David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Helena Rasiowa (1963). The Mathematics of Metamathematics. Warszawa, Państwowe Wydawn. Naukowe.
Joseph R. Shoenfield (1967). Mathematical Logic. Reading, Mass.,Addison-Wesley Pub. Co..
Chen Chung Chang (1966). Continuous Model Theory. Princeton, Princeton University Press.
Didier DuBois (1997). Fuzzy Sets and Systems: Theory and Applications. Academic Press, Inc..
C. C. Chang & H. J. Keisler (1976). Model Theory. Journal of Symbolic Logic 41 (3):697-699.
Citations of this work BETA
Giangiacomo Gerla & Roberto Tortora (1990). Fuzzy Natural Deduction. Mathematical Logic Quarterly 36 (1):67-77.
Similar books and articles
Petr Hájek (2001). Fuzzy Logic and Arithmetical Hierarchy III. Studia Logica 68 (1):129-142.
V. Di Gesù, F. Masulli & Alfredo Petrosino (eds.) (2006). Fuzzy Logic and Applications: 5th International Workshop, Wilf 2003, Naples, Italy, October 9-11, 2003: Revised Selected Papers. [REVIEW] Springer.
Petr Hájek & Petr Cintula (2006). On Theories and Models in Fuzzy Predicate Logics. Journal of Symbolic Logic 71 (3):863 - 880.
Andrea Bonarini (ed.) (1996). New Trends in Fuzzy Logic: Proceedings of the Wilf '95, Italian Workshop on Fuzzy Logic, Naples, Italy, 21-22 September 1995. [REVIEW] World Scientific.
Nicholas J. J. Smith (2011). Fuzzy Logic and Higher-Order Vagueness. In Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.), Understanding Vagueness: Logical, Philosophical and Linguistic Perspectives. College Publications 1--19.
L. A. Zadeh (1975). Fuzzy Logic and Approximate Reasoning. Synthese 30 (3-4):407-428.
Merrie Bergmann (2008). An Introduction to Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems. Cambridge University Press.
Charles Grady Morgan & Francis Jeffry Pelletier (1977). Some Notes Concerning Fuzzy Logics. Linguistics and Philosophy 1 (1):79 - 97.
Giangiacomo Gerla (2005). Fuzzy Logic Programming and Fuzzy Control. Studia Logica 79 (2):231 - 254.
Added to index2009-01-28
Total downloads24 ( #124,740 of 1,726,249 )
Recent downloads (6 months)2 ( #289,836 of 1,726,249 )
How can I increase my downloads?