Abstract: Triangular norms and implication operators are interdependent and basic operators in logic algebras, but WBR0-algebras are logic algebras that are defined on general set only using implication operators. The WBR0-algebras have been studied in depth. The form of Pt-norm（t-norms on posets） on WBR0-algebras is given; the equivalence representation of WBR0-algebras has been obtained on posets through Pt-norms and implication operators; it is proved that the binary operation [⊕] in the original definition of the WBR0-algebras is the Ps-norm（s-norm on posets） of  WBR0-algebras. The results of this paper have positive reference value to the further study of WBR0-algebras and the relevant logic algebras.

Key words: logic algebra, WBR0-algebra, poset, Pt-norm, Ps-norm

摘要： 三角模和蕴涵算子是逻辑代数中的一对相互关联的基本算子，而WBR0-代数是仅以蕴涵算子为基本算子定义于一般集合上的逻辑代数。对WBR0-代数进行了再研究。给出了WBR0-代数的Pt-模（偏序集上的t-模）的表现形式；在偏序集上通过 Pt-模结合蕴涵算子给出了WBR0-代数的表示形式；证明了WBR0-代数原始定义中的二元运算[⊕]是WBR0-代数的Ps-模（偏序集上的s-模）。结果对进一步探讨WBR0-代数及其相关的逻辑代数有积极的参考价值。

关键词: 逻辑代数, WBR0-代数, 偏序集, Pt-模, Ps-模