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The Relationship of the Logic of Big-Stepped Probabilities to Standard Probabilistic Logics

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Foundations of Information and Knowledge Systems (FoIKS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 5956))

Abstract

Different forms of semantics have been proposed for conditionals of the form ”Usually, if A then B”, ranging from quantitative probability distributions to qualitative approaches using plausibility orderings or possibility distributions. Atomic-bound systems, also called big-stepped probabilities, allow qualitative reasoning with probabilities, aiming at bridging the gap between qualitative and quantitative argumentation and providing a model for the nonmonotonic reasoning system P. By using Goguen and Burstall’s notion of institutions for the formalization of logical systems, we elaborate precisely which formal connections exist between big-stepped probabilities and standard probabilities, thereby establishing the exact relationships among these logics.

The research reported here was supported by the Deutsche Forschungsgemeinschaft (grants BE 1700/7-1 and KE 1413/2-1).

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References

  1. Adams, E.W.: The Logic of Conditionals. D. Reidel, Dordrecht (1975)

    Book  MATH  Google Scholar 

  2. Arló Costa, H., Parikh, R.: Conditional probability and defeasible inference. Journal of Philosophical Logic 34, 97–119 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Beierle, C., Kern-Isberner, G.: Using institutions for the study of qualitative and quantitative conditional logics. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 161–172. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  4. Beierle, C., Kern-Isberner, G.: Looking at probabilistic conditionals from an institutional point of view. In: Kern-Isberner, G., Rödder, W., Kulmann, F. (eds.) WCII 2002. LNCS (LNAI), vol. 3301, pp. 162–179. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Beierle, C., Kern-Isberner, G.: Formal similarities and differences among qualitative conditional semantics. International Journal of Approximate Reasoning (2009) (to appear)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  7. Goguen, J., Burstall, R.: Institutions: Abstract model theory for specification and programming. Journal of the ACM 39(1), 95–146 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  8. Goguen, J.A., Rosu, G.: Institution morphisms. Formal Aspects of Computing 13(3-5), 274–307 (2002)

    Article  MATH  Google Scholar 

  9. Hawthorne, J.: On the logic of nonmonotonic conditionals and conditional probabilities. Journal of Philosophical Logic 25(2), 185–218 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  10. Hawthorne, J., Makinson, D.: The quantitative/qualitative watershed for rules of uncertain inference. Studia Logica 86(2), 247–297 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Herrlich, H., Strecker, G.E.: Category theory. Allyn and Bacon, Boston (1973)

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  13. Kyburg Jr., H.E., Teng, C.-M., Wheeler, G.R.: Conditionals and consequences. J. Applied Logic 5(4), 638–650 (2007)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  15. Lewis, D.: Counterfactuals. Harvard University Press, Cambridge (1973)

    Google Scholar 

  16. Nute, D.: Topics in Conditional Logic. D. Reidel Publishing Company, Dordrecht (1980)

    Book  MATH  Google Scholar 

  17. Pearl, J.: Probabilistic semantics for nonmonotonic reasoning: A survey. In: Shafer, G., Pearl, J. (eds.) Readings in uncertain reasoning, pp. 699–710. Morgan Kaufmann, San Mateo (1989)

    Google Scholar 

  18. Snow, P.: The emergence of ordered belief from initial ignorance. In: Proceedings AAAI 1994, Seattle, WA, pp. 281–286 (1994)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, FernUniversität in Hagen, 58084, Hagen, Germany

    Christoph Beierle

  2. Dept. of Computer Science, TU Dortmund, 44221, Dortmund, Germany

    Gabriele Kern-Isberner

Authors
  1. Christoph Beierle
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  2. Gabriele Kern-Isberner
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Editor information

Editors and Affiliations

  1. School of Information Management, The Victoria University of Wellington, Wellington, New Zealand

    Sebastian Link

  2. IRIT, University of Toulouse III, 118 route de Narbonne, 31062, Toulouse, Cedex 9, France

    Henri Prade

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Beierle, C., Kern-Isberner, G. (2010). The Relationship of the Logic of Big-Stepped Probabilities to Standard Probabilistic Logics. In: Link, S., Prade, H. (eds) Foundations of Information and Knowledge Systems. FoIKS 2010. Lecture Notes in Computer Science, vol 5956. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11829-6_14

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  • DOI: https://doi.org/10.1007/978-3-642-11829-6_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11828-9

  • Online ISBN: 978-3-642-11829-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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