逻辑推理与算术运算合并系统的理论分析  

A Theoretical Analysis of Combining System from Logical Reasoning to Arithmetic

作　　者：周青[1] 伍丽华[2] 

机构地区：[1]中山大学软件研究所,广州510275 [2]中山大学数学与计算科学学院,广州510275

出　　处：《计算机学报》2004年第8期1109-1114,共6页Chinese Journal of Computers

摘　　要：提出一个逻辑推理与算术运算合并系统的形式定义 ,通过合并算子把逻辑推理合并到算术系统中 ,使得在需要解决逻辑推理中的数值计算时 ,直接把问题转化为纯算术系统中的运算 ;文章对该形式系统作了理论上的分析 ,考察了合并系统的语法描述和语义解释 ,对其中的合并算子进行了定义和讨论 ,证明了该系统的可靠性与完备性 .由于该系统基于一阶逻辑 ,所以比Ohlbach和Koehler提出的基于集合的系统[1]A formal system, which combines logical reasoning languages to arithmetic languages through Combining operators, is proposed, so it can be used to solve numeric calculating problems in logical reasoning within pure arithmetic computing systems. The theoretic issue of the system is carefully analysed; the syntactical description and the semantical interpretation of the system are invested; and the notion of combining operators is formally defined and discussed in detail. This system is of the first order logic base and hence it is more powerful than the algorithm proposed by Ohlbach and Koehler in paper . The formal definition of this combining language is given; and the soundness and completeness theorems of this formal system are proved.

关 键 词：合并语言 合并算子 相对可靠性 相对完备性 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]