THE DISTRIBUTION OF TRUTH DEGREE IN G(o)del LOGIC AND L* LOGIC
G(o)del逻辑和L*逻辑中公式的真度分布

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.