Dynamic Temporal Logic of Subjective Homophily

Abstract

Homophily, which means similarity breeds association, is one of the most fundamental principles in social organization. However, in some cases, homophily is not significant, because actors’ perceptions of others differ from the real situation. In this article, we use the term “subjective homophily” to describe the homophily where the perceived similarity of objects is considered. In addition, we also consider social influence, which is closely related to homophily and represents the diffusion of some attributes through associations. In short, the dynamic temporal logic LoSHG,MSC we propose in this article is based on computation tree logic (CTL), which is used to describe the evolution of networks by subjective homophily, and dynamic logic (DL), which provides the dynamic update operator for representing active social influence. Furthermore, we prove that the model checking problem and the validity checking problem for LoSHG,MSC are both PSPACE-complete. Finally, we use an example, named false consensus, to illustrate how logic captures the subjective homophily evolution of networks and the impact of active social influence on evolution and structure.

Keywords

• social network
• subjective homophily
• social influence
• computation tree logic
• dynamic logic
• model checking