摘要
研究了逻辑系统W ,W ,Wk 中F(S)的分划问题及其升级算法的一些性质 .分别在W ,W ,Wk 中利用可达广义重言式的概念给出F(S)的一个关于 同余的分划 ,并证明了 :在W (W )中 ,重言式不可能由对非重言式利用升级算法得到 ;在Wk中 ,对任一公式最多进行 k + 12 次升级算法即可得到重言式 .
Partitions of F(S) and properties of its upgrade algorithm are studied. And congruence partitions about on F(S) have been given in logic system W,W,W k , respectively by using the concepts of accessible generalized tautology and α contradiction. It is proved that in logic system W,W, tautologies can not be get by using upgrade algorithm to non tautologies within finite many times. In logic system W k , tautologies can be get by using the upgrade algorithm to an arbitrary formula of F(S) at most k+12 times.
出处
《陕西师大学报（自然科学版）》
CSCD
北大核心
2000年第2期12-17,共6页
Journal of Shaanxi Normal University(Natural Science Edition)
关键词
命题演算
可达α^+-重言式
升级算法
逻辑系统
propositional calculus
accessible α + tautology
partition
upgrade algorithm
α contradiction
