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An Extension of Gödel Logic for Reasoning under Both Vagueness and Possibilistic Uncertainty

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Advances in Computational Intelligence (IPMU 2012)

Abstract

In this paper we introduce a logic called FNG~(ℚ) that combines the well-known Gödel logic with a strong negation, rational truth-constants and Possibilistic logic. In this way, we can formalize reasoning involving both vagueness and (possibilistic) uncertainty. We show that the defined logical system is useful to capture the kind of reasoning at work in the medical diagnosis system CADIAG-2, and we finish by pointing out some of its potential advantages to be developed in future work.

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References

  1. Choquet, G.: Theory of capacities. Annales de l’Institut Fourier (5), 131–295 (1953)

    Google Scholar 

  2. Ciabattoni, A., Picado Muiño, D., Vetterlein, T., El-Zekey, M.: Formal approaches to rule-based systems in medicine: the case of CADIAG-2 (submitted)

    Google Scholar 

  3. Ciabattoni, A., Vetterlein, T.: On the (fuzzy) logical content of CADIAG-2. Fuzzy Sets and Systems 161, 1941–1958 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dubois, D., Esteva, F., Godo, L., Prade, H.: Fuzzy-set based logics - An history-oriented presentation of their main developments. In: Gabbay, D.M., Woods, J. (eds.) Handbook of the History of Logic. The many valued and nonmonotonic turn in logic, vol. 8, pp. 325–449 (2007)

    Google Scholar 

  5. Dubois, D., Lang, J., Prade, H.: Possibilistic logic. In: Gabbay, et al. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming. Nonmonotonic Reasoning and Uncertain Reasoning, vol. 3, pp. 439–513. Oxford University Press (1994)

    Google Scholar 

  6. Dubois, D., Prade, H.: Possibility theory: an approach to computerized processing of uncertainty. Plenum Press, New York (1988)

    MATH  Google Scholar 

  7. Dubois, D., Prade, H.: Possibilistic logic: a retrospective and prospective view. Fuzzy Sets and Systems 144, 3–23 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Esteva, F., Godo, L., Hájek, P., Navara, M.: Residuated fuzzy logics with an involutive negation. Archive for Mathematical Logic 39(2), 103–124 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Esteva, F., Gispert, J., Godo, L., Noguera, C.: Adding truth-constants to logics of a continuous t-norm: axiomatization and completeness results. Fuzzy Sets and Systems 158, 597–618 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Flaminio, T., Godo, L.: A logic for reasoning about the probability of fuzzy events. Fuzzy Sets and Systems 158(6), 625–638 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Flaminio, T., Godo, L., Marchioni, E.: On the Logical Formalization of Possibilistic Counterparts of States over n-Valued Lukasiewicz Events. Journal of Logic and Computation 21(3), 429–446 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Halpern, J.Y.: Reasoning about uncertainty. MIT Press, Cambridge (2003)

    MATH  Google Scholar 

  13. Hájek, P.: Metamathematics of fuzzy logic. Trends in Logic—Studia Logica Library, vol. 4. Kluwer Academic Publishers, Dordrecht (1998)

    Book  MATH  Google Scholar 

  14. Picado-Muiño, D.: A probabilistic interpretation of the medical expert system CADIAG-2. Soft Computing 15(10), 2013–2020 (2011)

    Article  MATH  Google Scholar 

  15. Picado-Muiño, D.: Measuring and repairing inconsistency in probabilistic knowledge bases. International Journal of Approximate Reasoning 52(6), 828–840 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Shafer, G.: A mathematical theory of evidence. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  17. Sugeno, M.: Theory of Fuzzy Integrals and its Applications. PhD thesis, Tokyo Institute of Technology, Tokio, Japan (1974)

    Google Scholar 

  18. Walley, P.: Statistical reasoning with imprecise probabilities. Monographs on Statistics and Applied Probability, vol. 42. Chapman and Hall Ltd., London (1991)

    MATH  Google Scholar 

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El-Zekey, M., Godo, L. (2012). An Extension of Gödel Logic for Reasoning under Both Vagueness and Possibilistic Uncertainty. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31715-6_24

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  • DOI: https://doi.org/10.1007/978-3-642-31715-6_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31714-9

  • Online ISBN: 978-3-642-31715-6

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