Model Checking Social Network Models

TL;DR

This paper investigates the verification of knowledge-based privacy policies in social network models by proving decidability, establishing soundness, providing encodings, and demonstrating efficiency improvements over traditional methods.

Contribution

It introduces a decidable model checking approach for epistemic properties in social network models and compares its efficiency to standard Kripke model-based methods.

Findings

Model checking for epistemic properties in SNMs is decidable.

SNMs can be encoded into Kripke models while preserving satisfaction.

Model checking in SNMs is more efficient than in standard Kripke models.

Abstract

A social network service is a platform to build social relations among people sharing similar interests and activities. The underlying structure of a social networks service is the social graph, where nodes represent users and the arcs represent the users' social links and other kind of connections. One important concern in social networks is privacy: what others are (not) allowed to know about us. The "logic of knowledge" (epistemic logic) is thus a good formalism to define, and reason about, privacy policies. In this paper we consider the problem of verifying knowledge properties over social network models (SNMs), that is social graphs enriched with knowledge bases containing the information that the users know. More concretely, our contributions are: i) We prove that the model checking problem for epistemic properties over SNMs is decidable; ii) We prove that a number of properties of knowledge that are sound w.r.t. Kripke models are also sound w.r.t. SNMs; iii) We give a satisfaction-preserving encoding of SNMs into canonical Kripke models, and we also characterise which Kripke models may be translated into SNMs; iv) We show that, for SNMs, the model checking problem is cheaper than the one based on standard Kripke models. Finally, we have developed a proof-of-concept implementation of the model-checking algorithm for SNMs.