研究蕴涵格的性质及其结构。借助数学软件给出8阶及以下蕴涵格的完全分类,说明了真蕴涵格与优蕴涵格的存在性,并纠正了多个文献中关于蕴涵格的一些错误结论。同时,引入局部有限蕴涵格和次结合蕴涵格的概念,证明了局部有限蕴涵格是优蕴涵格。
The properties and structure of implication lattices are investigated. The classification of implication lattices with 8(and lower) orders is solved by Mathematica programs,and some mistakes of references are pointed out.Moreover,the notions of locally finite implication lattice and sub-associative implication lattice are introduced,some properties of them are discussed,and the following result is proved: every locally finite implication lattice is well implication lattice.