First-order fuzzy logic

Studia Logica 46 (1):87 - 109 (1987)
  Copy   BIBTEX


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.



    Upload a copy of this work     Papers currently archived: 86,592

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library


Added to PP

68 (#205,800)

6 months
5 (#193,533)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Fuzzy logic and arithmetical hierarchy, II.Petr Hájek - 1997 - Studia Logica 58 (1):129-141.
Approximate Reasoning Based on Similarity.M. Ying, L. Biacino & G. Gerla - 2000 - Mathematical Logic Quarterly 46 (1):77-86.
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.

Add more citations

References found in this work

Mathematical logic.Joseph R. Shoenfield - 1967 - Reading, Mass.,: Addison-Wesley.
The mathematics of metamathematics.Helena Rasiowa - 1963 - Warszawa,: Państwowe Wydawn. Naukowe. Edited by Roman Sikorski.
Model Theory.Gebhard Fuhrken - 1976 - Journal of Symbolic Logic 41 (3):697-699.
Continuous model theory.Chen Chung Chang - 1966 - Princeton,: Princeton University Press. Edited by H. Jerome Keisler.

Add more references