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We provide a semantic framework to specify information propagation in social networks; our semantic framework features both the operational description of information propagation and the epistemic aspects in social networks. In our framework, based on annotated labelled transition systems, actions are decorated with function views to specify different types of announcements. Our function views enforce various common types of local privacy policies, i.e. those policies concerning a single action. Furthermore, we specify global privacy policies, those concerning multiple actions, using a combination of modal $\mu $-calculus and epistemic logic. To illustrate the applicability of our framework, we apply it to the specification of a real-world case study. As a fundamental property for the epistemic aspect of our semantic model, we prove that its indistinguishability relations are equivalence relations, namely they are reflexive, symmetric and transitive. We also study the complexity bounds for the model-checking problem concerning a subset of our logic and show that model checking is PSPACE-complete for the studied subset.

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