Reasoning about opinion dynamics in social networks

This article introduces a logic to reason about a well-known model of opinion dynamics in social networks initially developed by Morris DeGroot as well as Keith Lehrer and Carl Wagner. The proposed logic is an extension of Łukasiewicz' fuzzy logic with additional equational expressivity, modal operators, machinery from hybrid logic and dynamic modalities. The model of opinion dynamics in social networks is simple enough to be easily grasped, but still complex enough to have interesting mathematical properties and applications. Thus, developing a logic to reason about this particular model serves as a paradigmatic example of how logic can be useful in social network analysis.