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Probabilistic Approach to Nonmonotonic Consequence Relations

  • Conference paper
Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2011)

Abstract

The paper offers a probabilistic characterizations of determinacy preservation, fragmented disjunction and conditional excluding middle for preferential relations. The paper also presents a preferential relation that is above Disjunctive rationality and strictly below Rational monotonicity. This so called ε,μ-relation is constructed using a positive infinitesimal ε and a finitely additive hyperreal valued probability measure μ on the set of propositional formulas.

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References

  1. Beierle, C., Kern-Isberner, G.: The Relationship of the Logic of Big-Stepped Probabilities to Standard Probabilistic Logics. In: Link, S., Prade, H. (eds.) FoIKS 2010. LNCS, vol. 5956, pp. 191–210. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  2. Benferhat, S., Duboas, D., Prade, H.: Possibilistic and standard probabilistic semantics of conditional knowledge bases. Journal of Logic and Computation 9(6), 873–895 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bezzazi, H., Pino Pérez, R.: Rational Transitivity and its models. In: Proceedings of the 26th International Symposium on Multiple-Valued Logic, pp. 160–165. IEEE Computer Society Press, Los Alamitos (1996)

    Google Scholar 

  4. Bezzazi, H., Makinson, D., Pino Pérez, R.: Beyond rational monotony: some strong non-Horn rules for nonmonotonic inference relations. Journal of Logic and Computation 7(5), 605–631 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  5. Doder, D., Rašković, M., Marković, Z., Ognjanović, Z.: Measures of inconsistency and defaults. International Journal of Approximate Reasoning 51, 832–845 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dubois, D., Fargier, H., Prade, H.: Ordinal and Probabilistic Representations of Acceptance. J. Artificial Intelligence Research 22, 23–56 (2004)

    MathSciNet  MATH  Google Scholar 

  7. Freund, M.: Injective models and disjunctive relations. Journal of Logic and Computation 3(3), 231–247 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  8. Freund, M., Lehmann, D.: On negation rationality. Journal of Logic and Computation 6(2), 263–269 (1996)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  10. Gabbay, D.: Theoretical foundations for non-monotonic reasoning in expert systems. In: Logics and Models of Concurrent Systems, pp. 439–457. Springer, Heidelberg (1985)

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  13. Makinson, D.: General patterns in nonmonotonic reasoning. In: Handbook of Logic in Artificial Intelligence and Logic Programming. Non Monotonic Reasoning and Uncertain Reasoning, vol. 3, pp. 35–110. Clarendon Press, Oxford (1994)

    Google Scholar 

  14. Bhaskara Rao, K.P.S., Bhaskara Rao, M.: Theory of charges. Academic Press, London (1983)

    MATH  Google Scholar 

  15. Rašković, M., Ognjanović, Z., Marković, Z.: A logic with approximate conditional probabilities that can model default reasoning. International Journal of Approximate Reasoning 49(1), 52–66 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Stalnaker, R.C.: A theory of conditionals. In: Rescher, N. (ed.) Studies in Logical Theory. American Philosophical Quarterly Monograph Series, vol. 2. Blackwell, Oxford (1968)

    Google Scholar 

  17. Stroyan, K.D., Luxemburg, W.A.J.: Introduction to the theory of infinitesimals. Academic Press, London (1976)

    MATH  Google Scholar 

  18. Weydert, E.: Doxastic Normality Logic: A Qualitative Probabilistic Modal Framework for Defaults and Belief. In: Logic, Action and Information, pp. 152–172. Walter de Gruyter, Berlin (1996)

    Google Scholar 

  19. Weydert, E.: Defaults, Logic and Probability – A Theoretical Perspective. KI 15(4), 44–49 (2001)

    Google Scholar 

  20. Zhu, Z., Xiao, W.: Two Representation Theorems for Non-monotonic Inference Relations. Journal of Logic and Computation 17(4), 727–747 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. Zhu, Z., Zhang, D., Chen, S., Zhu, W.: Some contributions to nonmonotonic consequence. Journal of Computer Science and Technology 16(4), 297–314 (2001)

    Article  MathSciNet  MATH  Google Scholar 

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Doder, D., Perović, A., Ognjanović, Z. (2011). Probabilistic Approach to Nonmonotonic Consequence Relations. In: Liu, W. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2011. Lecture Notes in Computer Science(), vol 6717. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22152-1_39

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  • DOI: https://doi.org/10.1007/978-3-642-22152-1_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22151-4

  • Online ISBN: 978-3-642-22152-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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