Laconic and Precise Justifications in OWL

  • Matthew Horridge
  • Bijan Parsia
  • Ulrike Sattler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5318)

Abstract

A justification for an entailment in an OWL ontology is a minimal subset of the ontology that is sufficient for that entailment to hold. Since justifications respect the syntactic form of axioms in an ontology, they are usually neither syntactically nor semantically minimal. This paper presents two new subclasses of justifications—laconic justifications and precise justifications. Laconic justifications only consist of axioms that do not contain any superfluous “parts”. Precise justifications can be derived from laconic justifications and are characterised by the fact that they consist of flat, small axioms, which facilitate the generation of semantically minimal repairs. Formal definitions for both types of justification are presented. In contrast to previous work in this area, these definitions make it clear as to what exactly “parts of axioms” are. In order to demonstrate the practicability of computing laconic, and hence precise justifications, an algorithm is provided and results from an empirical evaluation carried out on several published ontologies are presented. The evaluation showed that laconic/precise justifications can be computed in a reasonable time for entailments in a range of ontologies that vary in size and complexity. It was found that in half of the ontologies sampled there were entailments that had more laconic/precise justifications than regular justifications. More surprisingly it was observed that for some ontologies there were fewer laconic justifications than regular justifications.

References

  1. 1.
    Kalyanpur, A.: Debugging and Repair of OWL Ontologies. PhD thesis, The Graduate School of the University of Maryland (2006)Google Scholar
  2. 2.
    Kalyanpur, A., Parsia, B., Hendler, J.: A tool for working with web ontologies. International Journal on Semantic Web and Information Systems 1 (2005)Google Scholar
  3. 3.
    Horridge, M., Tsarkov, D., Redmond, T.: Supporting early adoption of owl 1.1 with protégé-owl and fact++. In: OWL: Experiences and Directions (2006)Google Scholar
  4. 4.
    Lam, S.C.J.: Methods for Resolving Inconsistencie. In Ontologies. PhD thesis, Department of Computer Science, Aberdeen (2007)Google Scholar
  5. 5.
    Kalyanpur, A., Parsia, B., Grau, B.C.: Beyond asserted axioms: Fine-grain justifications for OWL-DL entailments. In: Proc. of DL (2006)Google Scholar
  6. 6.
    Horrocks, I., Patel-Schneider, P.F., van Harmelen, F.: From \(\mathcal{SHIQ}\) and RDF to OWL: The making of a web ontology language. J. of Web Semantics 1(1), 7–26 (2003)CrossRefGoogle Scholar
  7. 7.
    Baader, F., Hollunder, B.: Embedding defaults into terminological representation systems. J. of Automated Reasoning 14, 149–180 (1995)CrossRefMATHGoogle Scholar
  8. 8.
    Schlobach, S., Cornet, R.: Non-standard reasoning services for the debugging of description logic terminologies. In: Proc. of IJCAI (2003)Google Scholar
  9. 9.
    Meyer, T., Lee, K., Booth, R., Pan, J.Z.: Finding maximally satisfiable terminologies for the description logic \(\mathcal{ALC}\). In: Proc. of AAAI (2006)Google Scholar
  10. 10.
    Baader, F., Hollunder, B.: Embedding defaults into terminological knowledge representation formalisms. In: Proc. of KR 1992, pp. 306–317. Morgan Kaufmann, San Francisco (1992)Google Scholar
  11. 11.
    Deng, X., Haarslev, V., Shiri, N.: Measuring inconsistencies in ontologies. In: Franconi, E., Kifer, M., May, W. (eds.) ESWC 2007. LNCS, vol. 4519, Springer, Heidelberg (2007)Google Scholar
  12. 12.
    Baader, F., Peñaloza, R., Suntisrivaraporn, B.: Pinpointing in the description logic el. In: Hertzberg, J., Beetz, M., Englert, R. (eds.) KI 2007. LNCS (LNAI), vol. 4667, pp. 52–67. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Plaisted, D.A., Greenbaum, S.: A structure-preserving clause form translation. Journal of Symbolic Computation (1986)Google Scholar
  14. 14.
    Motik, B., Shearer, R., Horrocks, I.: Optimized reasoning in description logics using hypertableaux. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 67–83. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  15. 15.
    Sirin, E., Parsia, B., Grau, B.C., Kalyanpur, A., Katz, Y.: Pellet: A practical OWL-DL reasoner. Journal of Web Semantics 5(2) (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Matthew Horridge
    • 1
  • Bijan Parsia
    • 1
  • Ulrike Sattler
    • 1
  1. 1.School of Computer ScienceThe University of ManchesterManchester

Personalised recommendations