The Generally Truth Degrees of Formulas in n-Valued Lukasiewicz Propositional Logic and the Estimation of Uncertainty Degree of Conclusion in Formal Inference

ZHANG Jia-lu; WU Xia

doi:10.3969/j.issn.0372-2112.2012.10.030

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The Generally Truth Degrees of Formulas in n-Valued Lukasiewicz Propositional Logic and the Estimation of Uncertainty Degree of Conclusion in Formal Inference

更新时间：2025-07-16

- The Generally Truth Degrees of Formulas in n-Valued Lukasiewicz Propositional Logic and the Estimation of Uncertainty Degree of Conclusion in Formal Inference
- Acta Electronica Sinica Vol. 40, Issue 10, Pages: 2085-2090(2012)
- 作者机构：
  
  湘南学院数学系,湖南,郴州,423000
- 作者简介：
- 基金信息：
  
  program supported by Construct Program of the Key Discipline in Hunan province;Science and Technology Research Program of Education Department of Hunan Province (No.10C1232)
- DOI：10.3969/j.issn.0372-2112.2012.10.030
  CLC： O142
- Published：2012
- 稿件说明：
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ZHANG Jia-lu, WU Xia. The Generally Truth Degrees of Formulas in n-Valued Lukasiewicz Propositional Logic and the Estimation of Uncertainty Degree of Conclusion in Formal Inference[J]. Acta Electronica Sinica, 2012, 40(10): 2085-2090.
DOI：

ZHANG Jia-lu, WU Xia. The Generally Truth Degrees of Formulas in n-Valued Lukasiewicz Propositional Logic and the Estimation of Uncertainty Degree of Conclusion in Formal Inference[J]. Acta Electronica Sinica, 2012, 40(10): 2085-2090. DOI： 10.3969/j.issn.0372-2112.2012.10.030.

摘要

在Lukasiewicz

值命题逻辑系统中引入命题公式的一般真度概念并讨论其性质

说明一般真度满足Kolmogorov公理.在形式推演中

引进公式的不可靠度和前提的必要度概念

证明在Lukasiewicz

值逻辑系统中

一个有效推理的结论的不可靠度不超过各前提的不可靠度与其必要度的乘积之和.通过不可靠度在全体公式集上建立逻辑伪距离空间

证明逻辑伪距离空间中没有孤立点

利用逻辑伪距离在全体公式集

(

)中提出两种不同形式的近似推理模式.

Abstract

This paper introduces the concept of truth degrees of propositions in

-valued Lukasiewicz logical system by means of the infinite product of probability on the value domain.By discussing the properties of truth degree we illustrate that the truth degree satisfies Kolmogorov axioms.By introducing the concepts of uncertainty degree of formulas and essentialness degree of premises we prove that the uncertainty degree of conclusion is less than or equal to the sum of the product of uncertainty degree of every premise and its essentialness degree in formal inference.By using uncertainty degree we establish logic pseudo-metric space on formulas

set

and proved that the logic pseudo-metric space has not isolated point.Moreover

we propose two different approximate reasoning models in the formulas set.

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