Abstract
As we sketched in [Godo and Hájek, 1996], most of fuzzy inference in Zadeh’s style is well formalized in the many-sorted many-valued Pavelka-style fuzzy predicate logic — and this can be done in several ways. The most important fact is that patterns of fuzzy inference can be presented as sound deduction rules, with all necessary assumptions expressed by some formulas of predicate logic (with the usual quantifiers ∀, ∃) in the premisse part of the rule. Here we complement the presentation of [Godo and Hájek, 1996] by a somewhat unexpected formalization of Zadeh’s Generalized Modus Ponens (GMP, cf. e.g. Zadeh [1988; 1990; 1994]). We shall be sketchy; a full detailed presentation is to be found in [Godo and Hájek, to appear]. For the reader’s convenience we repeat the definition of the many-sorted RQL (rational quantification logic, cf. [Hájek, 1995; Hájek, 1997]).
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Godo, L., Hájek, P. (1999). A Note on Fuzzy Inference as Deduction. In: Dubois, D., Prade, H., Klement, E.P. (eds) Fuzzy Sets, Logics and Reasoning about Knowledge. Applied Logic Series, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1652-9_15
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DOI: https://doi.org/10.1007/978-94-017-1652-9_15
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