概念格在二值命题逻辑命题集约简中的应用

The Application of Concept Lattice Theory in the Reduction of the Proposition Set in Two-Valued Propositional Logic

概念格的属性约简理论和命题逻辑系统中命题集的约简理论似乎是独立发展的两个研究分支,本文在二值命题逻辑中引入由命题集Γ所诱导的形式背景的概念,并基于此建立了概念格;在二值命题逻辑中提出了命题集Γ的约简理论,即在保持Γ推理能力不变的前提下对Γ中的成员进行约简;运用概念格的方法从Γ及其子集的关系出发给出了Γ约简的判定定理以及求Γ约简的方法.

Attribute reduction theory and the F-reduction theory in propositional logic arose in two rather different fields.In this paper, by introducing the formal context induced by Γ, the mutual relationship between them are investigated, then the concept lattices are built based on the formal context induced by Γ. The main purpose of this paper is to introduce the theory of Γ-reduction in two-valued propositional logic,which is the minimal set Γ0 lohtain in Γ such that D（Γ0） = D（Γ） .Several ways to determine the Γ-reduction are studied by investigating the relationship between Γ and their subsets; an algorithm to explore the reduction by concept lattice theory is given.