Collins and Hoon Hong. Partial cylindrical algebraic decomposition. Journal of Symbolic 
Computation, 12:299328,1991.
4.	Andreas Dolzmann and Thomas Sturm. REDLOG  Computer Algebra Meets Computer
Logic. Technical Report MIP-9603, Universitt Passau, Passau, Germany, February 1996.
5.	H. W. Gusgen. Spatial reasoning based on Allens temporal logic. Technical Report TR-89-
049, ICSI, August 1989.
6.	P. Hanschke. A Declarative Integration of Terminological, Constraint-Based, Data-driven,
and Goal-directed Reasoning. Dissertation, Universitt Kaiserslautern, 1993.
7.	H. Hong. RISC-CLP(Real): Constraint Logic Programming over the real numbers. In Constraint 
Logic Programming: Selected Research. MIT Press, Cambridge, MA, 1993.
8.	John E. Hopcroft and Jeffrey Ullman. Introduction to automata theory languages and computation. 
Addison-Wesley, 1979.
9.	Gerd Kamp. Using Description Logics for Knowledge Intensive Case-based Reasoning.
In I. Smith and B. Faltings, editors, Advances in Case-Based Reasoning, pages 204218,
Lausanne, Switzerland, November 1996. Springer Verlag.
10.	Gerd Kamp and Bernd Neumann. Knowledge-based Inference Methods for Modeling Technical 
Systems. In Proc. 30th Hawaiian International Conference on System Sciences, Wailea,
HA, 1997. Computer Science Press.
11.	Gerd Kamp and Holger Wache. CTL  a description logic with expressive concrete domains,
Technical report, LKI, 1996.
12.	Gerd Kamp and Holger Wache. Using Description Logics for Consistency-based Diagnosis.
In International Description Logics  Collected Papers from the 1996 Workshop , number
WS-96-05, pages 136140, Boston, MA, November 1996. AAAI Press.
13.	O. Matz, A. Miller, A. Potthoff, W. Thomas, and B. Valkema. Report on the Program
AMoRE. Technical Report 9507, Universitt Kiel, Germany, October 1995.
14.	Alfred Tarski. A Decision Method for Elementary Algebra and Geometry. University of
California Press, Berkeley and Los Angeles, CA, 1951.
15.	Alfred Tarski. Andrzej Mostowski, and Raphael M. Robinson. Undecidable Theories. Studies 
in Logic and the Foundations of Mathematics. North-Holland, Amsterdam, Netherlands,
1971.
