中介命题扩张系统MP*推理规则集的简化

摘要

中介系统是以中介原则为基础，以中介逻辑演算为工具的一种新的数学理论系统。狭义的中介系统仅指中介逻辑ML，它由中介命题系统MP及其扩张系统MP*、中介谓词演算系统MF及其扩张系统MF*，以及带等词的中介谓词演算系统ME*组成。本文讨论中介命题扩张系统MP*推理规则集SA的简化。对于一个形式系统的推理规则而言，在保证其相容性、完备性和独立性的前提下，形式系统的推理规则集越简洁，使用越方便。本文对规则集SA进行了简化，方法是：如果SA中某条规则可由SA中其余规则推导出来，并且推导过程所用形式定理的证明未用到此规则，则此规则可被简化而不影响SA的效力。作者简化了SA中8条规则并且证明简化后的规则集与原规则集SA等价。%The medium system is a new mathematical theoretical system, in which the medium principle is used as base and the medium logic calculus as a means. The narrow medium system only consists of the medium propositional system MP and its expansion MP* ,the medium predicate calculus system MF and its expansion MF* and the system ME*. This paper discusses the simplicity of the system MP＇s inference rules SA. On the premise of compatibility,comperfection and independence,the more brief inference rules of the formal system make the rules more convenient. So the rules SA is simplified. We can infer a rule of SA from the others of SA and the proof of the formal theorem does not involve the rule, then we can omit it from SA without discending SA＇s function. The paper simplifies 8 rules of SA and proves that the simplified rules of SA are equivalent to the rules SA.