Advertisement

Reasoning Support for Expressive Ontology Languages Using a Theorem Prover

  • Ian Horrocks
  • Andrei Voronkov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3861)

Abstract

It is claimed in [45] that first-order theorem provers are not efficient for reasoning with ontologies based on description logics compared to specialised description logic reasoners. However, the development of more expressive ontology languages requires the use of theorem provers able to reason with full first-order logic and even its extensions. So far, theorem provers have extensively been used for running experiments over TPTP containing mainly problems with relatively small axiomatisations. A question arises whether such theorem provers can be used to reason in real time with large axiomatisations used in expressive ontologies such as SUMO. In this paper we answer this question affirmatively by showing that a carefully engineered theorem prover can answer queries to ontologies having over 15,000 first-order axioms with equality. Ontologies used in our experiments are based on the language KIF, whose expressive power goes far beyond the description logic based languages currently used in the Semantic Web.

Keywords

Theorem Prover Description Logic Predicate Symbol Ontology Language Query Answering 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bachmair, L., Ganzinger, H.: Resolution theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, ch. 2, vol. I, pp. 19–99. Elsevier Science, Amsterdam (2001)CrossRefGoogle Scholar
  2. 2.
    Bechhofer, S., Horrocks, I., Goble, C., Stevens, R.: OilEd: A reason-able ontology editor for the semantic web. In: Baader, F., Brewka, G., Eiter, T. (eds.) KI 2001. LNCS (LNAI), vol. 2174, pp. 396–408. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Bechhofer, S., van Harmelen, F., Hendler, J., Horrocks, I., McGuinness, D.L., Patel-Schneider, P.F., Stein, L.A.: OWL web ontology language 1.0 reference. W3C Recommendation, February 10 (2004), Available at http://www.w3.org/TR/owl-ref/
  4. 4.
    Berardi, D., Grüninger, M., Hull, R., McIlraith, S.: Towards a first-order ontology for semantic web services (September 2004), http://www.w3.org/2004/08/ws-cc/mci-20040904
  5. 5.
    Berners-Lee, T., Hendler, J., Lassila, O.: The semantic Web. Scientific American 284(5), 34–43 (2001)CrossRefGoogle Scholar
  6. 6.
    Boley, H., Dean, M., Grosof, B., Sintek, M., Spencer, B., Tabet, S., Wagner, G.: First-Order-Logic RuleML (2004), http://www.ruleml.org/fol/
  7. 7.
    Claessen, K., Sörensson, N.: New techniques that improve mace-style model finding. In: Proceedings of the Workshop Model Computation 2003 (2003)Google Scholar
  8. 8.
    Degtyarev, A., Nieuwenhuis, R., Voronkov, A.: Stratified resolution. Journal of Symbolic Computations 36(1-2), 79–99 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Emmen, A.: The grid needs ontologies—onto-what? (2002), http://www.hoise.com/primeur/03/articles/monthly/AE-PR-02-03-7.html
  10. 10.
    Fikes, R., Hayes, P., Horrocks, I.: OWL-QL—a language for deductive query answering on the Semantic Web. Journal of Web Semantics (2004) (to appear)Google Scholar
  11. 11.
    Foster, I., Kesselman, C., Nick, J., Tuecke, S.: The physiology of the grid: An open grid services architecture for distributed systems integration (2002), http://www.globus.org/research/papers/ogsa.pdf
  12. 12.
    Ganzinger, H., Stuber, J.: Superposition with equivalence reasoning and delayed clause normal form transformation. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 335–349. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Haarslev, V., Möller, R.: RACER User’s Guide and Reference Manual. Version 1.7.7 (September 2003)Google Scholar
  14. 14.
