  Gossip protocols are programs used in a setting in which each agent holds a
secret and the aim is to reach a situation in which all agents know all
secrets. Such protocols rely on a point-to-point or group communication.
Distributed epistemic gossip protocols use epistemic formulas in the component
programs for the agents. The advantage of the use of epistemic logic is that
the resulting protocols are very concise and amenable for a simple
verification.
  Recently, we introduced a natural modal logic that allows one to express
distributed epistemic gossip protocols and to reason about their correctness.
We proved that the resulting protocols are implementable and that all aspects
of their correctness, including termination, are decidable. To establish these
results we showed that both the definition of semantics and of truth of the
underlying logic are decidable. We also showed that the analogous results hold
for an extension of this logic with the 'common knowledge' operator.
  However, several, often deceptively simple, questions about this logic and
the corresponding gossip protocols remain open. The purpose of this paper is to
list and elucidate these questions and provide for them an appropriate
background information in the form of partial of related results.
