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Complexity of Conservative Extensions and Inseparability in the Description Logic \({\mathcal {EL}}^\lnot \)

  • Yuming ShenEmail author
  • Ju Wang
Conference paper
  • 590 Downloads
Part of the Communications in Computer and Information Science book series (CCIS, volume 480)

Abstract

The notations of conservative extensions and inseparability are suggested as the effective tool for comparing, merging, and modularizing description logic ontologies. It has been shown that the complexity of conservative extensions for expressive descriptions logics such as \({\mathcal {ALC}}\) and \({\mathcal {ALCQI}}\) are 2ExpTime-complete and ExpTime-complete for \({\mathcal {EL}}\) itself. However, the problem of the complexity of conservative extensions in a few extensions of \({\mathcal {EL}}\) which used in applications has hardly been addressed. The aim of this paper is to study the complexity of conservative extensions and inseparability in the description logic \({\mathcal {EL}}^\lnot ,\) which is the extension of \({\mathcal {EL}}\) with atomic concept negation. By adding many countable new concept names which correspond to the complex negative concepts, we establish a translation from \({\mathcal {ALC}}\) to \({\mathcal {EL}}^\lnot \) and reduce the problem of conservative extensions in \({\mathcal {ALC}}\) to the case of \({\mathcal {EL}}^\lnot .\) Since deciding conservative extensions and inseparability in \({\mathcal {ALC}}\) is 2ExpTime-complete, we get 2ExpTime-completeness of both inseparability and conservative extensions in \({\mathcal {EL}}^\lnot .\)

Keywords

Ontology Conservative extension Computational complexity 

Notes

Acknowledgments

The work was supported by the National Natural Science Foundation of China under Grant Nos.60573010, 61103169.

References

  1. 1.
    Baader, F., Nutt, W.: Basic description logics. In: Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Scheider, P.F. (eds.) The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)Google Scholar
  2. 2.
    Baader, F., Brandt, S., Lutz, C.: Pushing the \({\cal EL}\) envelope. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI’05), pp. 364–369. AAAI Press (2005)Google Scholar
  3. 3.
    Diaconescu, R., Goguen, J., Stefaneas, P.: Logical support for modularisation. In: Huet, G., Plotkin, G. (eds.) Logical Environments. Cambridge University Press, New York (1993)Google Scholar
  4. 4.
    Fara, M., Williamson, T.: Counterparts and actuality. Mind 114, 1–30 (2005)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Fink, M.: Equivalences in answer-set programming by countermodels in the logic of here-and-there. In: Garcia de la Banda, M., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 99–113. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Forbes, G.: Canonical counterpart theory. Analysis 42, 33–37 (1982)CrossRefGoogle Scholar
  7. 7.
    Ghilardi, S., Lutz, C., Wolter, F.: Did I damage my ontology? a case for conservative extensions in description logics. In: Proceedings of KR06, pp. 187–197. AAAI Press (2006)Google Scholar
  8. 8.
    Grau, B.C., Horrocks, I., Kazakov, Y., Sattler, U.: Modular reuse of ontologies: theory and practice. J. Artif. Intell. Res. 31, 273–318 (2008)zbMATHGoogle Scholar
  9. 9.
    Konev, B., Lutz, C., Walther, D., Wolter, F.: Semantic modularity and module extraction in description logics. In: Proceedings of ECAI’08, pp. 55–59 (2008)Google Scholar
  10. 10.
    Kontchakov, R., Wolter, F., Zakharyaschev, M.: Logic-based ontology comparison and module extraction with an application to DL-Lite. J. Artif. Intell. 174, 1093–1141 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Lewis, D.: Counterpart theory and quantified modal logic. J. Philos. 65, 113–126 (1968)CrossRefGoogle Scholar
  12. 12.
    Lutz, C., Walther, D., Wolter, F.: Conservative extensions in expressive description logics. In: Proceedings of IJCAI07, pp. 453–458. AAAI Press (2007)Google Scholar
  13. 13.
    Lutz, C., Wolter, F.: Deciding inseparability and conservative extensions in the description logic EL. J. Symbolic Comput. 45, 194–228 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Maibaum, T.: Conservative extensions, interpretations between theories and all that!. In: Bidoit, M., Dauchet, M. (eds.) CAAP, FASE and TAPSOFT 1997. LNCS, vol. 1214, pp. 40–66. Springer, Heidelberg (1997)Google Scholar
  15. 15.
    Pearce, D., Valverde, A.: Synonymous theories in answer set programming and equilibrium logic. In: Proceedings of the 16th European Conference on Artificial Intelligence (ECAI 2004), pp. 388–392 (2004)Google Scholar
  16. 16.
    Sioutos, N., de Coronado, S., Haber, M., Hartel, F., Shaiu, W., Wright, L.: NCI thesaurus: a semantic model integrating cancer-related clinical and molecular information. J. Biomed. Inform. 40, 30–43 (2006)CrossRefGoogle Scholar
  17. 17.
    Spackman K. Managing clinical terminology hierarchies using algorithmic calculation of subsumption: Experience with SNOMED-RT. (2000) Fall Symposium Special IssueGoogle Scholar
  18. 18.
    Blake, J.A., et al.: The gene ontology: enhancements for 2011. Nucleic Acids Res. 40, 559–564 (2012)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Shen, Y., Ma, Y., Cao, C., Sui, Y., Wang, J.: Logical properties on translations between logics. Chin. J. Comput. 32, 2091–2098 (2009)CrossRefMathSciNetGoogle Scholar
  20. 20.
    Shen, Y., Sui, Y., Wang, J.: On the translation from quantified modal logic into the counterpart theory revisited. In: Xiong, H., Lee, W.B. (eds.) KSEM 2011. LNCS, vol. 7091, pp. 377–386. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  21. 21.
    Shen, Y., Ma, Y., Cao, C., Sui, Y., Wang, J.: Faithful and full translations between logics. Ruan Jian Xue Bao/J. Softw. 24, 1626–1637 (2013). (in Chinese)MathSciNetGoogle Scholar
  22. 22.
    Ramachandran, M.: An alternative translation scheme for counterpart theory. Analysis 49, 131–141 (1989)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Cisco School of InformaticsGuangdong University of Foreign StudiesGuangzhouChina
  2. 2.School of Computer Science and Information EngineeringGuangxi Normal UniversityGuilinChina

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