计量逻辑中真度的均值表示形式及应用

doi:10.3969/j.issn.0372-2112.2012.09.019

电子学报 ›› 2012, Vol. 40 ›› Issue (9): 1822-1828.DOI: 10.3969/j.issn.0372-2112.2012.09.019

计量逻辑中真度的均值表示形式及应用

吴洪博, 周建仁

陕西师范大学数学与信息科学学院, 陕西西安 710062

收稿日期:2011-11-03 修回日期:2012-03-27 出版日期:2012-09-25
- 作者简介:
- 吴洪博 男,1959出生,陕西咸阳人,博士,陕西师范大学数学与信息科学学院教授.研究方向为格上拓扑学与非经典数理逻辑. E-mail:wuhb@snnu.edu.cn
- 基金资助:
- 国家自然科学基金 (No.11171196); 陕西省教育厅专项科研计划项目 (No.11JK0512)

The Form of Mean Representation of Truth Degree with Applications in Quantitative Logic

WU Hong-bo, ZHOU Jian-ren

College of Mathematics and Information Science, Shaanxi Normal Universtity, Xi'an, Shaanxi 710062, China

Received:2011-11-03 Revised:2012-03-27 Online:2012-09-25 Published:2012-09-25
- Supported by:
- National Natural Science Foundation of China (No.11171196); Research Project of Education Department of Shaanxi Province (No.11JK0512)

摘要/Abstract

摘要： 命题真度是计量逻辑学中的基础概念.本文对真度的性质和计算方法进行了再研究.首先给出了计量逻辑中真度定义的均值表示形式;其次利用真度定义的均值表示形式推广了连接有限值逻辑系统和连续值逻辑系统中真度理论的极限定理,并得到了真度的对称性定理;最后在n-值命题逻辑系统和连续值命题逻辑系统中给出了析取规范型命题和合取规范型命题的真度的计算公式.

关键词: 计量逻辑, 真度, 均值表示, 极限定理, 对称性定理, 规范型, 计算公式

Abstract: The truth degree of formula is the basic concept in quantitative logic from which other concepts are derived.In the present paper the properties and the computation method of truth degree are investigated more in-depth.Firstly,a form of mean representation of definition of truth degree of formula is given in quantitative logic;secondly,with the help of the form of mean representation,the limit theorem is generalized that is a connection of the theories of truth degrees in n-valued logic system and continuity-valued logic system,and the symmetrical characteristic of truth degree is obtained;thirdly,the computational formulas of truth degrees of the propositions with normal forms is given.

Key words: quantitative logic, truth degree, mean representation, limit theorem, symmetry theorem, normal form, calculation formula

中图分类号:

O141.1

吴洪博, 周建仁. 计量逻辑中真度的均值表示形式及应用[J]. 电子学报, 2012, 40(9): 1822-1828.

WU Hong-bo, ZHOU Jian-ren . The Form of Mean Representation of Truth Degree with Applications in Quantitative Logic[J]. Acta Electronica Sinica, 2012, 40(9): 1822-1828.

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计量逻辑中真度的均值表示形式及应用

The Form of Mean Representation of Truth Degree with Applications in Quantitative Logic

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