The Logic of Homophily Dynamics in Heterogeneous Networks: Axiomatization, Model Checking and Validity Checking

Abstract

Social networks have received considerable attention from the modal logic community. In this article, we study and characterize one of the most important principles in the field of social networks. Homophily, which means similarity breeds association, reveals the nature of social organization. In order to be able to express similarity and association together, we generalize the basic network and then define the heterogeneous network. The heterogeneous network is also defined to provide a good foundation for the use of logical approaches. The Logic of Homophily LHG,M that we propose in this article is based on Computation Tree Logic and Formal Concept Analysis. LHG,M describes the homophily dynamics of the heterogeneous networks at a specified similarity coefficient. Furthermore, we not only axiomatize the LHG,M and prove that the axiom system LHG,Mn is sound and complete, but we also prove that the model checking and the validity checking for LHG,M are both PSPACE-complete.