强伪Ockham代数与剩余格

Strong Pseudo-Ockham Algebra and Residual Lattice

引入了伪Ockham代数的概念,讨论了伪Ockham代数与剩余格的关系.进一步引入强伪Ockham代数概念,并给出了它的基本性质.然后,将著名的R0蕴涵和R0算子推广到伪Ockham代数上,证明了添加广义R0蕴涵和广义R0算子后的伪Ockham代数L成为剩余格的充要条件是L为强伪Ockham代数.最后给出注记,以此说明强伪Ockham代数的条件是独立的.

In this paper,the notion of pseudo-Ockham algebras is introduced,and the relation between pseudo-Ockham algebras and residual lattices are investigated.Further,the notion of strong pseudo-Ockham algebras is presented,and its elementary properties are given.The famous R0 implication and R0 operator are developed into pseudo-Ockham algebras,which are called general R0 implication and general R0 operator.The necessary and sufficient condition are proved as follows：a pseudo-Ockham algebras L with general R0 implication and general R0 operator become a residual lattice if and only if L is a strong pseudo-Ockham algebra. Finally,a note is given to show that three conditions of strong pseudo-Ockham algebras are independent.