Axiomatic extensions of n-valued Goguen propositional logic system is first studied in this paper,which is denoted as H _,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 П _,Δbetween 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 П _,Δ,and obtains the relationship between relative randomized divergence degree and relative randomized consistency degree.%本文首先对n值Goguen命题逻辑进行公理化扩张Goguen_,Δ,记为П_,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П_.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П_,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.
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