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

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.