摘要
一阶逻辑是公理系统的标准形式逻辑之一,其中包含的程度化推理等研究内容,是一个研究热点也是难点。文中从一阶逻辑演算的语义理论出发,利用可满足性及完备性定理研究了一阶逻辑中公理化真度。首先给出并、交运算可满足性的定义,其次说明了两个特殊公式与逻辑有效公式以及定理的关系,最后得出与公式等价的前束范式。上述结果将为谓词逻辑程度化研究做准备。
First-order logic,as one of the standard formal logics of axiomatics systems,contains the research contents such as degree reasoning,which is a hot and difficult point.Based on the semantic theory of first-order logic calculus,this paper studies the axiomatic truth degree of first-order logic by using the satisfiability and completeness theorem.Firstly,the definition of the satisfiability of union and intersection operation is given.Secondly,the relationship between two special formulas and logical effective formulas and theorems is explained.Finally,the prenex normal form equivalent to formulas is obtained.The above results will prepare for the research of predicate logic degree.
作者
郝娇
惠小静
马硕
金明慧
HAO Jiao;HUI Xiao-jing;MA Shuo;JIN Ming-hui(School of Mathematics and Computer Science,Yan’an University,Yan’an,Shaanxi 716000,China)
出处
《计算机科学》
CSCD
北大核心
2021年第S02期669-671,712,共4页
Computer Science
基金
国家自然科学基金项目(11471007,61763045)
国家级大学生创新创业训练计划项目(201910719023)
延安大学研究生教改研究项目(YDYJG2018022,YDYJG2017024)。
关键词
一阶逻辑
逻辑有效公式
可满足性
定理
前束范式
First-order logic
Logically valid formula
Satisfiability
Theorem
Prenex normal form
