Forgetting Concept and Role Symbols in \(\mathcal{ALCH}\)-Ontologies

  • Patrick Koopmann
  • Renate A. Schmidt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8312)

Abstract

We develop a resolution-based method for forgetting concept and role symbols in \(\mathcal{ALCH}\) ontologies, or for computing uniform interpolants in \(\mathcal{ALCH}\). Uniform interpolants use only a restricted set of symbols, while preserving logical consequences of the original ontology involving these symbols. While recent work towards practical methods for uniform interpolation in expressive description logics limits attention to forgetting concept symbols, we believe most applications would benefit from the possibility to forget both role and concept symbols. We focus on the description logic \(\mathcal{ALCH}\), which allows for the formalisation of role hierarchies. Our approach is based on a recently developed resolution-based calculus for forgetting concept symbols in \(\mathcal{ALC}\) ontologies, which we extend by redundancy elimination techniques to make it practical for larger ontologies. Experiments on \(\mathcal{ALCH}\) fragments of real life ontologies suggest that our method is applicable in a lot of real-life applications.

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References

  1. 1.
    Ackermann, W.: Untersuchungen über das Eliminationsproblem der mathematischen Logik. Mathematische Annalen 110(1), 390–413 (1935)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Calvanese, D., Giacomo, G.D., Lenzerini, M.: Reasoning in expressive description logics with fixpoints based on automata on infinite trees. In: Proc. IJCAI 1999, pp. 84–89. Morgan Kaufmann (1999)Google Scholar
  3. 3.
    Gabbay, D., Ohlbach, H.J.: Quantifier elimination in second-order predicate logic. In: Proc. KR 1992, pp. 425–435. Morgan Kaufmann (1992)Google Scholar
  4. 4.
    Gabbay, D.M., Schmidt, R.A., Szalas, A.: Second Order Quantifier Elimination: Foundations, Computational Aspects and Applications. College Publ. (2008)Google Scholar
  5. 5.
    Grau, B.C., Motik, B.: Reasoning over ontologies with hidden content: The import-by-query approach. J. Artificial Intelligence Research 45, 197–255 (2012)MATHGoogle Scholar
  6. 6.
    Herzig, A., Mengin, J.: Uniform interpolation by resolution in modal logic. In: Hölldobler, S., Lutz, C., Wansing, H. (eds.) JELIA 2008. LNCS (LNAI), vol. 5293, pp. 219–231. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Horridge, M., Parsia, B., Sattler, U.: The state of bio-medical ontologies. Bio-Ontologies 2011 (2011)Google Scholar
  8. 8.
    Konev, B., Walther, D., Wolter, F.: Forgetting and uniform interpolation in large-scale description logic terminologies. In: Proc. IJCAI 2009, pp. 830–835 (2009)Google Scholar
  9. 9.
    Koopmann, P., Schmidt, R.A.: Forgetting concept and role symbols in \(\mathcal{ALCH}\)-ontologies. Technical Report (2013), http://www.cs.man.ac.uk/~koopmanp
  10. 10.
    Koopmann, P., Schmidt, R.A.: Implementation and evaluation of forgetting in \(\mathcal{ALC}\)-ontologies. In: Proc. WoMO 2013. CEUR-WS.org (2013)Google Scholar
  11. 11.
    Koopmann, P., Schmidt, R.A.: Uniform interpolation of \(\mathcal{ALC}\)-ontologies using fixpoints. In: Fontaine, P., Ringeissen, C., Schmidt, R.A. (eds.) FroCoS 2013. LNCS (LNAI), vol. 8152, pp. 87–102. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  12. 12.
    Ludwig, M., Konev, B.: Towards practical uniform interpolation and forgetting for \(\mathcal{ALC}\) TBoxes. In: Proc. DL 2013, pp. 377–389. CEUR-WS.org (2013)Google Scholar
  13. 13.
    Lutz, C., Seylan, I., Wolter, F.: An automata-theoretic approach to uniform interpolation and approximation in the description logic \(\mathcal{EL}\). In: Proc. KR 2012. AAAI Press (2012)Google Scholar
  14. 14.
    Lutz, C., Wolter, F.: Foundations for uniform interpolation and forgetting in expressive description logics. In: Proc. IJCAI 2011, pp. 989–995. AAAI Press (2011)Google Scholar
  15. 15.
    Nikitina, N.: Forgetting in general \(\mathcal{EL}\) terminologies. In: Proc. DL 2011. CEUR-WS.org. (2011)Google Scholar
  16. 16.
    Nonnengart, A., Szałas, A.: A fixpoint approach to second-order quantifier elimination with applications to correspondence theory. In: Logic at Work, pp. 307–328. Springer (1999)Google Scholar
  17. 17.
    Sattler, U., Schneider, T., Zakharyaschev, M.: Which kind of module should I extract? In: Proc. DL 2009. CEUR-WS.org (2009)Google Scholar
  18. 18.
    Shearer, R., Motik, B., Horrocks, I.: HermiT: A highly-efficient OWL reasoner. In: Proc. OWLED 2008, pp. 26–27. CEUR-WS.org (2008)Google Scholar
  19. 19.
    Szałas, A.: Second-order reasoning in description logics. J. Appl. Non-Classical Logics 16(3-4), 517–530 (2006)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Wang, K., Wang, Z., Topor, R., Pan, J.Z., Antoniou, G.: Eliminating concepts and roles from ontologies in expressive descriptive logics. Computational Intelligence (2012)Google Scholar
  21. 21.
    Wang, Z., Wang, K., Topor, R., Zhang, X.: Tableau-based forgetting in \(\mathcal{ALC}\) ontologies. In: Proc. ECAI 2010, pp. 47–52. IOS Press (2010)Google Scholar
  22. 22.
    Wang, Z., Wang, K., Topor, R.W., Pan, J.Z.: Forgetting for knowledge bases in DL-Lite. Ann. Math. Artif. Intell. 58(1-2), 117–151 (2010)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Patrick Koopmann
    • 1
  • Renate A. Schmidt
    • 1
  1. 1.The University of ManchesterUK

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