Skip to main content
SpringerLink
Log in

A fuzzy extension for SHOIQ based on comparisons between degrees of membership

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

The current fuzzy extensions for description logics do not support representing and reasoning with complex fuzzy knowledge about comparisons between degrees of membership, which is very useful in practical applications. We investigate a novel approach of extending the description logic SHOIQ to SHOIQFC by annotating concepts and roles based on comparison expressions. SHOIQFC provides the ability to represent complex fuzzy knowledge, in addition to the expressive power of the fuzzy description logic FSHOIQ. The main contributions are a decidability proof for the consistency problem of SHOIQFC knowledge bases, as well as its tableau-based reasoning algorithm.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Baader F, Calvanese D, McGuinness D L, et al., eds. The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge: Cambridge University Press, 2003

    Google Scholar 

  2. Shi Z Z, Dong M K, Jiang Y C, et al. A logical foundation for the semantic Web. Sci China Ser E-Tech Sci, 2004, 34: 1123–1138

    Google Scholar 

  3. Zhao J, Boley H. Knowledge representation and reasoning in fuzzy description logics. In: Canadian Semantic Web: Technologies and Applications. Berlin/Heidelberg: Springer, 2010. 27–53

    Google Scholar 

  4. Straccia U. Reasoning within fuzzy description logics. J Artif Intell Res, 2001, 14: 137–166

    MathSciNet  MATH  Google Scholar 

  5. Hölldobler S, Störr H P, Khang T D. The fuzzy description logic ALCFH with hedge algebras as concept modifiers. Int J Adv Comput Intell Intell Inform, 2003, 7: 294–305

    Google Scholar 

  6. Sanchez D, Tettamanzi G. Generalizing quantification in fuzzy description logic. In: Proceedings of the 8th Fuzzy Days, Dortmund, Germany, 2004

    Google Scholar 

  7. Straccia U. Description logics with fuzzy concrete domains. In: Proceedings of the 21st Conference on Uncertainty in Artificial Intelligence, Edinburgh, UK, 2005

  8. Hajek P. Making fuzzy description logic more general. Fuzzy Sets Syst, 2005, 154: 1–15

    Article  MATH  Google Scholar 

  9. Stoilos G, Straccia U, Stamou G, et al. General concept inclusions in fuzzy description logics. In: Proceedings of the 17th International Conference on Artificial Intelligence, 2006. 457–461

    Google Scholar 

  10. Stoilos G, Stamou G, Pan J Z, et al. Reasoning with very expressive fuzzy description logics. J Artif Intell Res, 2007, 30: 273–320

    MathSciNet  MATH  Google Scholar 

  11. Bobillo F, Delgado M, Gmez-Romero J. A crisp representation for fuzzy SHOIN with fuzzy nominals and general concept inclusions. In: Proceedings of the 2nd International Workshop on Uncertainty Reasoning for the Semantic Web, Athens, Georgia, 2006

  12. Straccia U. A fuzzy description logic for the semantic web. In: Sanchez E, ed. Fuzzy Logic and the Semantic Web. Amsterdam: Elsevier B. V., 2006. 73–90

    Chapter  Google Scholar 

  13. Stoilos G, Stamou G, Pan J. Fuzzy extensions of OWL: Logical properties and reduction to fuzzy description logics. Int J Approx Reason, 2010, 51: 656–679

    Article  MathSciNet  MATH  Google Scholar 

  14. Bobillo F, Delgado M, Gomez-Romero J, et al. Fuzzy description logics under Godel semantics. Int J Approx Reason, 2009, 50: 494–514

    Article  MathSciNet  MATH  Google Scholar 

  15. Bobillo F, Bou F, Straccia U. On the failure of the finite model property in some fuzzy description logics. Fuzzy Sets Syst, 2011, 172: 1–12

    Article  MathSciNet  MATH  Google Scholar 

  16. Jiang Y C, Wang J, Deng P, et al. Reasoning within expressive fuzzy rough description logics. Fuzzy Sets Syst, 2009, 160: 3403–3424

    Article  MathSciNet  MATH  Google Scholar 

  17. Jiang Y C, Tang Y, Wang J, et al. Expressive fuzzy description logics over lattices. Knowl Based Syst, 2010, 23: 150–161

    Article  Google Scholar 

  18. Horrocks I, Sattler U. A tableau decision procedure for SHOIQ. J Automat Reason, 2007, 39: 245–429

    Article  MathSciNet  Google Scholar 

  19. Jiang Y C, Shi Z Z, Tang Y, et al. Fuzzy description logic for semantics representation of the semantic Web. J Softw, 2007, 18: 1257–1269

    Article  MathSciNet  MATH  Google Scholar 

  20. Kang D Z, Xu B W, Lu J J, et al. Reasoning within extended fuzzy description logic supporting terminological axiom restrictions. J Softw, 2007, 18: 1563–1572

    Article  MathSciNet  MATH  Google Scholar 

  21. Kang D Z, Xu B W, Lu J J, et al. Extended fuzzy description logics with comparisons between fuzzy membership degrees. J Softw, 2008, 19: 2498–2507

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computing Science and Technology, Nanjing University, Nanjing, 210093, China

    DaZhou Kang, BaoWen Xu & YanHui Li

  2. Jiangsu Institute of Software Quality, Nanjing, 210096, China

    BaoWen Xu

Authors
  1. DaZhou Kang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. BaoWen Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. YanHui Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to BaoWen Xu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kang, D., Xu, B. & Li, Y. A fuzzy extension for SHOIQ based on comparisons between degrees of membership. Sci. China Inf. Sci. 56, 1–11 (2013). https://doi.org/10.1007/s11432-011-4423-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-011-4423-4

Keywords

Search

Navigation