Syntax theory of finite lattice-valued propositional logic

被引：2
|
作者：
Pan XiaoDong
Meng Dan
Xu Yang
机构：
[1] School of Mathematics, Southwest Jiaotong University, Sichuan
[2] Intelligent Control Development Center, Southwest Jiaotong University, Sichuan
[3] School of Economics Information Engineering, Southwestern University of Finance and Ecnomics, Sichuan
来源：
SCIENCE CHINA-INFORMATION SCIENCES | 2013年 / 56卷 / 08期
基金：
中国国家自然科学基金;
关键词：
Lattice-valued propositional logic; syntax theory; inference rule; generalized deduction theorem; completeness; FUZZY-LOGIC;
D O I：
10.1007/s11432-012-4580-0
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we establish the graded syntax theory of lattice-valued propositional logic based on finite lattice implication algebras, define the notions of syntactic consequence operation and formal proof, and develop a kind of graded finite lattice-valued propositional calculus. By generalizing classic provable equivalence relation, we present a kind of generalized provable equivalence relation, and establish the corresponding quotient algebra. Finally, we establish the generalized deduction theorem by syntactic consequence operation, and establish the completeness in Pavelka's sense based on finite chains.
引用
收藏
页码：1 / 12
页数：12
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