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Using Sums-of-Products for Non-standard Reasoning

  • Rafael Peñaloza
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6031)

Abstract

An important portion of the current research in Description Logics is devoted to the expansion of the reasoning services and the developement of algorithms that can adequatedly perform so-called non-standard reasoning. Applications of non-standard reasoning services cover a wide selection of areas such as access control, agent negotiation, or uncertainty reasoning, to name just a few. In this paper we show that some of these non-standard inferences can be seen as the computation of a sum of products, where “sum” and “product” are the two operators of a bimonoid. We then show how the main ideas of automata-based axiom-pinpointing, combined with weighted model counting, yield a generic method for computing sums-of-products over arbitrary bimonoids.

Keywords

Description Logic Inference Relation Minimal Utility Concept Term Valuation Versus 
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.

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References

  1. 1.
    Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  2. 2.
    Baader, F., Knechtel, M., Peñaloza, R.: A generic approach for large-scale ontological reasoning in the presence of access restrictions to the ontology’s axioms. In: Bernstein, A., Karger, D.R., Heath, T., Feigenbaum, L., Maynard, D., Motta, E., Thirunarayan, K. (eds.) ISWC 2009. LNCS, vol. 5823, pp. 49–64. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Baader, F., Lutz, C., Suntisrivaraporn, B.: CEL — A polynomial-time reasoner for life science ontologies. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 287–291. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Baader, F., Peñaloza, R.: Axiom pinpointing in general tableaux. In: Olivetti, N. (ed.) TABLEAUX 2007. LNCS (LNAI), vol. 4548, pp. 11–27. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Baader, F., Peñaloza, R.: Automata-based axiom pinpointing. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 226–241. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Baader, F., Peñaloza, R.: Automata-based axiom pinpointing. Journal of Automated Reasoning (2010); Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 226–241. Springer, Heidelberg (2008)Google Scholar
  7. 7.
    Baader, F., Peñaloza, R.: Axiom pinpointing in general tableaux. Journal of Logic and Computation 20(1), 5–34 (2010); Special Issue: Tableaux ’07 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Bacchus, F., Dalmao, S., Pitassi, T.: Solving #SAT and Bayesian inference with backtracking search. J. of Art. Intel. Research 34, 391–442 (2009)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Bobillo, F., Straccia, U.: Fuzzy description logics with general t-norms and datatypes. Fuzzy Sets and Systems 160(23), 3382–3402 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Haarslev, V., Möller, R.: RACER system description. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, p. 701. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  11. 11.
    Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (2001)Google Scholar
  12. 12.
    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 Sem. 1(1), 7–26 (2003)Google Scholar
  13. 13.
    Kazakov, Y.: Consequence-driven reasoning for Horn SHIQ ontologies. In: Boutilier, C. (ed.) Proc. of IJCAI 2009, Pasadena, California, pp. 2040–2045 (2009)Google Scholar
  14. 14.
    Lukasiewicz, T.: Expressive probabilistic description logics. Artif. Intel. 172(6-7), 852–883 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    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
  16. 16.
    Peñaloza, R.: Reasoning with weighted ontologies. In: Grau, B.C., Horrocks, I., Motik, B., Sattler, U. (eds.) Proc. of DL ’09. CEUR-WS, vol. 477 (2009)Google Scholar
  17. 17.
    Ragone, A., Noia, T.D., Donini, F.M., Sciascio, E.D., Wellman, M.P.: Computing utility from weighted description logic preference formulas. In: Baldoni, M., van Riemsdijk, M.B. (eds.) DALT 2009. LNCS, vol. 5948, pp. 158–173. Springer, Heidelberg (2010)Google Scholar
  18. 18.
    Ragone, A., Noia, T.D., Donini, F.M., Sciascio, E.D., Wellman, M.P.: Weighted description logics preference formulas for multiattribute negotiation. In: Godo, L., Pugliese, A. (eds.) SUM 2009. LNCS, vol. 5785, pp. 193–205. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Schmidt-Schauß, M., Smolka, G.: Attributive concept descriptions with complements. Artif. Intel. 48(1), 1–26 (1991)zbMATHCrossRefGoogle Scholar
  20. 20.
    Sebastiani, R., Vescovi, M.: Axiom pinpointing in lightweight description logics via Horn-SAT encoding and conflict analysis. In: Schmidt, R.A. (ed.) Automated Deduction – CADE-22. LNCS, vol. 5663, pp. 84–99. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  21. 21.
    Sirin, E., Parsia, B.: Pellet: An OWL DL reasoner. In: Proc. of DL ’04, pp. 212–213 (2004)Google Scholar
  22. 22.
    Tsarkov, D., Horrocks, I.: FaCT++ description logic reasoner: System description. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 292–297. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  23. 23.
    Tseitin, G.S.: On the complexity of derivations in the propositional calculus. In: Studies in Mathematics and Mathematical Logic, Part II (1968)Google Scholar
  24. 24.
    Zadeh, L.A.: Fuzzy sets. Information and Control 8(3), 338–353 (1965)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Rafael Peñaloza
    • 1
  1. 1.Theoretical Computer ScienceTU DresdenGermany

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