Godel逻辑和L*逻辑中公式的真度分布

李成允;张兴芳

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (10) : 1417-1428.

PDF(343 KB)
PDF(343 KB)
系统科学与数学 ›› 2010, Vol. 30 ›› Issue (10) : 1417-1428. DOI: 10.12341/jssms09279
论文

Godel逻辑和L*逻辑中公式的真度分布

    李成允, 张兴芳

作者信息 +

The Distribution of Truth Degree in Godel Logic and L* Logic

    LI Chengyun, ZHANG Xingfang
Author information +
文章历史 +

摘要

研究了G\"{o}del逻辑系统和L逻辑系统中公式的真度的分布情况. 结果表明在G\"{o}del逻辑系统和L逻辑系统中含有n个原子命题的公式(n元公式)的真度集分别为{i(n+1)!|0i(n+1)!,iN}{i(n+1)!|0i2n(n+1)!,iN}. 进而得到了G\"{o}del逻辑系统和L逻辑系统中公式的真度集均为[0,1]上的有理数集. 最后,还给出了两系统中公式的相似度,伪距离的分布情况.

Abstract

In this paper, the distribution of truth degree in G\"{o}del logic system and L logic system is studied. It is shown that the sets of the truth degrees of n-ary formulas in the G\"{o}del logic system and L logic system are
{i(n+1)!|0i(n+1)!,iN}and {i(n+1)!|0i2n(n+1)!,iN} respectively. Furthermore, these truth degrees are all rational in [0,1]. Finally, the distribution of similarity degree and pseudo-metric are defined.

关键词

G\"{o}del逻辑系统 / L逻辑系统 / 逻辑公式 / 真度 / 相似度 / 伪距离.

Key words

G\"{o}del logic system / L logic system / logical formula / truth degree / similarity degree / pseudo-metric.

引用本文

导出引用
李成允 , 张兴芳. Godel逻辑和L*逻辑中公式的真度分布. 系统科学与数学, 2010, 30(10): 1417-1428. https://doi.org/10.12341/jssms09279
LI Chengyun , ZHANG Xingfang. The Distribution of Truth Degree in Godel Logic and L* Logic. Journal of Systems Science and Mathematical Sciences, 2010, 30(10): 1417-1428 https://doi.org/10.12341/jssms09279
中图分类号: 03B50    03B52   
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