A Research On Information Flow In Social Networks And Perfect Recall Of Agents

In the past ten years,studying information flow in agents from the perspective of social network has become a hot field of modern logic.The purpose of this study is to provide a formal analysis method for information flow in groups.The reason why information flow can be studied from the perspective of social network is that the different positions of agents in the social network determine that they will get different opportunities and be subject to different restrictions in the interaction of agents.The study of information flow based on social network has great significance for the study of changes of agent's cognition,as well as for the study of correct prediction and effective intervention of agent's behavior.This paper focuses on such a kind of information flow:agents don't know the social network and don't know each other's initial cognitive state,and unrelated agents cannot predict the possible actions.This kind of information flow is the research object of this paper,it includes recall activity of new information after the flow of information.The main research objectives of this paper are as follows:firstly,give a logical model for the change of agent's cognitive state caused by information flow in social network;Secondly,give a logical model for perfect recall activity of multi-agent.Since knowledge is a special kind of information and secret is a special kind of knowledge,so secret diffusion is a special kind of information flow.In order to achieve the two research objective,Firstly,this paper studies the general information flow and give a model for the change of agent's cognitive state in the general information flow.Then,the influence mechanism of secret diffusion on the cognitive state of agents is discussed.Finally,we study how to recall new information perfectly after information flow.According to these research contents,the main contribution of this paper is shown in the following three parts:Firstly,propose social network doxastic logic in chapter 3.Social network doxastic logic is obtained by combining social network and some ideas of doxastic logic.It can describe the change of agent's belief in the general information flow.This paper draws lessons from Ditmarsch H V(2014)'s classification of announcement,and classifies agent's announcement into three categories based on the belief of the declarator:truthful announcement,lying,and bluffing.All three types of announcement can make receivers believe the declaration.Social network doxastic logic absorbed the technical idea that doxastic logic delete only relations but not possible worlds when dealing with lies.In social network doxastic logic,agents can take actions to change social network,and the belief state of group members can be changed through various announcements.According to the new semantic definition,some valid,invalid and semantic equivalent formulas are proved.Secondly,propose social network epistemic logic in chapter 4.Social network epistemic logic can describe secret diffusion phenomenon in social networks.Secret is a special kind of knowledge.In this paper,we define individual secret and group secret by using operator K.In social network epistemic logic,the interpretation of knowledge is no longer based on kripke semantics,and agent's cognitive state is no longer subject to the present world.In social network epistemic logic,agents can take actions to change social network,the declarator is formalized,and the declared formulas can only be objective formulas.On the model,announcement only changes the cognitive state of some agents,while the cognitive state of other agents do not change.According to the new semantic definition,some valid,invalid and semantic equivalent formulas are proved.Thirdly,propose S5~tC~t system in chapter 5,which can describe the recall activity.Perfect recall means that rational agents can always remember their previous knowledge.Assuming that agent has perfect recall plays an important role in theoretical research.For example,in repeated games,it is necessary to assume that the participants can recall the history of the game perfectly(such as choosing honesty or deception before).This paper sorts out the understanding of perfect recall by different logics and their characteristics,and finds that the KT5 system which is given by Sato M(1977)is better than narrow temporal epistemic logic,also better than public announcement logic in formalizing the individual's of perfect recall.In order to extend the KT5 system to groups that can recall their common knowledge perfectly,S5~tC~t system is constructed in chapter 5.The study of perfect recall is independent of social network.S5~tC~t system can well describe perfect recall of multi-agent.In terms of formal language,it adds time coordinates to the epistemic operators.Thus,we have to give a time coordinate when we talk about agent's epistemic state.In the model,the system assigns different sets of indistinguishable worlds to agents at different time points,which intuitively means that the sets of indistinguishable worlds gradually decrease as time goes by.We prove the soundness and completeness of S5~tC~t system,and prove that S5~tC~t system is stronger than KT5 system in expressivity.The work of this paper theoretically enriches the existing theories on information flow in social networks,and establishes some important conclusions.The above logic theory constructed in this paper have certain guiding significance for social activities such as simulating the evolution of public opinion,guiding public opinion,and effectively intervening in group behavior.Therefore,the research of this paper has not only theoretical significance,but also important practical significance.