命题演算两个推理系统的等价性

J4 ›› 2013, Vol. 35 ›› Issue (9): 104-109.

命题演算两个推理系统的等价性

宋方敏,殷熙尧

（南京大学计算机科学与技术系，江苏南京 210023）

出版日期:2013-09-25 发布日期:2013-09-24
基金资助:
江苏省自然科学基金资助项目（2011560）

On the equivalence between deduction systems
H and G in propositional calculus

SONG Fangmin，YIN Xiyao

（Department of Computer Science and Technology，Nanjing University,Nanjing 210023，China）

Online:2013-09-25 Published:2013-09-24

摘要/Abstract

摘要：

首先介绍命题演算的Gentzen型系统G，然后给出一个命题演算的永真推理系统H，最后证明一个命题在G中可证当且仅当它在H中可证，从而G与H是等价的。关键词：符号逻辑;命题演算;推理系统

Abstract:

Firstly, a deduction system G for the propositional calculus in the style of Gentzen is introduced. Secondly, a deduction system H for the propositional calculus in the style of Hilbert is proposed. Thirdly, it is proved that G is equivalent to H in the sense that G and H have the same set of theorems.

Key words: symbolic logic；propositional logic；deduction system

宋方敏,殷熙尧. 命题演算两个推理系统的等价性[J]. J4, 2013, 35(9): 104-109.

SONG Fangmin，YIN Xiyao. On the equivalence between deduction systems
H and G in propositional calculus [J]. J4, 2013, 35(9): 104-109.