基于证据支持度的信念逻辑研究

On the Logic of Belief Based on the Degree of Evidence Support

一个智能主体对某一信息的相信及相信程度分别与证据和证据支持度密切相关。本文试图通过模态逻辑方法,从语义及公理化角度探究证据支持度和信念强度之间的联系。在文中,分别用KD45和KD正规模态表达强信念算子和带程度的信念算子,用带程度的模态算子表达含程度的证据,通过在模型上加约束条件的方式将证据关系和信念关系联系起来,表达出了证据支持度和信念强度之间的联系,并建立了一个可靠且完全的公理系统。这实现了证据支持度和信念强度联系的形式化研究,为处理不确定信息提供了定性和定量相结合的分析方法。

The belief and degree of belief of an intelligent agent for some information are closely related to evidence and the degree of evidence support.This paper aims to explore the connections between the degree of evidence support and belief strength from semantic and axiomatic perspectives by modal logic.Specifically,KD45 and KD normal modalities are used respectively to express the strong belief operator and the belief operator with degree.The modal operator with degree is utilized to express the evidence with degree.By introducing constraints to the belief logic model based on the degree of evidence support,we establish the connections between the relation of evidence and the relation of belief,thereby the connections between the degree of evidence support and the belief strength are expressed.Additionally,a sound and complete axiomatic system is established.These measures help to formalize the connections between the degree of evidence support and the belief strength,and thus a method integrating qualitative analysis with quantitative analysis for dealing with uncertain information is provided.