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

WU Hong-bo; ZHOU Jian-ren

doi:10.3969/j.issn.0372-2112.2012.09.019

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

更新时间：2025-07-16

- The Form of Mean Representation of Truth Degree with Applications in Quantitative Logic
- Acta Electronica Sinica Vol. 40, Issue 9, Pages: 1822-1828(2012)
- 作者机构：
  
  陕西师范大学数学与信息科学学院,陕西,西安,710062
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.11171196);Research Project of Education Department of Shaanxi Province (No.11JK0512)
- DOI：10.3969/j.issn.0372-2112.2012.09.019
  CLC： O141.1
- Published：2012
- 稿件说明：
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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.
DOI：

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. DOI： 10.3969/j.issn.0372-2112.2012.09.019.

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.

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

-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.

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