Graded consequence relations of lattice-valued propositional logic LP(X)

Author

Wang, Xuefang ; Meng, Dan ; Xu, Yang ; Qin, Keyun

Author_Institution

Dept. of Appl. Math., Southwest Jiaotong Univ., Chengdu, China

Volume

5

fYear

2003

fDate

5-8 Oct. 2003

Firstpage

5004

Abstract

In this paper, graded consequence relations in lattice-valued propositional logic LP(X) are studied. First, valuation sets in LP(X) are defined and their properties are discussed. Based on these, a graded semantic consequence relation between an L-fuzzy set of formulae and a formula is specified. Accordingly, graded syntactic consequence relation is also given. It is demonstrated that these two classes of graded consequence relations are generalizations of counterparts in classical logic and even in LP(X). Furthermore, graded soundness problem, graded completeness theorem and graded deduction theorem for them are given and proven.

Keywords

formal logic; set theory; L-fuzzy set; classical logic; graded completeness theorem; graded consequence relations; graded deduction theorem; graded semantic consequence relation; graded soundness problem; graded syntactic consequence relation; lattice-valued propositional logic; valuation sets; Algebra; Cost accounting; Fuzzy sets; Lattices; Logic functions; Mathematics;

fLanguage

English

Publisher

ieee

Conference_Titel

Systems, Man and Cybernetics, 2003. IEEE International Conference on

ISSN

1062-922X

Print_ISBN

0-7803-7952-7

Type

conf

DOI

10.1109/ICSMC.2003.1245776

Filename

1245776