• 论文 •

### 离散数学中与量词有关的推理规则

1. 北京航空航天大学 计算机科学与工程系
• 收稿日期:1998-12-11 发布日期:2010-11-19
• 作者简介:何自强(1943-),男,北京人,副教授,100083,北京.

### Rules of Inference for Quantifiers in Discrete Mathematics

HE Zi-qiang

1. Beijing University of Aeronautics and Astronautics,Dept. of Computer Science and Engineering
• Received:1998-12-11 Published:2010-11-19

Abstract: The conditions satisfied for the existential instantiation and the universal generalization in the natural deduction system are described clear, whereas they are described rather vaguely in many textbooks on discrete mathematics. Contrasting with that the existential instantiation in some textbooks is used only for formulas without free variables, according to the condition we given, it may be also used for formulas with free variables and the ability to reason has increased. Introducing the equivalence between interpretations and the equivalence between assignments with respect to a set of formulas, it is proved that the system is sound, that is, in a proof, the conclusion is a logical consequence of the premises.