形式演绎系统L~*中封闭理论的性质及其应用

The Properties of Closed Theories with Its Application in the Formal Deductive System L~*

本文在模糊命题演算的形式演绎系统L^＊中引入了封闭理论的概念，讨论了封闭理论的基本性质，并利用封闭理论给出了形式演绎系统L^＊的基于公式集的完备性的证明．首先，在形式演绎系统L^＊中引入了封闭理论的概念，给出了理论封闭化扩张的方法；其次，在形式演绎系统L^＊中引入了完全封闭理论的概念，证明了满足相关条件的完全封闭理论的存在性；第三，对形式演绎系统L^＊中的封闭理论确定的同余关系性质进行了讨论，在公式集中引入了强同余关系的概念，给出了封闭理论和强同余关系相互决定的方法；第四，在形式演绎系统L^＊中证明了封闭理论型L^＊-Lindenbaum代数是R0代数，并且封闭理论型L^＊-Lindenbaum代数是全序的当且仅当封闭理论是完全的；最后，利用完全封闭理论型L^＊-Lindenbaum代数完成了形式系统L^＊完备性的证明，并改进了原有的结果．

In the Formal Deductive System L^＊ of Fuzzy Propositional Calculus, the notion of closed theory is introduced and its properties are investigated. Furthermore, the completeness of Formal Deductive System L^＊ is proved through closed theory based on formula set F（S）. At first, in the formal.deductive system L^＊, a concept of closed theory is introduced, and a method for extending theories to closed theories is given; at second, in the formal deductive system L^＊, a concept of total closed theory is introduced, and the existence of a total closed theory satisfying relevant conditions is proved; at third, in the formal deductive system L^＊, the properties of congruence relations determined by closed theories are investigated, a concept of strong congruence relations is introduced to formulas set F（S）, and methods of changing each other between strong congruence relations and closed theories are revealed; at fourth, in the formal deductive system L^＊, it is proved that closed theory style L^＊-Lindenbaum algebras determined by closed theories are R0-algebras, and a closed theory-L^＊-Lindenbaum algebra is linear if and only if a closed theory is total; at last, the completeness of the formal deductive system L^＊ is accomplished by making use of total closed theory style L^＊-Lindenbaum algebras, and the results obtained before have been improved.