| 逻辑系统$G_3$中命题的真度值之集在[0,1]上的分布 |
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| 引用本文： | 李骏,李尧龙,黎锁平.逻辑系统$G_3$中命题的真度值之集在[0,1]上的分布[J].数学研究与评论,2006,26(3):605-612. |
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| 作者姓名： | 李骏 李尧龙 黎锁平 |
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| 作者单位： | 1. 兰州理工大学理学院,甘肃,兰州,730050
2. 渭南师范学院数学系,陕西,渭南,714000 |
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| 基金项目： | 甘肃省自然科学基金(ZS032-B52-031)，兰州理工大学优秀青年基金 |
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| 摘 要： | 利用势为3的均匀概率空间的无穷乘积在G■del三值命题逻辑中引入了公式的真度概念,给出了真度推理规则,证明了全体公式的真度值之集在0,1]上是稠密的,并给出了公式真度的表达通式,为进一步建立三值命题逻辑的近似推理理论奠定了基础．
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| 关 键 词： | 真度 真度推理规则 稠密 |
| 文章编号： | 1000-341X(2006)03-0605-08 |
| 收稿时间： | 03 28 2004 12:00AM |
| 修稿时间： | 06 26 2005 12:00AM |
Theory of Truth Degrees in G\"{o}del 3-Valued Propositional Logic |
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| LI Jun,LI Yao-long and LI Suo-ping.Theory of Truth Degrees in G\"{o}del 3-Valued Propositional Logic[J].Journal of Mathematical Research and Exposition,2006,26(3):605-612. |
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| Authors: | LI Jun LI Yao-long and LI Suo-ping |
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| Institution: | School of Science, Lanzhou University of Technology, Gansu 730050, China;Dept. of Math., Weinan Teachers College, Shaanxi 714000, China;School of Science, Lanzhou University of Technology, Gansu 730050, China |
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| Abstract: | Base on the infinite product of evenly distributed probability space,this paper introduces the theory of truth degrees in G(?)del 3-valued propositional logic and inference rules with truth degrees are given.Moreover,it is proved that the set of truth degrees of propositions is dense in 0,1],and expressions of truth degrees are obtained.This paves the way for the further study on approximate reasoning. |
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| Keywords: | truth degree inference rule with truth degree dense |
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