Title :
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
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;
Conference_Titel :
Systems, Man and Cybernetics, 2003. IEEE International Conference on
Print_ISBN :
0-7803-7952-7
DOI :
10.1109/ICSMC.2003.1245777
