Probability Truth Degrees of Formulas in MTL-Algebras Semantics

ZUO Wei-bing

doi:10.3969/j.issn.0372-2112.2015.02.014

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Probability Truth Degrees of Formulas in MTL-Algebras Semantics

更新时间：2025-07-16

- Probability Truth Degrees of Formulas in MTL-Algebras Semantics
- Acta Electronica Sinica Vol. 43, Issue 2, Pages: 293-298(2015)
- 作者机构：
  
  1. 华北水利水电大学数学与信息科学学院,河南,郑州,450046
  2. 华北水利水电大学数学与信息科学学院,河南,郑州,450046
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.11201145);Natural Science Foundation of Education Department of Henan Province (No.13A110719);Humanities and Social Science Research Project of Education Department of Henan Province (No.2013-QN-295)
- DOI：10.3969/j.issn.0372-2112.2015.02.014
  CLC： O141.1O189.2
- Published：2015
- 稿件说明：
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ZUO Wei-bing. Probability Truth Degrees of Formulas in MTL-Algebras Semantics[J]. Acta Electronica Sinica, 2015, 43(2): 293-298.
DOI：

ZUO Wei-bing. Probability Truth Degrees of Formulas in MTL-Algebras Semantics[J]. Acta Electronica Sinica, 2015, 43(2): 293-298. DOI： 10.3969/j.issn.0372-2112.2015.02.014.

摘要

基于L-赋值理论

通过在MTL代数赋值格和全体公式集上分别建立概率测度

利用积分方法提出了MTL代数语义上公式的概率真度.证明了概率真度的MP规则、HS规则及交推理规则;同时引入公式间的概率相似度和伪距离

建立了概率逻辑度量空间.将计量逻辑学中的相关理论推广到基于MTL代数语义的格值逻辑上

使得在格值逻辑上进行程度化推理成为可能.

Abstract

Based on L-evaluation theory and by defining probability measure in MTL-algebra evaluation lattice and set of all formulas respectively

the concept of probability truth degree of formulas in MTL-algebras semantics is introduced by the integral method.The MP rule

HS rule and meet inference rules of probability truth degree are proved.At the meantime

the concept of probability similarity degree and pseudo-distances between formulas are introduced and the probability logic metric space is built.The theory of quantitative logic is expanded to lattice-valued logic based on MTL-algebra semantics

which makes it possible in graded reasoning in lattice-valued logic.

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Related Author

ZUO Wei-bing

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Department of Mathematics and Information Science, North China Vniversity of Water Resources and Electric Power

Department of Mathematics and Information Science North China Vniversity of Water Resources and Electric Power Zhengzhou Henan China

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Department of Mathematics and Information ScienceNorth China Institute of Water Conservancy and Hydroelectric PowerZhengzhouHenan 450046China

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