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MTL代数语义上逻辑公式的概率真度
引用本文:左卫兵.MTL代数语义上逻辑公式的概率真度[J].电子学报,2015,43(2):293-298.
作者姓名:左卫兵
作者单位:华北水利水电大学数学与信息科学学院, 河南郑州 450046
基金项目:国家自然科学基金(No .11201145);河南省教育厅自然科学基金(No .13A110719);河南省教育厅人文社会科学研究项目
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.

关 键 词:MTL代数  L-赋值  概率真度  概率逻辑度量空间  程度化推理  
收稿时间:2013-08-23

Probability Truth Degrees of Formulas in MTL-Algebras Semantics
ZUO Wei-bing.Probability Truth Degrees of Formulas in MTL-Algebras Semantics[J].Acta Electronica Sinica,2015,43(2):293-298.
Authors:ZUO Wei-bing
Institution:College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou, Henan 450046, China
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.
Keywords:monoidal t-norm based logic algebra  lattice valued evaluation  probability truth degree  probability logic metric space  graded reasoning
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