基于BL系统的演绎系统集代数的剩余格属性  

Properties of residuated lattice of deduction systems set algebra in BL system

作　　者：梁颖 崔艳丽[1] 吴洪博[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710119

出　　处：《山东大学学报（理学版）》2017年第11期65-70,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(61572016;11531009;61673250)

摘　　要：在命题逻辑系统BL中提出了演绎系统的概念,并且给出了由F(S)的子集生成演绎系统的方法,证明了命题逻辑系统BL中演绎系统和结论之集的同一性;其次,在命题逻辑系统BL中证明了在包含偏序关系下所有演绎系统构成的集族D(F)中上,下确界的存在性;最后,在D(F)中定义了二元运算∧,∨,*,→,证明了集代数(D(F),∧,∨,*,→,0,1)是满足可除性的完备剩余格。Firstly,the concept of deduction system of the basic propositional logic system BL is defined,and the method generating deduction system from a subset of formula set F（ S） is obtained,and the identity of deduction system and conclusions set is proved. Secondly,in propositional logic system BL the existence of supremum and infimum is proved in family D（ F） consisting of all deductive systems with partial order relation of =; Moreover,binary operations ＊,→ are defined in family D（ F）,and it is proved that set algebra（ D（ F）,∧,∨,＊,→,⊥,F（ S）） is a complete residuated lattice satisfying divisibility.

关 键 词：模糊逻辑 命题逻辑系统BL 演绎系统 剩余格 可除性 

分 类 号：O141[理学—数学]