Gdel逻辑系统中的广义重言式理论

Theory of Generalized Tautology in Godel’s Logic System

本文将王国俊教授在逻辑系统 W,W,Wk中的广义重言式理论进行推广并应用到了Goo¨ del逻辑系统 G,G,Gn 中。主要结果是 :在逻辑系统 G,G中 ,重言式不可能由对非重言式进行有限次升级算法得到 ;在逻辑系统 Gn 中 ,对任一公式最多进行 n次升级算法即可得到重言式 ;利用可达广义重言式概念和 α-矛盾式概念分别在 G,G,Gn 中给出了 F( S)的一个关于 同余的分划。

Theory of generalized tautology in Logic system ,W,W k is generalized, both of which is introduced by Professor Wang Guojun, and an application of it is made to Go o ¨del's Logic System.The main results are:In logic system ,G,tautologies can not be get by using upgrade algorithm to non tautologies within finite many times;In logic system G n,tautologies can be get by using upgrade algorithm to an arbitrary formula of F(S) at most n times; Congruence partitions about  on F(S) have been given in logic system ,G,G n , respectively by utilizing the concepts of accessible generalized tautology and α contradiction.