【摘要】 首先引入偏序集上的基础蕴涵代数和蕴涵代数的概念,得到了偏序集上基础蕴涵代数和蕴涵代数的若干基本性质;给出了偏序集上基础蕴涵代数和蕴涵代数之偏序集的特征刻画,又从格论的角度出发;给出了偏序集上基础蕴涵代数和蕴涵代数之偏序集的一些格的性质以及蕴涵代数之偏序集成为格的一些条件.更多还原

【Abstract】 The concept of a basic implication algebra and an implication algebra on a partial ordered set are obtained by studying the conditions that the implicative operator in a logic system should be satisfied.The basic properties with different conditions and the characterizes of the implication algebra are given. The iff conditions for a basic implication algebra to be a implication algebra are discussed. The relations between the basic implication algebra and the implication algebra are gained. From the view of lattices, some lattice properties of the implication algebra and the conditions under which a implication algebra is a lattice are found.更多还原