First-order fuzzy logic

Studia Logica 46 (1):87 - 109 (1987)
This paper is an attempt to develop the many-valued first-order fuzzy logic. The set of its truth, values is supposed to be either a finite chain or the interval 0, 1 of reals. These are special cases of a residuated lattice L, , , , , 1, 0. It has been previously proved that the fuzzy propositional logic based on the same sets of truth values is semantically complete. In this paper the syntax and semantics of the first-order fuzzy logic is developed. Except for the basic connectives and quantifiers, its language may contain also additional n-ary connectives and quantifiers. Many propositions analogous to those in the classical logic are proved. The notion of the fuzzy theory in the first-order fuzzy logic is introduced and its canonical model is constructed. Finally, the extensions of Gödel's completeness theorems are proved which confirm that the first-order fuzzy logic is also semantically complete.
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DOI 10.1007/BF00396907
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References found in this work BETA
Joseph R. Shoenfield (1967). Mathematical Logic. Reading, Mass.,Addison-Wesley Pub. Co..
Chen Chung Chang (1966). Continuous Model Theory. Princeton, Princeton University Press.
C. C. Chang & H. J. Keisler (1976). Model Theory. Journal of Symbolic Logic 41 (3):697-699.

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