One new model of infinite valued for medium proposition logic and its meaning

doi:10.3778/j.issn.1002-8331.2010.31.013

Computer Engineering and Applications ›› 2010, Vol. 46 ›› Issue (31): 45-49.DOI: 10.3778/j.issn.1002-8331.2010.31.013

• 研究、探讨 • Previous Articles Next Articles

One new model of infinite valued for medium proposition logic and its meaning

ZHANG Sheng-li^1，2，PAN Zheng-hua²

1.Department of Computer Science，Xingyi Normal College for Nationalities，Xingyi，Guizhou 562400，China
2.School of Science，Jiangnan University，Wuxi，Jiangsu 214122，China

Received:2009-05-13 Revised:2009-06-22 Online:2010-11-01 Published:2010-11-01
Contact: ZHANG Sheng-li

中介命题逻辑一种新的无穷值语义模型及意义

张胜礼^1，2，潘正华²

1.兴义民族师范学院计算机科学系，贵州兴义 562400
2.江南大学理学院，江苏无锡 214122

通讯作者: 张胜礼

Abstract

Abstract: Since three-valued model of medium logic（ML） is established，ML has been affirmed one kind of three-valued logic by many scholars.However，for medium proposition logic（MP） being as kernel theory of ML，Pan gave out a model of infinite valued of MP，and proved the theorems of completeness and reliability.Based on this，this paper sets up a new model of infinite valued of MP whose truth valued range is [0,λ)∪(λ,1](λ∈(0.5,1)),some properties of the model are investigated，and the theorems of completeness and reliability are proved.This improved model not only further shows that “medium proposition logic is one kind of three valued logic” is incorrect，but also rightly depicts the medium principle which is basic idea of MP，and offers foundation for MP used in more other fields.

Key words: medium proposition logic, three-valued model, infinite-valued model, completeness, soundness

摘要： 中介逻辑ML（Medium Logic），自建立了它的三值语义模型后，ML就被许多学者认定为三值逻辑。对于中介逻辑核心理论的中介命题逻辑系统，潘给出了一种无穷值语义模型，并证明了中介命题逻辑在此模型下具有可靠性与完备性。在此基础上，给出一种真值域为[0,λ)∪(λ,1](λ∈(0.5,1))的无穷值语义模型，研究了它的性质，证明了中介命题逻辑在该模型下也具有可靠性与完备性。新模型的存在进一步表明，认定中介逻辑是一种三值逻辑的理由是不充分的。新模型不仅反映了中介逻辑的基本思想，而且为中介逻辑在其他领域的应用提供了基础。

关键词: 中介命题逻辑, 三值模型, 无穷值模型, 完备性, 可靠性

CLC Number:

TP301.6

ZHANG Sheng-li^1，2，PAN Zheng-hua². One new model of infinite valued for medium proposition logic and its meaning[J]. Computer Engineering and Applications, 2010, 46(31): 45-49.

张胜礼^1，2，潘正华². 中介命题逻辑一种新的无穷值语义模型及意义[J]. 计算机工程与应用, 2010, 46(31): 45-49.

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One new model of infinite valued for medium proposition logic and its meaning

中介命题逻辑一种新的无穷值语义模型及意义

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