电子学报 ›› 2017, Vol. 45 ›› Issue (11): 2656-2662.DOI: 10.3969/j.issn.0372-2112.2017.11.012

• 学术论文 • 上一篇    下一篇

Goguen公理化扩张系统的Γ-k随机真度理论及性质

惠小静, 高晓莉, 朱乃调   

  1. 延安大学数学与计算机科学学院, 陕西延安 716000
  • 收稿日期:2016-06-23 修回日期:2016-12-19 出版日期:2017-11-25
  • 通讯作者: 惠小静
  • 作者简介:高晓莉,女,1992年出生,陕西延安人.现为延安大学数学与计算机科学学院在读研究生,研究方向为数理逻辑与不确定性推理.E-mail:951402445@qq.com;朱乃调,女,1990年出生,陕西米脂人.现为延安大学数学与计算机科学学院在读研究生,研究方向为数理逻辑与不确定性推理.E-mail:792266404@qq.com
  • 基金资助:
    国家自然科学基金(No.11471007); 陕西省自然科学基金(No.2014JM1020); 延安大学研究生创新基金(No.YCX201612)

The Theory and Properties of Γ-k Randomized Truth Degree on Axiomatic Extension of Goguen Propositional Logic System

HUI Xiao-jing, GAO Xiao-li, ZHU Nai-diao   

  1. College of Mathematics and Computer Science, Yan'an University, Yan'an, Shaanxi 716000, China
  • Received:2016-06-23 Revised:2016-12-19 Online:2017-11-25 Published:2017-11-25

摘要: 本文首先对n值Goguen命题逻辑进行公理化扩张Goguen~,Δ,记为∏~,Δ.利用赋值集的随机化方法,给出公式在kk取~或Δ)连接词下相对于局部有限理论Γ的Γ-k随机真度的定义;讨论了∏~,Δ中Γ-k随机真度的MP规则、HS规则等相关性质;接着,在Γ-k中定义了两公式间的Γ-k随机相似度与Γ-k随机伪距离,得到了公式在连接词下相对于局部有限理论Γ的Γ-k随机相似度与Γ-k随机伪距离所具有的一些良好性质;最后,在∏~,Δ中介绍了任意理论Γ相对于特定理论Γ0的相对随机发散度和相对随机相容度概念,得到了相对随机发散度与相对随机相容度之间联系的关系式.

关键词: Goguen命题逻辑系统, &Gamma, -k随机真度, &Gamma, -k随机相似度, &Gamma, -k随机伪距离, 相对随机发散度, 相对随机相容度

Abstract: Axiomatic extensions of n-valued Goguen propositional logic system is first studied in this paper,which is denoted as ∏ ~, Δ.Using the randomization method of valuation sets,the definition of Γ-k randomized truth degree of formula relative to local finite theory Γ under the k conjunction is given.The MP rule,HS rule,and some related properties are also discussed.Then,the definitions of Γ-k randomized similarity degree and Γ-k randomized pseudo-metric in ∏~,Δ between two formulas are given,and some desirable properties about Γ-k randomized similarity degree and Γ-k randomized pseudo-metric relative to local finite theory Γ under conjunction are obtained.Finally,the paper introduces the concepts of randomized relative divergence degree and relative randomized consistency degree of theory Γ relative to the fixed theory Γ0 in ∏~,Δ,and obtains the relationship between relative randomized divergence degree and relative randomized consistency degree.

Key words: Goguen propositional logic system, Γ-k randomized truth degree, Γ-k randomized similarity degree, Γ-k randomized pseudo-metric, relative randomized divergence degree, relative randomized consostency degree

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