中文摘要：

通过对n值Goguen命题逻辑进行公理化扩张Goguen～,△（Ⅱ～,△）。利用赋值集随机化的方法，在Ⅱ～,△。中提出了公式的k随机真度，讨论了k随机真度的MP规则，HS规则，给出了公式间的k随机相似度与k随机伪度量的概念和性质。同时介绍了三种近似推理模式并证明了三种推理模式之间的等价性。

英文摘要：

By axiomatic extension of n-valued Goguen propositional logic, which is denoted as Ⅱ～,△, using the randomization method of valuation set, the definition of k randomized truth degree of formula is put forward into Ⅱ～,△. The MP rule and HS rule of k randomized truth degree are also discussed. The concepts and properties of k randomized similarity degree and k randomized pseudometric for formulas are given. At the meantime, three different types of approximate reasoning patterns are introduced, and they are proved to be equivalent.