Skip to main content

Computing the Least Common Subsumer w.r.t. a Background Terminology

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3229))

Abstract

Methods for computing the least common subsumer (lcs) are usually restricted to rather inexpressive Description Logics (DLs) whereas existing knowledge bases are written in very expressive DLs. In order to allow the user to re-use concepts defined in such terminologies and still support the definition of new concepts by computing the lcs, we extend the notion of the lcs of concept descriptions to the notion of the lcs w.r.t. a background terminology. We will both show a theoretical result on the existence of the least common subsumer in this setting, and describe a practical approach (based on a method from formal concept analysis) for computing good common subsumers, which may, however, not be the least ones.

This work has been supported by DFG under grants GRK 334/3 and BA 1122/4-3.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baader, F.: Computing a minimal representation of the subsumption lattice of all conjunctions of concepts defined in a terminology. In: Ellis, G., Levinson, R.A., Fall, A., Dahl, V. (eds.) Knowledge Retrieval, Use and Storage for Efficiency: Proc. of the 1st Int. KRUSE Symposium (1995)

    Google Scholar 

  2. Baader, F.: Least common subsumers and most specific concepts in a description logic with existential restrictions and terminological cycles. In: Gottlob, G., Walsh, T. (eds.) Proc. of the 18th Int. Joint Conf. on AI., Morgan Kaufm., San Francisco (2003)

    Google Scholar 

  3. Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  4. Baader, F., Küsters, R.: Computing the least common subsumer and the most specific concept in the presence of cyclic ALN-concept descriptions. In: Herzog, O. (ed.) KI 1998. LNCS, vol. 1504, Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  5. Baader, F., Küsters, R., Molitor, R.: Computing least common subsumers in description logics with existential restrictions. In: Proc. of the 16th Int. Joint Conf. on AI, IJCAI 1999 (1999)

    Google Scholar 

  6. Baader, F., Küsters, R., Molitor, R.: Rewriting concepts using terminologies. In: Proc. of the 7th Int. Conf. on Principles of Knowledge Repr. and Reasoning, KR’2000 (2000)

    Google Scholar 

  7. Baader, F., Molitor, R.: Building and structuring description logic knowledge bases using least common subsumers and concept analysis. In: Ganter, B., Mineau, G. (eds.) Conceptual Structures: Logical, Linguistic, and Computational Issues – Proc. of the 8th Int. Conf. on Conceptual Structures (ICCS 2000), Springer, Heidelberg (2000)

    Google Scholar 

  8. Baader, F., Sertkaya, B.: Applying formal concept analysis to description logics. In: Eklund, P. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  9. Baader, F., Sertkaya, B., Turhan, A.-Y.: Computing the least common subsumer w.r.t. a background terminology. In: Proc. of the 2004 Int. Workshop on Description Logics, DL 2004 (2004)

    Google Scholar 

  10. Brandt, S., Küsters, R., Turhan, A.-Y.: Approximation and difference in description logics. In: Fensel, D., Giunchiglia, F., McGuiness, D., Williams, M.-A. (eds.) Proc. of the 8th Int. Conf. on Principles of Knowledge Repr. and Reasoning (KR2002), Morgan Kaufm., San Francisco (2002)

    Google Scholar 

  11. Brandt, S., Turhan, A.-Y., Küsters, R.: Extensions of non-standard inferences for description logics with transitive roles. In: Y. Vardi, M., Voronkov, A. (eds.) LPAR 2003. LNCS (LNAI), vol. 2850, Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  12. Cohen, W., Hirsh, H.: Learning the CLASSIC description logics: Theoretical and experimental results. In: Doyle, J., Sandewall, E., Torasso, P. (eds.) Proc. of the 4th Int. Conf. on Principles of Knowledge Repr. and Reasoning, KR 1994 (1994)

    Google Scholar 

  13. Frazier, M., Pitt, L.: CLASSIC learning. Machine Learning 25, 151–193 (1996)

    Article  MATH  Google Scholar 

  14. Ganter, B.: Finding all closed sets: A general approach. Order 8, 283–290 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  15. Ganter, B.: Attribute exploration with background knowledge. Theoretical Computer Science 217(2), 215–233 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  16. Ganter, B., Krause, R.: Pseudo models and propositional Horn inference. Technical Report MATH-AL-15-1999, Inst. f. Algebra, TU Dresden, Germany (1999)

    Google Scholar 

  17. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Berlin (1999)

    MATH  Google Scholar 

  18. Haarslev, V., Möller, R.: High performance reasoning with very large knowledge bases: A practical case study. In: Proc. of the 17th Int. Joint Conf. on AI, IJCAI 2001 (2001)

    Google Scholar 

  19. Haarslev, V., Möller, R.: RACER system description. In: Proc. of the Int. Joint Conf. on Automated Reasoning, IJCAR 2001 (2001)

    Google Scholar 

  20. Horrocks, I.: Using an expressive description logic: FaCT or fiction? In: Proc. of the 6th Int. Conf. on Principles of Knowledge Repr. and Reasoning, KR 1998 (1998)

    Google Scholar 

  21. Küsters, R.: Non-standard Inferences in Description Logics. LNCS (LNAI). Springer, Heidelberg (2001)

    Book  MATH  Google Scholar 

  22. Küsters, R., Borgida, A.: What’s in an attribute? Consequences for the least common subsumer. J. of AI. Research 14, 167–203 (2001)

    Google Scholar 

  23. Küsters, R., Molitor, R.: Approximating most specific concepts in description logics with existential restrictions. In: Baader, F., Brewka, G., Eiter, T. (eds.) KI 2001. LNCS (LNAI), vol. 2174, p. 33. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  24. Küsters, R., Molitor, R.: Computing least common subsumers in ALEN. In: Proc. of the 17th Int. Joint Conf. on AI, IJCAI 2001 (2001)

    Google Scholar 

  25. Rector, A., Horrocks, I.: Experience building a large, re-uSABLE medical ontology using a description logic with transitivity and concept inclusions. In: Proc. of the Workshop on Ontological Engineering, AAAI Spring Symposium (AAAI 1997), Stanford, CA, AAAI Press, Menlo Park (1997)

    Google Scholar 

  26. Schultz, S., Hahn, U.: Knowledge engineering by large-scale knowledge reuse— experience from the medical domain. In: Cohn, G., Giunchiglia, F., Selman, B. (eds.) Proc. of the 7th Int. Conf. on Principles of Knowledge Repr. and Reasoning (KR’2000), Morgan Kaufm., San Francisco (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Baader, F., Sertkaya, B., Turhan, AY. (2004). Computing the Least Common Subsumer w.r.t. a Background Terminology. In: Alferes, J.J., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2004. Lecture Notes in Computer Science(), vol 3229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30227-8_34

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30227-8_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23242-1

  • Online ISBN: 978-3-540-30227-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics