对称逻辑公式在L*3逻辑度量空间中的分布

摘要

In three-valued logic system L*3 , 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 L*3 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 the number of all formulas with n atoms converges to zero when n tends to infinite.It is also proved that the set of truth degrees of symmetric logic formulas is dense in [0,1].On the other hand, the set consisting of all symmetric logic formulas is a nowhere dense set in the logic metric space.%在三值逻辑系统L*3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L*3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.