Unified Theory of Truth Degrees in <i>n</i>-Valued <i>S-MTL</i> Propositional Logic

LI Jun; DENG Fu-xi

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Unified Theory of Truth Degrees in n-Valued S-MTL Propositional Logic

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- Unified Theory of Truth Degrees in n-Valued S-MTL Propositional Logic
- Acta Electronica Sinica Vol. 39, Issue 8, Pages: 1864-1868(2011)
- 作者机构：
  
  兰州理工大学理学院,甘肃,兰州,730050
- 作者简介：
- 基金信息：
- DOI：
  CLC： O142
- Published：2011
- 稿件说明：
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LI Jun, DENG Fu-xi. Unified Theory of Truth Degrees in n-Valued S-MTL Propositional Logic[J]. Acta Electronica Sinica, 2011, 39(8): 1864-1868.
DOI：

LI Jun, DENG Fu-xi. Unified Theory of Truth Degrees in n-Valued S-MTL Propositional Logic[J]. Acta Electronica Sinica, 2011, 39(8): 1864-1868. DOI：

摘要

给出了强正则蕴涵算子和

值

S-MTL

命题逻辑系统的定义.基于一般的概率测度定义了公式的真度

并给出了公式真度的积分表达式;基于公式真度的积分表达式证明了真度推理规则;在

值

S-MTL

命题逻辑系统的全体公式集上引入了一种伪距离

证明了逻辑运算关于这种伪距离是连续的.提出了一种近似推理机制

使得在

值

S-MTL

命题逻辑系统中展开近似推理成为可能.

Abstract

The concept of strong regular implication operator and the

-valued

S-MTL

propositional logic system are introduced.Based on probability measure the truth degree of formula is defined and its integral expression is given and the inference rules w.r.t the truth degrees is proved.Moreover

similarity degrees among formulas are proposed and a pseudo-metric is defined therefrom on the set of formulas.The continuity of logical operators w.r.t the pseudo-distance is proved

and hence a possible framework suitable for developing approximate reasoning theory in

-valued

S-MTL

propositional logic is established.

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Unified Theory of Truth Degrees in n-Valued S-MTL Propositional Logic

DOI：

摘要

Abstract

关键词

Keywords

references