  Kripke models are an effective and widely used tool for representing
epistemic attitudes of agents in multi-agent systems, including distributed
systems. Dynamic Epistemic Logic (DEL) adds communication in the form of model
transforming updates. Private communication is key in distributed systems as
processes exchanging (potentially corrupted) information about their private
local state should not be detectable by any other processes. This focus on
privacy clashes with the standard DEL assumption for which updates are applied
to the whole Kripke model, which is usually commonly known by all agents,
potentially leading to information leakage. In addition, a commonly known model
cannot minimize the corruption of agents' local states due to fault information
dissemination. The contribution of this paper is twofold: (I) To represent
leak-free agent-to-agent communication, we introduce a way to synthesize an
action model which stratifies a pointed Kripke model into private
agent-clusters, each representing the local knowledge of the processes: Given a
goal formula $\varphi$ representing the effect of private communication, we
provide a procedure to construct an action model that (a) makes the goal
formula true, (b) maintain consistency of agents' beliefs, if possible, without
causing "unrelated" beliefs (minimal change) thus minimizing the corruption of
local states in case of inconsistent information. (II) We introduce a new
operation between pointed Kripke models and pointed action models called
pointed updates which, unlike the product update operation of DEL, maintain
only the subset of the world-event pairs that are reachable from the point,
without unnecessarily blowing up the model size.
