中文摘要：

首先对n值Goguen命题逻辑进行公理化扩张，Goguen-，Δ，记为∏-，Δ.利用公式的诱导函数给出公式在k（k任取-或Δ）连接词下相对于局部有限理论Γ的Γ-k真度的定义；讨论了∏-，Δ中Γ-k真度的MP规则、HS规则等相关性质；最后，在Γ-k中定义了两公式间的Γ-k相似度与Γ-k伪距离，得到了公式在k连接词下相对于局部有限理论Γ-k的相似度与Γ-k伪距离所具有的一些良好性质.

英文摘要：

Axiomatic extensions of n-valued Goguen propositional logic system denoted as ∏-,Δ is first studied in this paper. Using induced function, the definition of Γ-k truth degree of formula relative to local finite theory Γ under the k conjunction is given. The MP rule, HS rule, and some correlation properties are also discussed. Finally, the definition of Γ-k similarity degree and Γ-k pseudo-metric in ∏-,Δ between two formulas is presented, and some good properties about Γ-k similarity degree and Γ-k pseudo-metric relative to local finite theory Γ under the k conjunction are simultaneously obtained.