An Extension of Gödel Logic for Reasoning under Both Vagueness and Possibilistic Uncertainty
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.
KeywordsFuzzy Logic Propositional Variable Boolean Formula Possibilistic Logic Necessity Measure
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- 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
- 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
- 17.Sugeno, M.: Theory of Fuzzy Integrals and its Applications. PhD thesis, Tokyo Institute of Technology, Tokio, Japan (1974)Google Scholar