On the Logical Basis of Approximate Reasoning

In this paper, we give arguments for an idea that many-valued fuzzy logic should stand behind the theory of approximate reasoning. We outline a general theory of approximate reasoning based on first-order fuzzy logic. The notions of a translation rule and a rule of inference are defined. It is demonstrated that approximate reasoning can be understood to be a derivation of a special kind of fuzzy sets of formulae using sets of proofs from a fuzzy set of special axioms.

[1]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[2]  Lotfi A. Zadeh,et al.  PRUF—a meaning representation language for natural languages , 1978 .

[3]  L. Zadeh A COMPUTATIONAL APPROACH TO FUZZY QUANTIFIERS IN NATURAL LANGUAGES , 1983 .

[4]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[5]  Brian R. Gaines,et al.  Fuzzy reasoning and its applications , 1981 .

[6]  Richard Bellman,et al.  Local and fuzzy logics , 1996 .

[7]  E. H. Mamdani,et al.  A GENERAL APPROACH TO LINGUISTIC APPROXIMATION , 1979 .

[8]  Witold Pedrycz,et al.  Fuzzy Sets and T-Norms in the Light of Fuzzy Logic , 1988, Int. J. Man Mach. Stud..

[9]  Lotfi A. Zadeh,et al.  Quantitative fuzzy semantics , 1971, Inf. Sci..

[10]  James C. Bezdek,et al.  Analysis of fuzzy information , 1987 .

[11]  Vilém Novák On the syntactico-semantical completeness of first-order fuzzy logic. II. Main results , 1990, Kybernetika.

[12]  V. Novák Fuzzy sets and their applications , 1989 .

[13]  Madan M. Gupta,et al.  Fuzzy Computing: Theory, Hardware, and Applications , 1988 .

[14]  Vilém Novák On the syntactico-semantical completeness of first-order fuzzy logic. I. Syntax and semantics , 1990, Kybernetika.

[15]  B. R. Gaines,et al.  Machine learning and uncertain reasoning , 1990 .

[16]  Madan M. Gupta,et al.  Fuzzy Logic in Knowledge-Based Systems, Decision and Control , 1988 .