%0 Journal Article
%T THE DISTRIBUTION OF TRUTH DEGREE IN G(o)del LOGIC AND L* LOGIC<br>G(o)del逻辑和L*逻辑中公式的真度分布
%A LI Chengyun
%A ZHANG Xingfang
%A <br>李成允
%A 张兴芳
%J 系统科学与数学
%D 2010
%I 
%X 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$\{ \frac{i}{{(n + 1)!}}|0 \le i \le (n + 1)!,\, i \in N\} $and $\{ \frac{i}{{(n + 1)!}}|0 \le i \le {2^n}(n + 1)!,\, i \in N\}$ respectively. Furthermore, these truth degrees are all rational in $0,1]$. Finally, the distribution of similarity degree and pseudo-metric are defined.
%K G\"{o}del logic system
%K ${L^*}$ logic system
%K logical formula
%K truth degree
%K similarity degree
%K pseudo-metric<br>G\"{o}del逻辑系统
%K $L^\ast
%K $逻辑系统
%K 逻辑公式
%K 真度
%K 相似度
%K 伪距离.
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=F40DE34681BFAC76026CCE5BE19D212A&yid=140ECF96957D60B2&vid=F3090AE9B60B7ED1&iid=F3090AE9B60B7ED1&sid=656BC79BFC7F0F4B&eid=1658FDEF8AE04907&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=0&reference_num=0