| 模糊逻辑系统中的演绎定理和HS规则 |
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| 作者姓名： | YANG Xiao-bin DENG Shu-xian |
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| 作者单位： | Department of Applied Mathematics，Shanghai University of Finance and Economics，Shanghai 200433，China; Department of Mathematics，Henan Textile College，Zhengzhou 450007，China |
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| 摘 要： | Cancelled the first axiom L1) or the third axiom L3) of the classical formal logic system we established two kinds of quasi-formal deductive system, LG-Rand LG, respectively. In LG-R we proved that neither the deduction theorem nor the hypothetical syllogism (HS) rule held but a deduction theorem and an HS rule are obtained in a weak sense. We also proved that both the deduction theorem and the hypothetical syllogism(HS) rule hold in LG.
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| 关 键 词： | 三段论法则 模糊逻辑 推论定理 弱HS法则 |
Deduction Theorem and Hypothetical Syllogism Rule on Fuzzy Logic System |
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| YANG Xiao-bin,DENG Shu-xian.Deduction Theorem and Hypothetical Syllogism Rule on Fuzzy Logic System[J].Chinese Quarterly Journal of Mathematics,2005,20(2):206-213. |
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| Authors: | YANGXiao-bin DENGShu-xian |
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| Institution: | [1]DepartmentofAppliedMathematics,ShanghaiUniversityofFinanceandEconomics,Shanghai200433,China [2]DepartmentofMathematics,HenanTextileCollege,Zhengzhou450007,China |
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| Abstract: | Cancelled the first axiom L1) or the third axiom L3) of the classical formal logic system we established two kinds of quasi-formal deductive system, LG-R^* and LG^* respectively. In LG-R^* we proved that neither the deduction theorem nor the hypothetical syllogism (HS) rule held but a deduction theorem and an HS rule are obtained in a weak sense. We also proved that both the deduction theorem and the hypothetical syllogism(HS) rule hold in LG^*. |
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| Keywords: | fuzzy logic system deduction theorem hypothetical syllogism(HS) rule weak HS rule |
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