Goguen命题逻辑系统公理化扩张的Γ-k真度理论及性质  

Theory and Property of Γ-k Truth Degree on Axiomatic Extension of Goguen Propositional Logic System

作　　者：高晓莉[1] 惠小静[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：《软件学报》2017年第7期1629-1639,共11页Journal of Software

基　　金：国家自然科学基金(11471007);陕西省自然科学基金(2014JM1020);延安大学研究生创新基金资助项目(YCX201612)~~

摘　　要：首先对n值Goguen命题逻辑进行公理化扩张,Goguen_(~,△),记为,Ⅱ_(~,△)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-k的Γ-k真度的定义;讨论了Ⅱ_(~,△)中Γ-k真度的MP规则、HS规则等相关性质;最后,在Ⅱ_(~,△)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Γ-k相似度与Γ-k伪距离所具有的一些良好性质.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.

关 键 词：Goguen命题逻辑系统 Γ-k真度 Γ-k相似度 Γ-k伪距离 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]