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