    Hayes, P., Menzel, C.: A semantics for the knowledge interchange format. In: IJCAI 2001 Workshop on the IEEE Standard Upper Ontology (2001)Google Scholar
  15. 15.
    Horrocks, I.: Using an expressive description logic: FaCT or fiction? In: Cohn, A., Schubert, L., Shapiro, S. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the Sixth International Conference (KR 1998), pp. 636–647. Morgan Kaufmann, San Francisco (1998)Google Scholar
  16. 16.
    Horrocks, I., Li, L., Turi, D., Bechhofer, S.: The instance store: DL reasoning with large numbers of individuals. In: Proc. of the 2004 Description Logic Workshop (DL 2004), pp. 31–40 (2004)Google Scholar
  17. 17.
    Horrocks, I., Patel-Schneider, P.F.: A proposal for an OWL rules language. In: Proc. of the Thirteenth International World Wide Web Conference (WWW 2004), pp. 723–731. ACM, New York (2004)Google Scholar
  18. 18.
    Horrocks, I., Patel-Schneider, P.F., Boley, H., Tabet, S., Grosof, B., Dean, M.: SWRL: A semantic web rule language combining owl and ruleml. W3C Note, May 21 (2004), Available at http://www.w3.org/Submission/SWRL/
  19. 19.
    Horrocks, I., Patel-Schneider, P.F., van Harmelen, F.: Reviewing the design of DAML+OIL: An ontology language for the semantic web. In: Proc. of the 18th National Conference on Artificial Intelligence (AAAI 2002), pp. 792–797. AAAI Press, Menlo Park (2002)Google Scholar
  20. 20.
    Horrocks, I., Patel-Schneider, P.F., van Harmelen, F.: From SHIQ and RDF to OWL: The making of a web ontology language. Journal of Web Semantics 1(1), 7–26 (2003)Google Scholar
  21. 21.
    Horrocks, I., Sattler, U.: The effect of adding complex role inclusion axioms in description logics. In: Proc. of the 18th Int. Joint Conf. on Artificial Intelligence (IJCAI 2003), pp. 343–348. Morgan Kaufmann, San Francisco (2003)Google Scholar
  22. 22.
    Horrocks, I., Tessaris, S.: Querying the semantic web: a formal approach. In: Horrocks, I., Hendler, J. (eds.) ISWC 2002. LNCS, vol. 2342, pp. 177–191. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  23. 23.
    Hustadt, U., Konev, B., Riazanov, A., Voronkov, A.: TeMP: A temporal monodic prover. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097, pp. 326–330. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  24. 24.
    Hustadt, U., Schmidt, R.A.: Using resolution for testing modal satisfiability and building models. In: Gent, I.P., van Maaren, H., Walsh, T. (eds.) SAT 2000: Highlights of Satisfiability Research in the Year 2000. Frontiers in Artificial Intelligence and Applications, vol. 63. IOS Press, Amsterdam (2000); Also to appear in a special issue of Journal of Automated ReasoningGoogle Scholar
  25. 25.
    Horrocks, P.P.-S.I.: Three theses of representation in the semantic web. In: Proceedings of the Twelfth International World Wide Web Conference, WWW 2003, Budapest, Hungary, pp. 39–47. ACM, New York (2003)CrossRefGoogle Scholar
  26. 26.
    Kutsia, T.: Theorem proving with sequence variables and flexible arity symbols. In: Baaz, M., Voronkov, A. (eds.) LPAR 2002. LNCS (LNAI), vol. 2514, pp. 278–291. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  27. 27.
    McCune, W.: Mace4 reference manual and guide. Technical Memorandum 264, Argonne National Laboratory (August. 2003)Google Scholar
  28. 28.
    McCune, W.: OTTER 3.3 reference manual. Technical Memorandum 263, Argonne National Laboratory (August 2003)Google Scholar
  29. 29.
    Mika, P., Oberle, D., Gangemi, A., Sabou, M.: Foundations for service ontologies: Aligning OWL-S dolce. In: Feldman, S., Uretsky, M., Najork, M., Wills, C. (eds.) WWW 2004, Proceedings of the 13th international conference on World Wide Web, pp. 563–572. ACM, New York (2004)CrossRefGoogle Scholar
  30. 30.
