Abstract
AbstractWe investigate quantifier elimination of first order logic over fuzzy algebras. Fuzzy algebras are defined from continuous t-norms over the unit interval, and subsume Łukasiewicz [28, 29], Gödel [16, 12] and Product [19] Logic as most prominent examples.We show that a fuzzy algebra has quantifier elimination iff it is one of the abovementioned logics. Moreover, we show quantifier elimination for various extensions of these logics, and observe other model-theoretic properties of fuzzy algebras.Further considerations are devoted to approximation of fuzzy logics by finite-valued logics.
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