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Computing the Least Common Subsumer in the Description Logic \(\mathcal{EL}\) w.r.t. Terminological Cycles with Descriptive Semantics

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Conceptual Structures for Knowledge Creation and Communication (ICCS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2746))

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Abstract

Computing the least common subsumer (lcs) is one of the most prominent non-standard inference in description logics. Baader, Küsters, and Molitor have shown that the lcs of concept descriptions in the description logic \(\mathcal{EL}\) always exists and can be computed in polynomial time. In the present paper, we try to extend this result from concept descriptions to concepts defined in a (possibly cyclic) \(\mathcal{EL}\)-terminology interpreted with descriptive semantics, which is the usual first-order semantics for description logics. In this setting, the lcs need not exist. However, we are able to define possible candidates P k (k ≥ 0) for the lcs, and can show that the lcs exists iff one of these candidates is the lcs. Since each of these candidates is a common subsumer, they can also be used to approximate the lcs even if it does not exist. In addition, we give a sufficient condition for the lcs to exist, and show that, under this condition, it can be computed in polynomial time.

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References

  1. Baader, F.: Least common subsumers, most specific concepts, and role-valuemaps in a description logic with existential restrictions and terminological cycles. LTCS-Report 02-07, TU Dresden, Germany (2002), See, http://lat.inf.tudresden.de/research/reports.html ; A short version will appear in Proc. IJCAI 2003 (2003)

  2. Baader, F.: Terminological cycles in a description logic with existential restrictions. LTCS-Report 02-02, Dresden University of Technology, Germany (2002), See http://lat.inf.tu-dresden.de/research/reports.html ; Some of the results in this report will also be published in Proc. IJCAI 2003 (2003)

  3. Baader, F., Molitor, R.: Building and structuring description logic knowledge bases using least common subsumers and concept analysis. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS (LNAI), vol. 1867. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  4. Baader, F., Küsters, R.: Computing the least common subsumer and the most specific concept in the presence of cyclic \(\mathcal{ALN}\)-concept descriptions. In: Herzog, O. (ed.) KI 1998. LNCS (LNAI), 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. IJCAI 1999 (1999)

    Google Scholar 

  6. Cote, R.A., Rothwell, D.J., Palotay, J.L., Beckett, R.S., Brochu, L.: The systematized nomenclature of human and veterinary medicine. Technical report, SNOMED International. College of American Pathologists, Northfield, IL (1993)

    Google Scholar 

  7. Henzinger, M.R., Henzinger, T.A., Kopke, P.W.: Computing simulations on finite and infinite graphs. In: 36th Annual Symposium on Foundations of Computer Science (1995)

    Google Scholar 

  8. 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 

  9. Nebel, B.: Terminological cycles: Semantics and computational properties. In: Sowa, J.F. (ed.) Principles of Semantic Networks. Morgan Kaufmann, San Francisco (1991)

    Google Scholar 

  10. Spackman, K.A.: Managing clinical terminology hierarchies using algorithmic calculation of subsumption: Experience with SNOMED-RT. J. of the American Medical Informatics Association (2000); Fall Symposium Special Issue

    Google Scholar 

  11. Spackman, K.A.: Normal forms for description logic expressions of clinical concepts in SNOMED RT. J. of the American Medical Informatics Association (2001); Symposium Supplement

    Google Scholar 

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Author information

Authors and Affiliations

  1. Theoretical Computer Science, TU Dresden, D-01062, Dresden, Germany

    Franz Baader

Authors
  1. Franz Baader
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Editors and Affiliations

  1. Institute of Algebra, University of Technology, Dresden, Germany

    Bernhard Ganter

  2. Semantics Technology and Applications Research Laboratory (STARLab), Department of Computer Science, Vrije Universiteit Brussel, Pleinlaan 2, B-1050, Brussels 5, Belgium

    Aldo de Moor

  3. Institut für Algebra, Technische Universität Dresden, 01062, Dresden, Germany

    Wilfried Lex

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Baader, F. (2003). Computing the Least Common Subsumer in the Description Logic \(\mathcal{EL}\) w.r.t. Terminological Cycles with Descriptive Semantics. In: Ganter, B., de Moor, A., Lex, W. (eds) Conceptual Structures for Knowledge Creation and Communication. ICCS 2003. Lecture Notes in Computer Science(), vol 2746. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45091-7_8

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  • DOI: https://doi.org/10.1007/978-3-540-45091-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40576-4

  • Online ISBN: 978-3-540-45091-7

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