On the Problem of Computing Small Representations of Least Common Subsumers

  • Franz Baader
  • Anni-Yasmin Turhan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2479)


For Description Logics with existential restrictions, the size of the least common subsumer (lcs) of concept descriptions may grow exponentially in the size of the input descriptions. The first (negative) result presented in this paper is that it is in general not possible to express the exponentially large concept description representing the lcs in a more compact way by using an appropriate (acyclic) terminology. In practice, a second and often more severe cause of complexity was the fact that concept descriptions containing concepts defined in a terminology must first be unfolded (by replacing defined names by their definition) before the known lcs algorithms could be applied. To overcome this problem, we present a modified lcs algorithm that performs lazy unfolding, and show that this algorithm works well in practice.


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  1. 1.
    F. Baader and R. Küsters. Computing the least common subsumer and the most specific concept in the presence of cyclic ALN-concept descriptions. In O. Herzog and A. Günter, eds., Proc. of KI-98, volume 1504 of Lecture Notes in Computer Science, p. 129–140, Bremen, Germany, 1998. Springer-Verlag.Google Scholar
  2. 2.
    F. Baader, R. Küsters, and R. Molitor. Computing least common subsumer in description logics with existential restrictions. In T. Dean, ed., Proc. of the 16th Int. Joint Conf. on Artificial Intelligence (IJCAI-99), p. 96–101, Stockholm, Sweden, 1999. Morgan Kaufmann, Los Altos. An extended version appeared as LTCS-Report LTCS-98-09, LuFG Theoretical Computer Science, RWTH Aachen, Germany, 1998. See Scholar
  3. 3.
    F. Baader, R. Küsters, and R. Molitor. Rewriting concepts using terminologies. In A.G. Cohn, F. Giunchiglia, and B. Selman, eds., Proc. of the 7th Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR-00), p. 297–308, San Francisco, CA, 2000. Morgan Kaufmann Publishers.Google Scholar
  4. 4.
    F. Baader and R. Molitor. Building and structuring description logic knowledge bases using least common subsumers and concept analysis. In B. Ganter and G. Mineau, eds., Proc. of ICCS-00, volume 1867 of Lecture Notes in Artificial Intelligence, p. 290–303. Springer-Verlag, 2000.Google Scholar
  5. 5.
    F. Baader and U. Sattler. Knowledge representation in process engineering. In Proc. ofDL-96, 1996.Google Scholar
  6. 6.
    F. Baader and A.-Y. Turhan. TBoxes do not yield a compact representation of the least common subsumer. In Proc. of DL-2001, 2001.Google Scholar
  7. 7.
    F. Baader, E. Franconi, B. Hollunder, B. Nebel, and H.-J. Profitlich. An empirical analysis of optimization techniques for terminological representation systems or: Making KRIS get a move on. Applied Artificial Intelligence. Special Issue on Knowledge Base Management, 4:109–132, 1994.Google Scholar
  8. 8.
    I. Horrocks. Optimising Tableaux Decision Procedures for Description Logics. PhD thesis, University of Manchester, 1997.Google Scholar
  9. 9.
    R. Küsters and R. Molitor. Approximating most specific concepts in description logics with existential restrictions. In T. Eiter, F. Baader, G. Brewka, eds., Proc. of the 24th German Annual Conf. on Artificial Intelligence (KI’01), number 2174 in Lecture Notes In Artificial Intelligence, p. 33–47. Springer-Verlag, 2001.Google Scholar
  10. 10.
    B. Nebel. Terminological reasoning is inherently intractable. Artificial Intelligence Journal, 43:235–249, 1990.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    U. Sattler. Terminological knowledge representation systems in a process engineering application. PhD thesis, RWTH Aachen, 1998.Google Scholar
  12. 12.
    A.-Y. Turhan and R. Molitor. Using lazy unfolding for the computation of least common subsumers. In Proc. of DL-2001, 2001.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Franz Baader
    • 1
  • Anni-Yasmin Turhan
    • 1
  1. 1.Theoretical Computer ScienceTU DresdenGermany

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