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Analytic Tableau Calculi for KLM Rational Logic R

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Logics in Artificial Intelligence (JELIA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4160))

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Abstract

In this paper we present a tableau calculus for the rational logic R of default reasoning, introduced by Kraus, Lehmann and Magidor. Our calculus is obtained by introducing suitable modalities to interpret conditional assertions, and makes use of labels to represent possible worlds. We also provide a decision procedure for R and study its complexity.

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References

  1. Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44(1-2), 167–207 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  2. Gardenförs, P.: Knowledge in Flux. MIT Press, Cambridge (1988)

    Google Scholar 

  3. Friedman, N., Halpern, J.Y.: Plausibility measures and default reasoning. Journal of the ACM 48(4), 648–685 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Friedman, N., Halpern, J.Y., Koller, D.: First-order conditional logic for default reasoning revisited. ACM TOCL 1(2), 175–207 (2000)

    Article  MathSciNet  Google Scholar 

  5. Benferhat, S., Dubois, D., Prade, H.: Nonmonotonic reasoning, conditional objects and possibility theory. Artificial Intelligence 92(1-2), 259–276 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  6. Benferhat, S., Saffiotti, A., Smets, P.: Belief functions and default reasoning. Artificial Intelligence 122(1-2), 1–69 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  7. Weydert, E.: System jlz - rational default reasoning by minimal ranking constructions. Journal of Applied Logic 1(3-4), 273–308 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Pearl, J.: System z: A natural ordering of defaults with tractable applications to nonmonotonic reasoning. In: Proc. of the 3rd Conference on Theoretical Aspects of Reasoning about Knowledge, pp. 121–135. Morgan Kaufmann Publishers Inc., San Francisco (1990)

    Google Scholar 

  9. Makinson, D.: Bridges from Classical to Nonmonotonic logic. Texts in Computing, vol. 5. King’s College Publications, London (2005)

    Google Scholar 

  10. Makinson, D.: Bridges between classical and nonmonotonic logic. Logic Journal of the IGPL 11(1), 69–96 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Arieli, O., Avron, A.: General patterns for nonmonotonic reasoning: From basic entailments to plausible relations. Logic Journal of the IGPL 8(2), 119–148 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  12. Dubois, D., Fargier, H., Perny, P., Prade, H.: Qualitative decision theory: from savages axioms to nonmonotonic reasoning. Journal of the ACM 49(4), 455–495 (2002)

    Article  MathSciNet  Google Scholar 

  13. Dubois, D., Fargier, H., Perny, P.: Qualitative decision theory with preference relations and comparative uncertainty: An axiomatic approach. Art. Int. 148(1-2), 219–260 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  14. Lehmann, D., Magidor, M.: What does a conditional knowledge base entail? Artificial Intelligence 55(1), 1–60 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  15. Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: Analytic Tableaux for KLM Preferential and Cumulative Logics. In: Sutcliffe, G., Voronkov, A. (eds.) LPAR 2005. LNCS (LNAI), vol. 3835, pp. 666–681. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  16. Crocco, G., Lamarre, P.: On the connection between non-monotonic inference systems and conditional logics. In: Proc. of KR 1992, pp. 565–571 (1992)

    Google Scholar 

  17. Boutilier, C.: Conditional logics of normality: a modal approach. Art. Int. 68(1), 87–154 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  18. Hughes, G., Cresswell, M.: A Companion to Modal Logic. Methuen (1984)

    Google Scholar 

  19. Artosi, A., Governatori, G., Rotolo, A.: Labelled tableaux for non-monotonic reasoning: Cumulative consequence relations. J. of Logic and Computation 12(6), 1027–1060 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  20. Giordano, L., Gliozzi, V., Olivetti, N., Schwind, C.: Tableau calculi for preference-based conditional logics. In: Cialdea Mayer, M., Pirri, F. (eds.) TABLEAUX 2003. LNCS (LNAI), vol. 2796, pp. 81–101. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  21. Giordano, L., Gliozzi, V., Olivetti, N., Schwind, C.: Extensions of tableau calculi for preference-based conditional logics. In: Proc. of M4M-4, Informatik-Bericht, vol. 194, pp. 220–234 (2005)

    Google Scholar 

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Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L. (2006). Analytic Tableau Calculi for KLM Rational Logic R . In: Fisher, M., van der Hoek, W., Konev, B., Lisitsa, A. (eds) Logics in Artificial Intelligence. JELIA 2006. Lecture Notes in Computer Science(), vol 4160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11853886_17

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  • DOI: https://doi.org/10.1007/11853886_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-39625-3

  • Online ISBN: 978-3-540-39627-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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