Abstract: The theory of Г-reduction in n-valued £ukasiewicz propositional logic is introduced，the formal context of the propositional set Г is introduced and investigated.Several ways to determine the Г-reduction are studied by investigating the relationship between Г and their subsets.The reduction of propositional set Г in £ukasiewicz infinite valued logic can be reduced to n-valued £ukasiewicz propositional logic.

Key words: £, ukasiewicz propositional logic, complete theorem, Г-reduction, formal context

摘要： 在n值£ukasiewicz命题逻辑中提出了命题集Г的约简理论，引入由命题集Г所诱导的形式背景的概念，从Г及其子集的关系出发给出了n值命题逻辑中有限命题集Г约简的判定定理以及求Г约简的方法。说明了无穷值£ukasiewicz命题逻辑中命题集Г的约简可转化为n值情形。

关键词: £, ukasiewicz命题逻辑, 完备性定理, Г约简, 形式背景