一阶逻辑中不含相同谓词符号公式的真度研究  

Research on the Truth Degree of First-Order Logic Without the Same Predicate Symbol Formula

作　　者：王波 惠小静[1] 鲁星 WANG Bo;HUI Xiaojing;LU Xing(College of Mathematics and Computer Science,Yan’an University,Yan’an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《贵州大学学报（自然科学版）》2022年第5期29-34,共6页Journal of Guizhou University:Natural Sciences

基　　金：国家自然科学基金资助项目(11471007,61763045)。

摘　　要：自真度概念被提出以来,命题逻辑的计量化得到了广泛的关注和发展。谓词逻辑的相关研究是一个难点,其中一阶逻辑的公理化真度以及程度化才刚刚起步。从文字的完全闭包及其合取的公理化真度出发,首先,证明了不含相同谓词符号广义合取式的真度计算公式;其次,通过合取范式的结构特点,证明了合取范式的真度计算公式;再次,证明了2个公式的逻辑等价性。所得结果为后续公理化真度性质研究奠定了基础。Since the concept of truth degree was put forward,the quantization of propositional logic has received extensive attention and been developed greatly.The related research of predicate logic is a difficult point,among which the research on axiomatic truth degree and degree of first-order logic is just beginning.Based on the complete closure of words and the axiomatic truth degree of their conjunction,this essay first proves the truth degree calculation formula of the generalized conjunction which does not contain the same predicate symbol,then proves the truth degree calculation formula of the conjunctive normal form through its structural characteristics,and finally proves the logical equivalence of the two formulas.The results will lay a foundation for the further study of axiomatic truth properties.

关 键 词：一阶逻辑 公式真度 合取范式 逻辑等价 

分 类 号：O141.1[理学—数学]