Analyzing Echo Chambers: A Logic of Strong and Weak Ties

Echo chamber is a widely used term describing a situation where certain information is reinforced within a closed network. To reason about echo chambers, we introduce a two-sorted hybrid logic of strong and weak ties based on a logic of positive and negative relations known from the literature. We show that some classical property definitions can be formalized and that a known claim from social network analysis is a validity. We also prove that the logic is axiomatizable, sound and strongly complete. We combine our results with research on homophily and social group formation to represent relations between similar agents. Lastly, we add a knowledge modality and dynamic operators to analyze change in these networks.