Timed Epistemic Knowledge Bases for Social Networks

Abstract

We present an epistemic logic equipped with time-stamps in atoms and epistemic operators, which enables reasoning about the moments at which events happen and knowledge is acquired or deduced. Our logic includes both an epistemic operator K and a belief operator B, to capture the disclosure of inaccurate information. Our main motivation is to describe rich privacy policies in online social networks (OSNs). Most of today’s privacy policy mechanisms in existing OSNs allow only static policies. In our logic it is possible to express rich dynamic policies in terms of the knowledge available to the different users and the precise time of actions and deductions. Our framework can be instantiated for different OSNs by specifying the effect of the actions in the evolution of the social network and in the knowledge disclosed to each user. We present an algorithm for deducing knowledge and propagating beliefs, which can also be instantiated with different variants of how the epistemic information is preserved through time. Policies are modelled as formulae in the logic, which are interpreted over timed traces. Finally, we show that the model checking problem for this logic, and in consequence policy conformance, is decidable.