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
Choquet, G.: Theory of capacities. Annales de l’Institut Fourier (5), 131–295 (1953)
Ciabattoni, A., Picado Muiño, D., Vetterlein, T., El-Zekey, M.: Formal approaches to rule-based systems in medicine: the case of CADIAG-2 (submitted)
Ciabattoni, A., Vetterlein, T.: On the (fuzzy) logical content of CADIAG-2. Fuzzy Sets and Systems 161, 1941–1958 (2010)
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)
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)
Dubois, D., Prade, H.: Possibility theory: an approach to computerized processing of uncertainty. Plenum Press, New York (1988)
Dubois, D., Prade, H.: Possibilistic logic: a retrospective and prospective view. Fuzzy Sets and Systems 144, 3–23 (2004)
Esteva, F., Godo, L., Hájek, P., Navara, M.: Residuated fuzzy logics with an involutive negation. Archive for Mathematical Logic 39(2), 103–124 (2000)
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)
Flaminio, T., Godo, L.: A logic for reasoning about the probability of fuzzy events. Fuzzy Sets and Systems 158(6), 625–638 (2007)
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)
Halpern, J.Y.: Reasoning about uncertainty. MIT Press, Cambridge (2003)
Hájek, P.: Metamathematics of fuzzy logic. Trends in Logic—Studia Logica Library, vol. 4. Kluwer Academic Publishers, Dordrecht (1998)
Picado-Muiño, D.: A probabilistic interpretation of the medical expert system CADIAG-2. Soft Computing 15(10), 2013–2020 (2011)
Picado-Muiño, D.: Measuring and repairing inconsistency in probabilistic knowledge bases. International Journal of Approximate Reasoning 52(6), 828–840 (2011)
Shafer, G.: A mathematical theory of evidence. Princeton University Press, Princeton (1976)
Sugeno, M.: Theory of Fuzzy Integrals and its Applications. PhD thesis, Tokyo Institute of Technology, Tokio, Japan (1974)
Walley, P.: Statistical reasoning with imprecise probabilities. Monographs on Statistics and Applied Probability, vol. 42. Chapman and Hall Ltd., London (1991)
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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
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