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.
出处
《计算机学报》
EI
CSCD
北大核心
2004年第8期1109-1114,共6页
Chinese Journal of Computers
关键词
合并语言
合并算子
相对可靠性
相对完备性
combined language
combined operators
relative soundness
relative completeness
