关于格蕴涵代数的几点注记

Some Remarks on Lattice Implication Algebra

给出了一般(2,1,0,0)型代数(L,→, ,0,1)成为格蕴涵代数的充要条件,证明了在有限链及非全序四元格上只有一种格蕴涵代数,且不存在非全序五元格蕴涵代数,为进一步讨论由语言真值构成的格蕴涵代数的结构提供了条件.

A sufficient and necessary consition for a general (2,1,0,0) type algebra (L,→,*,0,1) to be a lattice implication algebra is presented. It is proved that in a finite chain and in a nonlinear fourelement lattice there exists only one lattice implication algebra, but no implication algebra in a nonlinear fiveelement lattice. This provides the foundation for further study of the structure of lattice implication algebra that is composed of linguistic true values. 