Goguen公理化扩张系统的Γ-k随机真度理论及性质  

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

作　　者：惠小静[1] 高晓莉[1] 朱乃调 

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：《电子学报》2017年第11期2656-2662,共7页Acta Electronica Sinica

基　　金：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)

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k(k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Γ_0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.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 Γ_0 in ∏_(~,Δ),and obtains the relationship between relative randomized divergence degree and relative randomized consistency degree.

关 键 词：Goguen命题逻辑系统 Γ-k随机真度 Γ-k随机相似度 Γ-k随机伪距离 相对随机发散度 相对随机相容度 

分 类 号：O141.1[理学—数学]