Computer Science

Computer Science ›› 2021, Vol. 48 ›› Issue (11A): 669-671.doi: 10.11896/jsjkx.210200012

• Interdiscipline & Application • Previous Articles     Next Articles

Study on Axiomatic Truth Degree in First-order Logic

HAO Jiao, HUI Xiao-jing, MA Shuo, JIN Ming-hui   

  1. School of Mathematics and Computer Science,Yan'an University,Yan'an,Shaanxi 716000,China
  • Online:2021-11-10 Published:2021-11-12
  • About author:JIANG Hua-nan,born in 1988,master.His main research interests include high-performance computing,robotics and finite element simulation.
    ZHANG Shuai,born in 1986,Ph.D.His main research interests include robotics and CFD simulation.
  • Supported by:
    National Natural Science Foundation of China(11471007,61763045),National Innovation and Entrepreneurship Training Program for College Students(201910719023) and Postgraduate Education Reform Research Project of Yan'an University(YDYJG2018022,YDYJG2017024).

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Abstract: 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.

Key words: First-order logic, Logically valid formula, Prenex normal form, Satisfiability, Theorem

CLC Number: 

  • O141
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