Based on the production of other researchers such as professor xu yang and professor qin keyun , this paper discusses the structure and properties of lattice implication algebra , tautologies in some lattice - valued systems , automated reasoning methods , lattice - valued prepositional logic system 本文的工作是在徐扬教授、秦克云教授等研究成果的基础上，对格蕴涵代数的性质、结构、格值命题逻辑系统中的重言式、自动推理方法、格值命题逻辑系统等进行了一些研究。
Pointed out a family of congruence relations induced by a fuzzy filter of a lattice implication algebra and proved that this family of congruence relations is a complete chain , and then discussed the relations between the quotient lattice implication algebras induced by this family of congruence relations . 3 . discussed the property of fuzzy li - ideals , pointed out a family of congruence relations induced by a fuzzy li - ideal of a lattice implication algebra and proved that this family of congruence relations is a complete chain , and then discussed the relations between the quotient lattice implication algebras induced by this family of congruence relations 对模糊li -理想的性质作了进一步的研究，证明了利用格蕴涵代数上的一个模糊li -理想可以得到格蕴涵代数上的一簇同余关系，证明了这簇同余关系构成一个完备链，在此基础上讨论了这簇同余关系诱导的格蕴涵商代数之间的关系，并用一个例子说明了这簇同余关系的确可以包含更多的同余关系。
Fuzzy logic is studied with algebraic tools in this paper . a kind of algebraic abstract of fuzzy logic , implication algebra on a partial ordered set , is given . the relations between implication algebra and other algebraic structures , such as mv - algebra and heyting algebra etc . , and the filter and the structure of implication algebra on a partial ordered set are studied 本文的目的是使用代数工具对模糊逻辑进行研究，给出模糊逻辑的一类代数抽象，即偏序集上的蕴涵代数，研究偏序集上蕴涵代数与其它代数结构，如mv -代数， heyting代数之间的关系，以及偏序集上蕴涵代数的滤子与其结构等。
