Paraconsistent Reasoning for OWL 2

  • Yue Ma
  • Pascal Hitzler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5837)


A four-valued description logic has been proposed to reason with description logic based inconsistent knowledge bases. This approach has a distinct advantage that it can be implemented by invoking classical reasoners to keep the same complexity as under the classical semantics. However, this approach has so far only been studied for the basic description logic \(\mathcal{ALC}\). In this paper, we further study how to extend the four-valued semantics to the more expressive description logic \(\mathcal{SROIQ}\) which underlies the forthcoming revision of the Web Ontology Language, OWL 2, and also investigate how it fares when adapted to tractable description logics including \(\mathcal{EL++}\), DL-Lite, and Horn-DLs. We define the four-valued semantics along the same lines as for \(\mathcal{ALC}\) and show that we can retain most of the desired properties.


Description Logic Classical Semantic Class Inclusion Inclusion Transformation Inclusion Axiom 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Belnap, N.D.: A useful four-valued logic. Modern uses of multiple-valued logics, 7–73 (1977)Google Scholar
  2. 2.
    Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Poggi, A., Rosati, R.: Linking data to ontologies: The description logic DL-Lite-A. In: Proc. of the 2nd Int. Workshop on OWL: Experiences and Directions (OWLED 2006). CEUR Electronic Workshop Proceedings, vol. 216 (2006),
  3. 3.
    Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Tractable reasoning and efficient query answering in description logics: The DL-Lite family. J. Autom. Reasoning 39(3), 385–429 (2007)zbMATHCrossRefGoogle Scholar
  4. 4.
    Grosof, B.N., Horrocks, I., Volz, R., Decker, S.: Description logic programs: combining logic programs with description logic. In: Proceedings of the 12th International World Wide Web Conference (WWW 2003), Budapest, Hungary, pp. 48–57. ACM, New York (2003)Google Scholar
  5. 5.
    Haase, P., van Harmelen, F., Huang, Z., Stuckenschmidt, H., Sure, Y.: A Framework for Handling Inconsistency in Changing Ontologies. In: Gil, Y., Motta, E., Benjamins, V.R., Musen, M.A. (eds.) ISWC 2005. LNCS, vol. 3729, pp. 353–367. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Hitzler, P., Krötzsch, M., Rudolph, S.: Foundations of Semantic Web Technologies. Chapman & Hall/CRC (2009)Google Scholar
  7. 7.
    Horrocks, I., Patel-Schneider, P.F., van Harmelen, F.: From \(\mathcal{SHIQ}\) and RDF to OWL: The making of a web ontology language. Journal of Web Semantics 1(1), 7–26 (2003)Google Scholar
  8. 8.
    Huang, Z., van Harmelen, F., ten Teije, A.: Reasoning with inconsistent ontologies. In: Kaelbling, L.P., Saffiotti, A. (eds.) IJCAI, pp. 454–459. Professional Book Center (2005)Google Scholar
  9. 9.
    Hustadt, U., Motik, B., Sattler, U.: Data Complexity of Reasoning in Very Expressive Description Logics. In: Proc. of the 19th Int. Joint Conference on Artificial Intelligence (IJCAI 2005), Edinburgh, UK, July 30 – August 5, pp. 466–471. Morgan Kaufmann Publishers, San Francisco (2005)Google Scholar
  10. 10.
    Ji, Q., Haase, P., Qi, G., Hitzler, P., Stadtmüller, S.: Radon - repair and diagnosis in ontology networks. In: Aroyo, L., Traverso, P., Ciravegna, F., Cimiano, P., Heath, T., Hyvönen, E., Mizoguchi, R., Oren, E., Sabou, M., Simperl, E.P.B. (eds.) ESWC 2009. LNCS, vol. 5554, pp. 863–867. Springer, Heidelberg (2009)Google Scholar
  11. 11.
    Krötzsch, M., Rudolph, S., Hitzler, P.: Complexity boundaries for Horn description logics. In: AAAI, pp. 452–457. AAAI Press, Menlo Park (2007)Google Scholar
  12. 12.
    Krötzsch, M., Rudolph, S., Hitzler, P.: ELP: Tractable rules for OWL 2. In: Sheth, A.P., Staab, S., Dean, M., Paolucci, M., Maynard, D., Finin, T., Thirunarayan, K. (eds.) ISWC 2008. LNCS, vol. 5318, pp. 649–664. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Ma, Y., Hitzler, P., Lin, Z.: Algorithms for paraconsistent reasoning with OWL. In: Franconi, E., Kifer, M., May, W. (eds.) ESWC 2007. LNCS, vol. 4519, pp. 399–413. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Ma, Y., Hitzler, P., Lin, Z.: Paraconsistent reasoning for expressive and tractable description logics. In: Baader, F., Lutz, C., Motik, B. (eds.) Proceedings of the 21st International Workshop on Description Logics, DL 2008, Dresden, Germany, May 2008. CEUR Workshop Proceedings, vol. 353 (2008)Google Scholar
  15. 15.
    Ma, Y., Lin, Z., Lin, Z.: Inferring with inconsistent OWL DL ontology: A multi-valued logic approach. In: Grust, T., Höpfner, H., Illarramendi, A., Jablonski, S., Mesiti, M., Müller, S., Patranjan, P.-L., Sattler, K.-U., Spiliopoulou, M., Wijsen, J. (eds.) EDBT 2006. LNCS, vol. 4254, pp. 535–553. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Ma, Y., Qi, G., Hitzler, P., Lin, Z.: Measuring inconsistency for description logics based on paraconsistent semantics. In: Mellouli, K. (ed.) ECSQARU 2007. LNCS (LNAI), vol. 4724, pp. 30–41. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  17. 17.
    McGuinness, D.L., van Harmelen, F. (eds.): OWL Web Ontology Language Overview. W3C Recommendation, February 10 (2004),
  18. 18.
    Motik, B.: Reasoning in description logics using resolution and deductive databases. PhD thesis, University of Karlsruhe, Germany (2006)Google Scholar
  19. 19.
    Motik, B., Grau, B.C., Horrocks, I., Wu, Z., Fokoue, A., Lutz, C. (eds.): OWL 2 Web Ontology Language: Profiles. W3C Candidate Recommendation, June 11 (2009),
  20. 20.
    Patel-Schneider, P.F.: A four-valued semantics for terminological logics. Artificial Intelligence 38, 319–351 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Schlobach, S., Cornet, R.: Non-standard reasoning services for the debugging of description logic terminologies. In: Gottlob, G., Walsh, T. (eds.) IJCAI, pp. 355–362. Morgan Kaufmann, San Francisco (2003)Google Scholar
  22. 22.
    Staab, S., Studer, R.: Handbook on Ontologies, 2nd edn. International Handbooks on Information Systems. Springer, Heidelberg (2009)Google Scholar
  23. 23.
    Straccia, U.: A sequent calculus for reasoning in four-valued description logics. In: Galmiche, D. (ed.) TABLEAUX 1997. LNCS, vol. 1227, pp. 343–357. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  24. 24.
    W3C OWL Working Group. OWL 2 Web Ontology Language: Document Overview (2009),

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Yue Ma
    • 1
  • Pascal Hitzler
    • 2
  1. 1.Institute LIPNUniversité Paris-Nord (LIPN - UMR 7030)France
  2. 2.Institute AIFBUniversität KarlsruheGermany

Personalised recommendations