On The Logic About Belief,Evidence And Trust

The formation of an agent’s belief and the strength of belief are closely related to evidence and trust.For example,the information supported by evidence can be believed by an agent,the degree of evidence support often affects the intensity of belief,and the latter trust affects the conversion of the ever acquired information into belief,and so on.In addition,beliefs are often easily changeable after they are formed,but some of them are firm and unchangeable.These phenomena play very important roles in human cognition,and the study of them will help to understand more deeply the laws of human thinking,enrich the theories of belief,evidence and trust themselves,and research related fields such as artificial intelligence and game theory.This paper attempts to study the above phenomena.There are two main objectives of this paper as follows:Firstly,we will explore the influence of evidence and trust on an agent’s belief formation.To begin with,the connection between belief and evidence will be studied formally.Next,the connection between belief intensity and support degree of evidence will be studied formally.Last,Churn-Jung Liau has answered the question of the formalization of the connection between belief and trust.But his axiomatic system can only characterize the influence of the current trust on the conversion of the current acquired information into belief,but can not characterize the influence of the latter trust on the conversion of the ever acquired information into belief.In this paper,we will use the temporal epistemic logic of Sato’s style to characterize the latter.Secondly,this paper will use the temporal epistemic logic of Sato’s style to formalize the part of an agent’s belief that remains unchanging.In view of these aspects,the research results of this paper are as follows:First,in the third chapter,we considers the formalization of the connection between belief and evidence on the basis of belief logic and evidence logic.In the logical model of belief and evidence,belief relation and evidence relation are independent,which means belief and evidence can not be connected.The constraints added to the logical model link belief relation and evidence relation,then the connection between belief and evidence is expressed through the axioms in BE.Thus,the formalization of the connection is realized.We also have proved soundness and completeness of the system.Second,in the fourth chapter of this paper,we integrate degree symbol into belief operator and evidence operator to express strength of belief and support degree of evidence.The corresponding relations of them are linked by restriction conditions,and the connection between them is expressed by the axioms in BE*.We also have proved soundness and completeness of the system.Third,in the sixth chapter,on the basis of the research of Churn-Jung Liau on the relationship between belief and trust,we use the temporal epistemic logic of Sato’s style to characterize the situation in which information once acquired is transformed into belief under the influence of later trust.We have constructed the BA~taxiomatic system,and proved its soundness and completeness.Fourth,in the seventh chapter,based on the temporal epistemic logic of Sato’s style,we have studied the unchangeable an agent’s belief formally,and constructed the Bt axiomatic system,and then proved its soundness and completeness.The work of this paper enriches the existing theory of belief,evidence and trust,and its conclusions have potential application value in the fields of artificial intelligence,legal reasoning,information security and game theory.