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

Mathematical Logic.Joseph Robert Shoenfield - 1967 - Reading, MA, USA: Reading, Mass., Addison-Wesley Pub. Co..
The Mathematics of Metamathematics.Helena Rasiowa - 1963 - Warszawa, Państwowe Wydawn. Naukowe.
Model Theory.Gebhard Fuhrken - 1976 - Journal of Symbolic Logic 41 (3):697-699.
Continuous Model Theory.Chen Chung Chang - 1966 - Princeton: Princeton University Press.

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Citations of this work BETA

Fuzzy Logic and Arithmetical Hierarchy, II.Petr Hájek - 1997 - Studia Logica 58 (1):129-141.
Fuzzy Natural Deduction.Giangiacomo Gerla & Roberto Tortora - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (1):67-77.
Fuzzy Natural Deduction.Giangiacomo Gerla & Roberto Tortora - 1990 - Mathematical Logic Quarterly 36 (1):67-77.
Approximate Reasoning Based on Similarity.M. Ying, L. Biacino & G. Gerla - 2000 - Mathematical Logic Quarterly 46 (1):77-86.

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