Algorithms for Paraconsistent Reasoning with OWL

  • Yue Ma
  • Pascal Hitzler
  • Zuoquan Lin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4519)


In an open, constantly changing and collaborative environment like the forthcoming Semantic Web, it is reasonable to expect that knowledge sources will contain noise and inaccuracies. Practical reasoning techniques for ontologies therefore will have to be tolerant to this kind of data, including the ability to handle inconsistencies in a meaningful way. For this purpose, we employ paraconsistent reasoning based on four-valued logic, which is a classical method for dealing with inconsistencies in knowledge bases. Its transfer to OWL DL, however, necessitates the making of fundamental design choices in dealing with class inclusion, which has resulted in differing proposals for paraconsistent description logics in the literature. In this paper, we build on one of the more general approaches which due to its flexibility appears to be most promising for further investigations. We present two algorithms suitable for implementation, one based on a preprocessing before invoking a classical OWL reasoner, the other based on a modification of the KAON2 transformation algorithms. We also report on our implementation, called ParOWL.


Description Logic Contradictory Information Atomic Concept Material Inclusion Class Inclusion 
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.


  1. 1.
    Hayes, P., Horrocks, I., Patel-Schneider, P.F.: OWL Web Ontology Language Semantics and Abstract Syntax. W3C Recommendation (10 February 2004)Google Scholar
  2. 2.
    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
  3. 3.
    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
  4. 4.
    Patel-Schneider, P.F.: A four-valued semantics for terminological logics. Artificial Intelligence 38, 319–351 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    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
  6. 6.
    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
  7. 7.
    Belnap, N.D.: A useful four-valued logic. In: Modern uses of multiple-valued logics, pp. 7–73 (1977)Google Scholar
  8. 8.
    Arieli, O., Avron, A.: The value of the four values. Artif. Intell. 102, 97–141 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Motik, B.: Reasoning in description logics using resolution and deductive databases. PhD theis, University Karlsruhe, Germany (2006)Google Scholar
  10. 10.
    Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  11. 11.
    Horrocks, I., Patel-Schneider, P.F.: Reducing OWL entailment to description logic satisfiability. J. Web Sem. 1, 345–357 (2004)Google Scholar
  12. 12.
    Arieli, O., Avron, A.: Reasoning with logical bilattices. Journal of Logic, Language and Information 5, 25–63 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Kamide, N.: Foundations of paraconsistent resolution. Fundamenta Informaticae 71, 419–441 (2006)zbMATHMathSciNetGoogle Scholar
  14. 14.
    Fitting, M.: First-Order Logic and Automated Theorem Proving, 2nd edn. Texts in Computer Science. Springer, Heidelberg (1996)zbMATHGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Yue Ma
    • 1
    • 2
  • Pascal Hitzler
    • 2
  • Zuoquan Lin
    • 1
  1. 1.Department of Information Science, Peking UniversityChina
  2. 2.AIFB, Universität KarlsruheGermany

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