在三值逻辑系统L3^*中引入了对称三值R0函数的概念,在此基础上给出了对称逻辑公式和准对称逻辑公式的定义.研究了在逻辑等价意义下对称逻辑公式的性质,给出了L3^*和经典逻辑系统L中对称逻辑公式之间的关系及其计数问题,证明了n元对称逻辑公式占全体n元逻辑公式的比例随n的增大而趋向于零,且全体对称逻辑公式的真度之集却在[0,1]中稠密.然而全体对称逻辑公式之集是逻辑度量空间中的无处稠密集.
In three-valued logic system L3^*, the concept of symmetric three-valued R0 function is proposed, and the concepts of symmetric logic formulas and pseudo-symmetric logic formulas are given. The properties of symmetric logic formulas under logically equivalence are studied. The relationship of symmetric logic formulas in L3^* and classical logical system L, and the number of them are given. It is proved that the ratio of the number of symmetric formulas with n atoms over