【摘要】 偏序集上的蕴涵代数是取值于偏序集上的蕴涵逻辑联结词的一种代数抽象.以偏序集上蕴涵代数中由蕴涵算子引入的逻辑运算t-余范为工具,讨论了偏序集上蕴涵代数的一些性质,然后引入了偏序集上蕴涵代数的素滤子的概念,讨论了素滤子在一定条件下的性质,并给出了一个MP滤子成为素滤子的条件.更多还原

【Abstract】 Implication Algebra on partially ordered set is a kind of algebraic abstraction of implicative connection in logic systems which values in a partially ordered set.In this paper, some properties of Implication Algebra on partially ordered set are obtained with the tool of t-conorm which is introduced by the implication operator in implication algebra.Then the concept of prime filter of this implication algebra is introduced.Properties of prime filter are discussed under certain conditions and a condition is given when a MP Alter comes to be a prime filter.更多还原