A Refinement Operator for Description Logics

  • Liviu Badea
  • Shan -Hwei Nienhuys-Cheng
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1866)


While the problem of learning logic programs has been extensively studied in ILP, the problem of learning in description logics (DLs) has been tackled mostly by empirical means. Learning in DLs is however worthwhile, since both Horn logic and description logics are widely used knowledge representation formalisms, their expressive powers being incomparable (neither includes the other as a fragment). Unlike most approaches to learning in description logics, which provide bottom-up (and typically overly specific) least generalizations of the examples, this paper addresses learning in DLs using downward (and upward) refinement operators. Technically, we construct a complete and proper refinement operator for the ALER description logic (to avoid overfitting, we disallow disjunctions from the target DL). Although no minimal refinement operators exist for ALER, we show that we can achieve minimality of all refinement steps, except the ones that introduce the ⊥ concept. We additionally prove that complete refinement operators for ALER cannot be locally finite and suggest how this problem can be overcome by an MDL search heuristic. We also discuss the influence of the Open World Assumption (typically made in DLs) on example coverage.


Description Logic Conjunctive Normal Form Inductive Logic Programming Closed World Assumption Refinement Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Baader F., Küsters R. Least common subsumer computation w.r.t. cyclic ALNterminologies. In Proc. Int. Workshop on Description Logics (DL’98), Trento, Italy.Google Scholar
  2. 2.
    Baader F., R. Küsters, R. Molitor. Computing Least Common Subsumers in Description Logics with Existential Restrictions. Proc. IJCAI’99, pp. 96–101.Google Scholar
  3. 3.
    Badea Liviu, Stanciu Monica. Refinement Operators Can Be (Weakly) Perfect. Proc. ILP-99, LNAI 1631, Springer, 1999, pp. 21–32.Google Scholar
  4. 4.
    Badea Liviu. Perfect Refinement Operators Can Be Flexible. Proc. ECAI-2000.Google Scholar
  5. 5.
    Borgida A. On the relative Expressiveness of Description Logics and Predicate Logics. Artificial Intelligence, Vol. 82, Number 1–2, pp. 353–367, 1996.CrossRefMathSciNetGoogle Scholar
  6. 6.
    Buchheit M., F. Donini, A. Schaerf. Decidable reasoning in terminological knowledge representation systems. J. Artificial Intelligence Research, 1:109–138, 1993.zbMATHMathSciNetGoogle Scholar
  7. 7.
    Cohen W.W., A. Borgida, H. Hirsh. Computing least common subsumers in description logics. Proc. AAAI-92, San Jose, California, 1992.Google Scholar
  8. 8.
    Cohen W.W., H. Hirsh. Learning the CLASSIC description logic: Theoretical and experimental results. InPrinciples of Knowledge Representation and Reasoning: Proceedings of the Fourth International Conference, pp. 121–133, 1994.Google Scholar
  9. 9.
    Donini F.M., M. Lenzerini, D. Nardi, W. Nutt. The complexity of concept languages. Information and Computation, 134:1–58, 1997.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Donini F.M., M. Lenzerini, D. Nardi, A. Schaerf AL-log: integrating datalog and description logics. Journal of Intelligent Information Systems, 10:227–252, 1998.CrossRefGoogle Scholar
  11. 11.
    Donini F.M., M. Lenzerini, D. Nardi, A. Schaerf, W. Nutt. An epistemic operator for description logics. Artificial Intelligence, 100(1–2), 225–274, 1998.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Kietz J.U., Morik K. A Polynomial Approach to the Constructive Induction of Structural Knowledge. Machine Learning, Vol. 14, pp. 193–217, 1994.zbMATHCrossRefGoogle Scholar
  13. 13.
    Kietz J.U. Some lower-bounds for the computational complexity of Inductive Logic Programming. Proc. ECML’93, LNAI 667, Springer, 1993.Google Scholar
  14. 14.
    Levy A., M.C. Rousset. CARIN: A Representation Language Combining Horn Rules and Description Logics. Proc. ECAI-96, Budapest, 1996.Google Scholar
  15. 15.
    Levy A., M.C. Rousset. The Limits on Combining Horn Rules with Description Logics. Proc. AAAI-96, Portland, 1996.Google Scholar
  16. 16.
    Muggleton S. Inverse entailment and Progol. New Generation Computing Journal, 13:245–286, 1995.CrossRefGoogle Scholar
  17. 17.
    van der Laag P., S.H. Nienhuys-Cheng. A Note on Ideal Refinement Operators in Inductive Logic Programming. Proceedings ILP-94, 247–260.Google Scholar
  18. 18.
    van der Laag P., S.H. Nienhuys-Cheng. Existence and Nonexistence of Complete Refinement Operators. ECML-94, 307–322.Google Scholar
  19. 19.
    Nienhuys-Cheng S.H., de Wolf R. Foundations of Inductive Logic Programming. LNAI 1228, Springer Verlag, 1997.Google Scholar
  20. 20.
    Nienhuys-Cheng S.-H., W. Van Laer, J. Ramon, and L. De Raedt. Generalizing Refinement Operators to Learn Prenex Conjunctive Normal Forms. Proc. ILP-99, LNAI 1631, Springer, 1999, pp. 245–256.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Liviu Badea
    • 1
  • Shan -Hwei Nienhuys-Cheng
    • 2
  1. 1.AI Lab, National Institute for Research and Development in InformaticsBucharestRomania
  2. 2.Erasmus University RotterdamRotterdamThe Netherlands

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