Model theory and closure operators of lattice-valued propositional logic LP(X)

Author

Wang, Xuefang ; Liu, Peishun

Author_Institution

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

Volume

5

fYear

2003

fDate

5-8 Oct. 2003

Firstpage

5010

Abstract

In this paper, model theory properties and closure operators of lattice-valued propositional logic LP(X) are studied. First, graded consistency, graded satisfiability and finite graded consistency, finite graded satisfiability of L-fuzzy sets on LP(X) is defined. Then the properties of the above notions and the relations between them are discussed. Furthermore, under special conditions, graded consistency theorem and compactness theorem on graded consistency are obtained. In addition, by two closure operators (semantic closure operator Con and syntactic closure operator (~C~on)), two families of classical closure operators are given. Finally, two tools for checking compactness properties of two closure operators are provided.

Keywords

formal logic; fuzzy set theory; L-fuzzy sets; closure operators; compactness theorem; finite graded consistency theorem; finite graded satisfiability; graded consistency; graded satisfiability; lattice-valued propositional logic; model theory properties; semantic closure operator; syntactic closure operator; Algebra; Educational institutions; Lattices; Logic functions; Mathematical model; Mathematics; Multivalued logic; Propulsion; Uncertainty;

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.2003.1245777

Filename

1245777