David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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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References found in this work BETA
Didier DuBois (1997). Fuzzy Sets and Systems: Theory and Applications. Academic Press, Inc..
Helena Rasiowa (1963). The Mathematics of Metamathematics. Warszawa, Państwowe Wydawn. Naukowe.
Citations of this work BETA
Giangiacomo Gerla & Roberto Tortora (1990). Fuzzy Natural Deduction. Mathematical Logic Quarterly 36 (1):67-77.
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