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Weak Implication in Terms of Conditional Uncertainty Measures

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4724))

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Abstract

We define weak implication \(H \longmapsto_{\varphi} E\) (“H weakly implies E under \(\mathit{\varphi}\)”) through the relation \(\mathit{\varphi}(E|H)\) = 1, where \(\mathit{\varphi}\) is a (coherent) conditional uncertainty measure. By considering various such measures with different levels of generality, we get different sets of “inferential rules”, that correspond to those of default logic when \(\mathit{\varphi}\) reduces to a conditional probability.

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References

  1. Bouchon-Meunier, B., Coletti, G., Marsala, C.: Independence and Possibilistic Conditioning. Annals of Mathematics and Artificial Intelligence 35, 107–124 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Coletti, G.: Coherent numerical and ordinal probabilistic assessments. IEEE Transactionson Systems, Man, and Cybernetics 24, 1747–1754 (1994)

    Article  MathSciNet  Google Scholar 

  3. Coletti, G., Mastroleo, M.: Conditional belief functions: a comparison among different definitions. In: Proc. of WUPES 2006, Mikulov, Czech Rep., pp. 24–35 (2006)

    Google Scholar 

  4. Coletti, G., Scozzafava, R.: Characterization of coherent conditional probabilitiesas a tool for their assessment and extension. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 4, 103–127 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  5. Coletti, G., Scozzafava, R.: From conditional events to conditional measures: a newaxiomatic approach. Annals of Mathematics and Artificial Intelligence 32, 373–392 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  6. Coletti, G., Scozzafava, R.: Probabilistic logic in a coherent setting. In: Trends inlogic, vol. 15. Kluwer, Dordrecht (2002)

    Google Scholar 

  7. Coletti, G., Scozzafava, R.: Toward a general theory of conditional beliefs. International Journal of Intellgent Systems 21, 229–259 (2006)

    Article  MATH  Google Scholar 

  8. Coletti, G., Scozzafava, R., Vantaggi, B.: Coherent conditional probability as a toolfor default reasoning. In: Bouchon-Meunier, B., Foulloy, L., Yager, R.R. (eds.) IntelligentSystems for Information Processing: from Representation to Applications, pp. 191–202. Elsevier, Amsterdam (2003)

    Chapter  Google Scholar 

  9. Coletti, G., Vantaggi, B.: Possibility theory: conditional independence. Fuzzy Sets and Systems 157, 1491–1513 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Coletti, G., Vantaggi, B.: Representability of ordinal relations on a set of conditional events. Theory and Decision 60, 137–174 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. de Finetti, B.: Sull’impostazione assiomatica del calcolo delle probabilità. Annali. Univ. Trieste 19, 3–55 (1949) (Engl. transl.: Probability, Induction, Statistics, ch.5. Wiley, London (1972))

    MATH  Google Scholar 

  12. Ferracuti, L., Vantaggi, B.: Independence and conditional possibilities for strictlymonotone triangular norms. International Journal of Intelligent Systems 21(3), 299–323 (2006)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  14. Paneni, T., Scozzafava, R.: Multi-valued conditional events avoid Lewis’ trivialityresult. In: Nielsen, T.D., Zhang, N.L. (eds.) ECSQARU 2003. LNCS (LNAI), vol. 2711, pp. 432–439. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  15. Reiter, R.: A Logic for Default Reasoning. Artificial Intelligence 13, 81–132 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  16. Russel, S.J., Norvig, P.: Artificial Intelligence, a Modern Approach. Prentice-Hall, New Jersey (1995)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Università di Perugia, Italy

    Giulianella Coletti

  2. Università di Roma “La Sapienza”, Italy

    Romano Scozzafava & Barbara Vantaggi

Authors
  1. Giulianella Coletti
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  2. Romano Scozzafava
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  3. Barbara Vantaggi
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Editor information

Editors and Affiliations

  1. LARODEC, Institut Supérieur de Gestion de Tunis, 41 Avenue de la liberté, 2000, Le Bardo, Tunisie

    Khaled Mellouli

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Coletti, G., Scozzafava, R., Vantaggi, B. (2007). Weak Implication in Terms of Conditional Uncertainty Measures. In: Mellouli, K. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2007. Lecture Notes in Computer Science(), vol 4724. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75256-1_15

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  • DOI: https://doi.org/10.1007/978-3-540-75256-1_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75255-4

  • Online ISBN: 978-3-540-75256-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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