| Lukasiewicz n值命题逻辑中命题的真度理论 |
| |
| 引用本文： | 李骏,黎锁平,夏亚峰.Lukasiewicz n值命题逻辑中命题的真度理论[J].数学学报,2004,47(4):769-780. |
| |
| 作者姓名： | 李骏 黎锁平 夏亚峰 |
| |
| 作者单位： | 兰州理工大学理学院,兰州,730050 |
| |
| 基金项目： | 甘肃省自然科学基金(ZS032-B25-031) |
| |
| 摘 要： | 利用势为 n的均匀概率空间的无穷乘积在 Lukasiewicz n值命题逻辑中引入了公式的真度概念,当3≤n≤17时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;利用真度定义了公式间的相似度,进而导出了全体公式集上的一种伪距离,为n值Lukasiewicz命题逻辑系统的近似推理理论提供了一种可能的框架。
|
| 关 键 词： | 真度 相似度 近似推理 |
| 文章编号： | 0583-1431(2004)04-0769-12 |
Theory of Truth Degrees in Lukasiewicz n-Valued Propositional Logic |
| |
| Jun LI,Suo Ping LI,Ya Feng XIA School of Science,Lanzhou University of Technology,Lanzhou ,P. R. China.Theory of Truth Degrees in Lukasiewicz n-Valued Propositional Logic[J].Acta Mathematica Sinica,2004,47(4):769-780. |
| |
| Authors: | Jun LI Suo Ping LI Ya Feng XIA School of Science Lanzhou University of Technology Lanzhou P R China |
| |
| Institution: | Jun LI;Suo Ping LI;Ya Feng XIA School of Science,Lanzhou University of Technology,Lanzhou 730050, P. R. China |
| |
| Abstract: | By the use of the infinite product of evenly distributed probability spaces,
this paper introduces the theory of truth degrees in Lukasiewicz n-valued propositional
logic. It is proved that the set of truth degrees of propositions with 3≤n≤17 is
dense in 0, 1], and the expressions of truth degrees are obtained. Morever, a pseudo-
metric on the set of propositions is defined by means of the concept of truth degrees of
propositions and a possible framework for approximate reasoning is proposed. |
| |
| Keywords: | Truth degree Similarity degree Approximate reasoning |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
| 点击此处可从《数学学报》浏览原始摘要信息 |
| 点击此处可从《数学学报》下载免费的PDF全文 |
|
