Facebook and the Epistemic Logic of Friendship

TL;DR

This paper develops a two-dimensional modal logic framework to analyze how knowledge and social relationships evolve in friendship networks, using general dynamic logic to model communication and social dynamics.

Contribution

It introduces a novel logical system combining dynamic and epistemic modalities to reason about social relationships and communication in friendship networks.

Findings

Provides a formal language for social epistemic reasoning

Models dynamic changes in social and knowledge states

Analyzes communication patterns in social networks

Abstract

This paper presents 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' [11]. 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 technical framework for this work is general dynamic dynamic logic (GDDL) [4], which provides a general method for extending modal logics with dynamic operators for reasoning about a wide range of model-transformations, starting with those definable in propositional dynamic logic (PDL) and extended to allow for the more subtle operators involved in, for example, private communication, as represented in dynamic epistemic logic (DEL) and related systems. We provide a hands-on introduction to GDDL, introducing elements of the formalism as we go, but leave the reader to consult [4] for technical details. Instead, the purpose of this paper is to investigate a number of conceptual issues that arise when considering communication between agents in such networks, both from one agent to another, and broadcasts to socially-defined groups of agents, such as the group of my friends.