关于格上蕴涵代数及其对偶代数

On Implication Algebras Based on Lattices and Their Dual Algebras

中文关键词:  FI代数  格蕴涵代数  MV代数  （弱）R₀代数  对偶代数

英文关键词:FI algebra  lattice implication algebra  MV algebra  （weak）R₀ algebra  dual algebra.

中文摘要:

      给出了格蕴涵代数、MV代数、R₀代数等一些格上蕴涵代数之间的关系,并建立了它们的对偶代数.其结果描述了这些代数内部结构的特征,同时也为从语义的角度进一步研究格值逻辑系统提供了一个新的途径.

英文摘要:

      This paper gives out that the relationship among lattice implication algebras, MV algebras, R₀ algebras and other implication algebras based on lattices, and their dual algebras are established. Those results describe the characterizations of interior structures of those algebras, and also offer a new way for further researching lattice-valued logic systems from the semantics.