摘要
将已有的不确定性测度概念引入到了Lukasiewicz命题逻辑中的全体赋值之集上,然后利用McNaughton函数关于该不确定性测度的Choquet积分定义了命题的Choquet积分真度概念.证明了当赋值空间上的不确定性测度满足有限可加性时Choquet积分真度函数就具有良好性质,由此可诱导出命题集上的一个伪距离,进而可建立逻辑度量空间并展开程度化推理,特别是证明了当赋值空间上的不确定性测度取为Borel概率测度时Choquet积分真度函数就退化为概率计量逻辑中的Borel概率真度函数.本文是已有命题逻辑概率计量化工作的继续与深入,为表示逻辑命题间不确定性的非线性关系提供了一种推理框架.
The notion of Choquet integral truth degrees of propositions in ?ukasiewicz propositional logic is introduced ,by means of the Choquet integral of McNaughton functions with respect to uncertainty measures on the set of all valuations .When the involved uncertainty measures satisfy finite additivity property ,the notion of Choquet integral truth degrees can induce in a natural way a pseudo-metric ,with which the set of all propositions becomes a pseudo metric space and thus several graded reasoning meth-ods can be established .The notion of Choquet integral truth degrees will reduce to the existing notion of Borel probability truth de-grees in probabilistically quantitative logic when the uncertainty measures are Borel probability measures .This paper is a continuation of probabilistically quantitative logic and provides a possible framework for reasoning about non-linear uncertainty of propositions .
出处
《电子学报》
EI
CAS
CSCD
北大核心
2013年第12期2327-2333,共7页
Acta Electronica Sinica
基金
国家自然科学基金(No.61005046
No.61103133)
教育部高等学校博士学科点专项科研基金(No.20100202120012)
陕西省自然科学基础研究计划(No.2010JQ8020)