基于有限格蕴涵代数的格值命题逻辑语法系统  

Syntactic System of Lattice-Valued Propositional Logic Based on Finite Lattice Implication Algebra

作　　者：马骏[1] 高雅[2] 秦克云[3] 徐扬[3] 

机构地区：[1]西南交通大学电气学院,四川成都610031 [2]西南交通大学计算机与通讯工程学院,四川成都610031 [3]西南交通大学理学院,四川成都610031

出　　处：《西南交通大学学报》2004年第1期90-94,共5页Journal of Southwest Jiaotong University

基　　金：国家自然科学基金资助项目(60074014)

摘　　要：以有限格蕴涵代数为真值域,建立了基于有限格蕴涵代数的格值命题逻辑系统;采用公理化的方法,给出了该系统在A水平上的语法导出、证明和协调性等基本定义,并证明了系统的可靠性定理、协调性定理、弱完备性定理和弱演绎定理.By taking finite lattice implication algebra as a truth-value field, a syntactic system of lattice-valued propositional logic based on finite lattice implication algebra was proposed. The basic definitions of syntactic implies, proof and consistency of the system on level A were given axiomatically. Finally, the soundness theorem, consistency theorem, weak complete theorem and weak deduction theorem of the system were proved.

关 键 词：多值逻辑 逻辑代数 格蕴涵代数 语法系统 格值命题逻辑 

分 类 号：O153.1[理学—数学] O141.1[理学—基础数学]