摘要
通常,人们认为Kiyoshi Iséki在20世纪60年代引入的BCI-代数是组合逻辑中BCI逻辑的代数对等物。然而这种广为人知的断言却是有问题的,因为BCI逻辑关于BCI代数是不完备的。在本文中,我们引入一种称为MPE的偏序代数。在MPE中的每个不等式对应BCI逻辑中的一个重言式且反之亦然,从而MPE代数是与BCI逻辑完备的代数类。
BCI-algebras were introduced by Kiyoshi Iseki in 1960＇s and they usually are regarded as algebraic formulations of BCI-system in the combinatory logic. This well-known assertion, however, are problematical in that BCI-logic is not complete with respect to BCI-algebras. In this paper, we introduce a class of partially ordered algebras called MPE-algebras such that each inequality in MPE-algebras correspondences to a theorem of BCI-logic and vice versa. Thus this algebra can be regarded as a class of complete algebraic counterpart of BCI-logic.
出处
《模糊系统与数学》
CSCD
北大核心
2007年第3期60-65,共6页
Fuzzy Systems and Mathematics
