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The Logical Difference Problem for Description Logic Terminologies

  • Boris Konev
  • Dirk Walther
  • Frank Wolter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5195)

Abstract

We consider the problem of computing the logical difference between distinct versions of description logic terminologies. For the lightweight description logic \(\mathcal{ EL}\), we present a tractable algorithm which, given two terminologies and a signature, outputs a set of concepts, which can be regarded as the logical difference between the two terminologies. As a consequence, the algorithm can also decide whether they imply the same concept implications in the signature. A prototype implementation CEX of this algorithm is presented and experimental results based on distinct versions of \(\textsc{Snomed ct}\), the Systematized Nomenclature of Medicine, Clinical Terms, are discussed. Finally, results regarding the relation to uniform interpolants and possible extensions to more expressive description logics are presented.

Keywords

Modal Logic Description Logic Class Hierarchy Conservative Extension Primitive Concept 
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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References

  1. 1.
    Baader, F.: Terminological cycles in a description logic with existential restrictions. In: Proceedings of IJCAI 2003, pp. 325–330. Morgan Kaufmann, San Francisco (2003); Long version available as LTCS Report 02-02Google Scholar
  2. 2.
    Baader, F., Lutz, C., Suntisrivaraporn, B.: CEL—a polynomial-time reasoner for life science ontologies. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 287–291. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Baader, F., Peñaloza, R., Suntisrivaraporn, B.: Pinpointing in the description logic \(\mathcal{EL}^+\). In: Hertzberg, J., Beetz, M., Englert, R. (eds.) KI 2007. LNCS (LNAI), vol. 4667, pp. 52–67. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
  5. 5.
    Flögel, A., Büning, H.K., Lettmann, T.: On the restricted equivalence of subclasses of propositional logic. ITA 27(4), 327–340 (1993)zbMATHGoogle Scholar
  6. 6.
    Ghilardi, S., Lutz, C., Wolter, F.: Did I damage my ontology? a case for conservative extensions in description logics. In: Proceedings of KR 2006, pp. 187–197. AAAI Press, Menlo Park (2006)Google Scholar
  7. 7.
    Ghilardi, S., Lutz, C., Wolter, F., Zakharyaschev, M.: Conservative extensions in modal logics. In: Proceedings of AiML-6, pp. 187–207. College Publications (2006)Google Scholar
  8. 8.
    Ghilardi, S., Zawadowski, M.: Undefinability of propositional quantifiers in the modal system S4. Studia Logica 55(2), 259–271 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Grau, B.C., Horrocks, I., Kazakov, Y., Sattler, U.: Just the right amount: extracting modules from ontologies. In: Proceedings of WWW 2007, pp. 717–726. ACM Press, New York (2007)CrossRefGoogle Scholar
  10. 10.
    Hofmann, M.: Proof-theoretic approach to description logic. In: Proceedings of LICS 2005, pp. 229–237. IEEE Computer Society Press, Los Alamitos (2005)Google Scholar
  11. 11.
    Konev, B., Walther, D., Wolter, F.: The logical difference problem for description logic terminologies (manuscript 2008), http://www.csc.liv.ac.uk/~frank/publ/publ.html
  12. 12.
    Lutz, C., Walther, D., Wolter, F.: Conservative extensions in expressive description logics. In: Proceedings of IJCAI 2007, pp. 453–458. AAAI Press, Menlo Park (2007)Google Scholar
  13. 13.
    Lutz, C., Wolter, F.: Conservative extensions in the lightweight description logic \(\mathcal{EL}\). In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 84–99. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Noy, N.F., Musen, M.: Promptdiff: A fixed-point algorithm for comparing ontology versions. In: Proceedings of AAAI 2002, pp. 744–750. AAAI Press, Menlo Park (2002)Google Scholar
  15. 15.
    Pitts, A.: On an interpretation of second-order quantification in first-order intuitionistic propositional logic. Journal of Symbolic Logic 57(1), 33–52 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Sofronie-Stokkermans, V.: Interpolation in local theory extensions. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 235–250. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  17. 17.
    Spackman, K.: Managing clinical terminology hierarchies using algorithmic calculation of subsumption: Experience with SNOMED-RT. In: JAMIA, Fall Symposium Special Issue (2000)Google Scholar
  18. 18.
    Visser, A.: Uniform interpolation and layered bisimulation. In: Gödel 1996 (Brno, 1996). Lecture Notes Logic, vol. 6, pp. 139–164. Springer, Heidelberg (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Boris Konev
    • 1
  • Dirk Walther
    • 1
  • Frank Wolter
    • 1
  1. 1.University of LiverpoolLiverpoolUK

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