    Pease, A., Niles, I., Li, J.: The Suggested Upper Merged Ontology: A large ontology for the Semantic Web and its applications. In: Working Notes of the AAAI-2002 Workshop on Ontologies and the Semantic Web, Edmonton, Canada (2002)Google Scholar
  31. 31.
    Protégé (2003), http://protege.stanford.edu/
  32. 32.
    Rector, A.: Analysis of propagation along transitive roles: Formalisation of the galen experience with medical ontologies. In: Proc. of DL 2002. CEUR (2002), http://ceur-ws.org/
  33. 33.
    Rector, A., Bechhofer, S., Goble, C.A., Horrocks, I., Nowlan, W.A., Solomon, W.D.: The Grail concept modelling language for medical terminology. Artificial Intelligence in Medicine 9, 139–171 (1997)CrossRefGoogle Scholar
  34. 34.
    Rector, A., Horrocks, I.: Experience building a large, re-usable medical ontology using a description logic with transitivity and concept inclusions. In: Proc. of the 13th Nat. Conf. on Artificial Intelligence, AAAI 1997 (1997)Google Scholar
  35. 35.
    Riazanov, A., Voronkov, A.: The design and implementation of Vampire. AI Communications 15(2-3), 91–110 (2002)zbMATHGoogle Scholar
  36. 36.
    Riazanov, A., Voronkov, A.: Limited resource strategy in resolution theorem proving. Journal of Symbolic Computations 36(1-2), 101–115 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  37. 37.
    Schulz, S., Hahn, U.: Parts, locations, and holes - formal reasoning about anatomical structures. In: Quaglini, S., Barahona, P., Andreassen, S. (eds.) AIME 2001. LNCS (LNAI), vol. 2101, p. 293. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  38. 38.
    Common Logic Standard, http://cl.tamu.edu/
  39. 39.
    Sekar, R., Ramakrishnan, I., Voronkov, A.: Term indexing. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, ch. 26, vol. II, pp. 1853–1964. Elsevier Science, Amsterdam (2001)CrossRefGoogle Scholar
  40. 40.
    Spackman, K.: Managing clinical terminology hierarchies using algorithmic calculation of subsumption: Experience with snomed-rt. J. of the Amer. Med. Informatics Ass. (2000) (Fall Symposium Special Issue)Google Scholar
  41. 41.
    Stevens, R., Goble, C., Horrocks, I., Bechhofer, S.: Building a bioinformatics ontology using OIL. IEEE Transactions on Information Technology in Biomedicine 6(2), 135–141 (2002)CrossRefGoogle Scholar
  42. 42.
    Tammet, T.: Completeness of resolution for definite answers. Journal of Logic and Computation 5(4), 449–471 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  43. 43.
    Tammet, T.: Gandalf. Journal of Automated Reasoning 18(2), 199–204 (1997)CrossRefGoogle Scholar
  44. 44.
    The DAML Services Coalition. DAML-S: Web service description for the semantic web. In: ISWC 2003. LNCS, vol. 2870. Springer, Heidelberg (2003)Google Scholar
  45. 45.
    Tsarkov, D., Riazanov, A., Bechhofer, S., Horrocks, I.: Using Vampire to reason with OWL. In: Semantic Web 2004. Springer, Heidelberg (2004) (to appear) Google Scholar
  46. 46.
    Tuecke, S., Czajkowski, K., Foster, I., Frey, J., Graham, S., Kesselman, C., Vanderbilt, P.: Grid service specification (draft). GWD-I draft, GGF Open Grid Services Infrastructure Working Group (2002)Google Scholar
  47. 47.
    Uschold, M., King, M., Moralee, S., Zorgios, Y.: The enterprise ontology. Knowledge Engineering Review 13 (1998)Google Scholar
  48. 48.
    van Harmelen, F., Patel-Schneider, P.F., Horrocks, I.: Reference description of the DAML+OIL, ontology markup langauge (March 2001)Google Scholar
  49. 49.
    Voronkov, A.: \(k\rotatebox[]{180}{K}\): a theorem prover for K. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 383–387. Springer, Heidelberg (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ian Horrocks
    • 1
  • Andrei Voronkov
    • 1
  1. 1.The University of Manchester 

Personalised recommendations