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.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
References found in this work BETA
Citations of this work BETA
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.
Similar books and articles
Fuzzy Logic and Applications: 5th International Workshop, Wilf 2003, Naples, Italy, October 9-11, 2003: Revised Selected Papers. [REVIEW]V. Di Gesù, F. Masulli & Alfredo Petrosino (eds.) - 2006 - Springer.
On Theories and Models in Fuzzy Predicate Logics.Petr Hájek & Petr Cintula - 2006 - Journal of Symbolic Logic 71 (3):863 - 880.
New Trends in Fuzzy Logic: Proceedings of the Wilf '95, Italian Workshop on Fuzzy Logic, Naples, Italy, 21-22 September 1995'. [REVIEW]Andrea Bonarini (ed.) - 1996 - World Scientific.
Fuzzy Logic and Higher-Order Vagueness.Nicholas J. J. Smith - 2011 - In Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.), Understanding Vagueness: Logical, Philosophical and Linguistic Perspectives. College Publications. pp. 1--19.
An Introduction to Fuzzy Logic for Practical Applications.Kazuo Tanaka - 1997 - Springer.
Added to index2009-01-28
Total downloads32 ( #159,614 of 2,164,654 )
Recent downloads (6 months)1 ( #348,012 of 2,164,654 )
How can I increase my downloads?