| 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. |
| 关键词: Goguen命题逻辑系统 Γ-k真度 Γ-k相似度 Γ-k伪距离 |
| DOI：10.13328/j.cnki.jos.005110 |
| 分类号: |
| 基金项目: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） |
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| Theory and Property of Γ-k Truth Degree on Axiomatic Extension of Goguen Propositional Logic System |
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GAO Xiao-Li, HUI Xiao-Jing, ZHU Nai-Diao
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College of Mathematics and Computer Science, Yan'an University, Yan'an 716000, China
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| Abstract: |
| 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. |
| Key words: Goguen propositional logic system Γ-k truth degree Γ-k similarity degree Γ-k pseudo-metric |
