An Adaptive Logic for Rational Closure

Chapter
Part of the Trends in Logic book series (TREN, volume 38)

Abstract

Lehmann and Magidor have proposed a powerful approach to model defeasible conditional knowledge: Rational Closure. Their account significantly strengthens previous proposals based on the so-called KLM-properties. In this chapter a dynamic proof theory for Rational Closure is presented.

Notes

Acknowledgments

I am thankful to Diderik Batens and Joke Meheus for many constructive comments which helped to improve this paper.

References

  1. 1.
    Straßer, C.: An adaptive logic for rational closure. In: Carnielli, W. Coniglio, M.E., D’Ottaviano I.M.L. (eds.) The Many Sides of Logic, pp. 47–67. College Publications (2009)Google Scholar
  2. 2.
    Clark, K.L.: Negation as failure. In: Logic and Data Bases, pp. 293–322 (1977)Google Scholar
  3. 3.
    McCarthy, J.: Circumscription—a form of non-monotonic reasoning. Artif. Intell. 13, 27–29 (1980)CrossRefGoogle Scholar
  4. 4.
    Reiter, R.: A logic for default reasoning. Artif. Intell. 13(1-2), 81–132 (1980)Google Scholar
  5. 5.
    Moore, R.C.: Possible-world semantics for autoepistemic logic. In: Proceedings of the Workshop on Non-monotonic Reasoning, pp. 344–354. AAAI (1984)Google Scholar
  6. 6.
    Gabbay, D.M.: Theoretical foundations for non-monotonic reasoning in expert systems. In: Logics and Models of Concurrent Systems, pp. 439–457. Springer-Verlag, New York, (1985)Google Scholar
  7. 7.
    Shoham, Y.: Reasoning About Change: Time and Causation from the Standpoint of Artificial Intelligence. M.I.T Press, Cambridge (1988)Google Scholar
  8. 8.
    Shoham, Y.: A semantical approach to nonmonotonic logics. In: Ginsberg, M.L. (ed.) Readings in Non-Monotonic Reasoning, pp. 227–249. Morgan Kaufmann, Los Altos (1987)Google Scholar
  9. 9.
    Kraus, S., Lehmann, D.J., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artif. Intell. 44, 167–207 (1990)CrossRefGoogle Scholar
  10. 10.
    Friedman, N., Halpern, J.Y.: Plausibility measures and default reasoning. J. ACM 48, 1297–1304 (1996)Google Scholar
  11. 11.
    Arieli, O., Avron, A.: General patterns for nonmonotonic reasoning: from basic entailments to plausible relations. Logic J. IGPL 8(2), 119–148 (2000)Google Scholar
  12. 12.
    Lehmann, D.J., Magidor, M.: What does a conditional knowledge base entail? Artif. Intell. 55(1), 1–60 (1992)CrossRefGoogle Scholar
  13. 13.
    Goldszmidt, M., Pearl, J.: On the relation between rational closure and system Z. In: Third International Workshop on Nonmonotonic Reasoning South Lake Tahoe, pp. 130–140 (1990)Google Scholar
  14. 14.
    Pearl, J.: System Z: a natural ordering of defaults with tractable applications to nonmonotonic reasoning. In: TARK ’90: Proceedings of the 3rd Conference on Theoretical Aspects of Reasoning About Knowledge, pp. 121–135. Morgan Kaufmann Publishers Inc., San Francisco, (1990)Google Scholar
  15. 15.
    Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.: Analytic tableau calculi for KLM rational logic R. In: Proceedings of the 10th European Conference on Logics in Artificial Intelligence, pp. 190–202. ACM, New York (2006)Google Scholar
  16. 16.
    Booth, R., Paris, J.: A note on the rational closure of knowledge bases with both positive and negative knowledge. J. Logic Lang. Inform. 7(2), 165–190 (1998)Google Scholar
  17. 17.
    Lehmann, D., Magidor, M.: Preferential logics: the predicate calculus case. In: TARK ’90: Proceedings of the 3rd Conference on Theoretical Aspects of Reasoning About Knowledge, pp. 57–72. Morgan Kaufmann Publishers Inc., San Francisco, (1990)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.GhentBelgium

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