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中文摘要：
研究了n值Lukasiewicz命题逻辑系统Ln中公式的真度、理论的发散度与相容度的分布问题.令H={k/nm｜k=0,…,nm;m=1,2,…},利用McNaughton函数证明了对任意k/nm∈H,都有公式A,使得A的真度为k/nm,从而全体公式的真度值之集在[0,1]中稠密.又由真度值之集的稠密性和系统Ln的广义演绎定理证明了理论的发散度取值之集为单位区间[0,1].最后由理论的相容度与发散度的关系得到了理论的相容度取值之集为{0}∪[1/2,1].
英文摘要：
The distributions of truth degrees, divergent degrees and consistency degrees in the nvalued Lukasiewicz propositional logic system Ln are discussed. Letting H=（k/n^m｜k=0,…,n^m ; m=1,2,…）, it is proved by means of McNaughton function that there exists a formula A with the truth degree k/n^m. Thus, the set of all truth degrees of formulas is dense in [0,1]. It is also proved that the set of all divergent degrees of theories is the unit interval [0,1] by the density of truth degrees of formulas and generalized deduction theorem of system Ln. According to the relation between consistency degrees and divergent degrees, it is induced that the set of all consistency degrees of theories is {0}∪[1/2,1].
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