Abstract:
In this talk I will present a two-dimensional modal logic for reasoning about the changing patterns of knowledge and social relationships in networks organised on the basis of a symmetric "friendship" relation, providing a precise language for exploring "logic in the community". Agents are placed in the model, allowing us to express such indexical facts as "I am your friend" and "You, my friends, are in danger".

The purpose of developing such a language is to investigate a number of conceptual issues that arise when considering communication between agents in social networks, both from one agent to another, and broadcasts to socially-defined groups of agents, such as the group of my friends. We extend the treatment of such communications to questions, in which agents are taken to be sincere and cooperative interlocutors, and consider network structure changing operations such as adding and deleting friends (with the permission of other agents) and, finally, explore the effect of all this on the concept of common knowledge, which is more varied and rich in the social network setting. These issues are illustrated by a number of examples about office gossip, cold-war spy networks and Facebook.

This is joint work with Jeremy Seligman and Patrick Girard. (PDF of the paper)