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Axiom Pinpointing in General Tableaux

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4548))

Abstract

Axiom pinpointing has been introduced in description logics (DLs) to help the user to understand the reasons why consequences hold and to remove unwanted consequences by computing minimal (maximal) subsets of the knowledge base that have (do not have) the consequence in question. The pinpointing algorithms described in the DL literature are obtained as extensions of the standard tableau-based reasoning algorithms for computing consequences from DL knowledge bases. Although these extensions are based on similar ideas, they are all introduced for a particular tableau-based algorithm for a particular DL.

The purpose of this paper is to develop a general approach for extending a tableau-based algorithm to a pinpointing algorithm. This approach is based on a general definition of “tableaux algorithms,” which captures many of the known tableau-based algorithms employed in DLs, but also other kinds of reasoning procedures.

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References

  1. Baader, F., Brandt, S., Lutz, C.: Pushing the \(\mathcal{EL}\) envelope. In: Proc. of IJCAI 2005, pp. 364–369. Morgan Kaufmann, Los Alamitos (2005)

    Google Scholar 

  2. Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.F.: The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  3. Baader, F., Hanschke, P.: A scheme for integrating concrete domains into concept languages. Technical Report RR-91-10, Deutsches Forschungszentrum für Künstliche Intelligenz (DFKI) (1991)

    Google Scholar 

  4. Baader, F., Hladik, J., Lutz, C., Wolter, F.: From tableaux to automata for description logics. Fundamenta Informaticae 57(2-4), 247–279 (2003)

    MATH  MathSciNet  Google Scholar 

  5. Baader, F., Hollunder, B.: Embedding defaults into terminological knowledge representation formalisms. J. of Automated Reasoning 14, 149–180 (1995)

    Article  MathSciNet  Google Scholar 

  6. Baader, F., Peñaloza, R.: Axiom pinpointing in general tableaux. LTCS-Report 07-01, TU Dresden, Germany (2007), http://lat.inf.tu-dresden.de/research/reports.html

  7. Baader, F., Sattler, U.: An overview of tableau algorithms for description logics. Studia Logica 69, 5–40 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bailey, J., Stuckey, P.J.: Discovery of minimal unsatisfiable subsets of constraints using hitting set dualization. In: Hermenegildo, M.V., Cabeza, D. (eds.) Practical Aspects of Declarative Languages. LNCS, vol. 3350, Springer, Heidelberg (2005)

    Google Scholar 

  9. Davydov, G., Davydova, I., Büning, H.K.: An efficient algorithm for the minimal unsatisfiability problem for a subclass of CNF. Ann.of Mathematics and Artificial Intelligence 23(3-4), 229–245 (1998)

    Article  MATH  Google Scholar 

  10. Garey, M.R., Johnson, D.S.: Computers and Intractability — A guide to NP-completeness. W.H. Freeman and Company, San Francisco (CA, USA) (1979)

    MATH  Google Scholar 

  11. Haarslev, V., Möller, R.: RACER system description. In Proc. of IJCAR 2001 (2001)

    Google Scholar 

  12. Hollunder, B.: Hybrid inferences in KL-ONE-based knowledge representation systems. In: Proc. of German Workshop on AI, pp. 38–47. Springer, Heidelberg (1990)

    Google Scholar 

  13. Horrocks, I.: Using an expressive description logic: FaCT or fiction. In: Proc. of KR 1998, pp. 636–647 (1998)

    Google Scholar 

  14. Horrocks, I., Patel-Schneider, P.F., van Harmelen, F.: From SHIQ and RDF to OWL: The making of a web ontology language. J. of Web Semantics 1(1), 7–26 (2003)

    Google Scholar 

  15. Kalyanpur, A., Parsia, B., Sirin, E., Cuenca-Grau, B., Hendler, J.: Swoop: A Web ontology editing browser. J. of Web Semantics 4(2) (2005)

    Google Scholar 

  16. Knublauch, H., Fergerson, R.W., Noy, N.F., Musen, M.A.: The Protégé OWL plugin: An open development environment for semantic web applications. In: Proceedings of the Third Int. Semantic Web Conf, Hiroshima, Japan (2004)

    Google Scholar 

  17. Liffiton, M.H., Sakallah, K.A.: On finding all minimally unsatisfiable subformulas. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, Springer, Heidelberg (2005)

    Google Scholar 

  18. Meyer, T., Lee, K., Booth, R., Pan, J.Z.: Finding maximally satisfiable terminologies for the description logic \(\mathcal{{ALC}}\). In: Proc. of AAAI 2006, AAAI Press/The MIT Press, Cambridge (2006)

    Google Scholar 

  19. Oberle, D., Volz, R., Motik, B., Staab, S.: An extensible ontology software environment. In: Handbook on Ontologies, International Handbooks on Information Systems, pp. 311–333. Springer, Heidelberg (2004)

    Google Scholar 

  20. Parsia, B., Sirin, E., Kalyanpur, A.: Debugging OWL ontologies. In: Proc. of WWW 2005, pp. 633–640. ACM, New York (2005)

    Chapter  Google Scholar 

  21. Reiter, R.: A theory of diagnosis from first principles. Artificial Intelligence 32(1), 57–95 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  22. Schlobach, S.: Diagnosing terminologies. In: Proc. of AAAI 2005, pp. 670-675. AAAI Press/The MIT Press, Cambridge (2005)

    Google Scholar 

  23. Schlobach, S., Cornet, R.: Non-standard reasoning services for the debugging of description logic terminologies. In: Proc. of IJCAI 2003, Acapulco, Mexico, pp. 355–362. Morgan Kaufmann, San Francisco, Los Alamitos (2003)

    Google Scholar 

  24. Schmidt-Schauß, M., Smolka, G.: Attributive concept descriptions with complements. Artificial Intelligence 48(1), 1–26 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  25. Sirin, E., Parsia, B.: Pellet: An OWL DL reasoner. In: Proc. of DL 2004, pp. 212–213 (2004)

    Google Scholar 

  26. Spackman, K.A., Campbell, K.E., Cote, R.A.: SNOMED RT: A reference terminology for health care. J. of the American Medical Informatics Association, Fall Symposium Supplement, pp. 640–644 (1997)

    Google Scholar 

  27. Zhang, L., Malik, S.: Validating SAT solvers using an independent resolution-based checker: Practical implementations and other applications. In: Proc. of DATE 2003, pp. 10880–10885. IEEE Computer Society Press, Washington (2003)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Theoretical Computer Science, TU Dresden, Germany

    Franz Baader

  2. Intelligent Systems, University of Leipzig, Germany

    Rafael Peñaloza

Authors
  1. Franz Baader
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  2. Rafael Peñaloza
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Nicola Olivetti

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© 2007 Springer-Verlag Berlin Heidelberg

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Baader, F., Peñaloza, R. (2007). Axiom Pinpointing in General Tableaux. In: Olivetti, N. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2007. Lecture Notes in Computer Science(), vol 4548. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73099-6_4

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  • DOI: https://doi.org/10.1007/978-3-540-73099-6_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73098-9

  • Online ISBN: 978-3-540-73099-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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