摘要
将王国俊教授于 1997年以来在逻辑系统 W、W、Wk中引入的广义重言式理论加以扩充、推广 ,引入α 矛盾式等概念并应用于G¨odel逻辑系统 G、G、Gn中 ,得到了 (1)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 ;(2 )在逻辑系统Gn中 ,对任一公式最多进行n - 1次升级算法即可得到重言式 ;(3)在逻辑系统Gn 中 ,C(Gn) ,in- 1-C(Gn) ,in- 1-T(Gn) ,T(Gn) ｜i∈ { 1,2 ,… ,n- 2 }是F(S)的一个关于同余的分划 ;在逻辑系统 G中 ,C( G) ,(12 ) - -C( G) ,12 -C( G) ,[1- ]-C( G) ,[0 +]-T( G) ,12 -T( G) ,(12 ) +-T( G) ,T( G)是F(S)的一个关于同余的分划。 (4)在 [0 ]-T(R) (R ∈ { G ,G ,Gn} )
Theory of generalized tautology in logic system ,W,W k is generalized, both of which was introduced in 1997 by professor Wangguo-jun,and an application of it is made to Gdel'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-1 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
出处
《工程数学学报》
CSCD
北大核心
2001年第4期61-68,共8页
Chinese Journal of Engineering Mathematics
