命题演算系统L~*中的Boole型理论

Boolean theory in the propositional logic system L~*

研究了命题演算系统L*中一类特殊理论——Boole型理论的内部结构.从语构、语义两个方面分别给出了一个理论为Boole型理论的几个充要条件.利用Boole型理论在全体公式集F(S)中引入了同余关系,证明了商代数是Boole代数,并找到了TH(L)为最小的Boole型闭理论.

To study the characterizations of a special theory-Boolean theory in the propositional logic system f. Some necessary and sufficient conditions for a theory to be Boolean are obtained from two aspects of syntactics and semantics, respectively. By means of Boolean theory a congruence relation on F（S） is defined and it is proved that the corresponding quotient algebra is a Boolean algebra. Moreover, the minimal closed Boolean theory TH（L） is given.