A gossip protocol is a procedure for spreading secrets among a group of agents, using a connection graph. The goal is for all agents to get to know all secrets, in which case we call the execution of the protocol successful. We consider distributed and dynamic gossip protocols. In distributed gossip the agents themselves instead of a global scheduler determine whom to call. In dynamic gossip not only secrets are exchanged but also telephone numbers (agent identities). This results in increased graph connectivity. We define six such distributed dynamic gossip protocols, and we characterize them in terms of the topology of the graphs on which they are successful, wherein we distinguish strong success (the protocol always terminates, possibly assuming fair scheduling) from weak success (the protocol sometimes terminates). For five of these protocols strong (fair) and weak success are characterized by weakly connected graphs. This result is surprising because the protocols are fairly different. In the sixth protocol an agent may only call another agent if it does not know the other agent's secret. Strong success for this protocol is characterized by graphs for which the set of non-terminal nodes is strongly connected. Weak success for this protocol is characterized by weakly connected graphs satisfying further topological constraints that we define in the paper. One direction of this characterization is surprisingly harder to prove than the other results in this contribution.

In public announcement logic it is assumed that all agents pay attention to the announcement. Weaker observational conditions can be modelled in action model logic. In this work, we propose a version of public announcement logic wherein it is encoded in the states of the epistemic model which agents pay attention to the announcement. This logic is called attention-based announcement logic. We give an axiomatization of the logic and prove that complexity of satisfiability is the same as that of public announcement logic, and therefore lower than that of action model logic. An attention-based announcement can also be described as an action model. We extend our logic by integrating attention change. Finally, we add the notion of common belief to the language, we exploit this to formalize the concept of joint attention, that has been widely discussed in the philosophical and cognitive science literature, and we provide a corresponding axiomatization. This axiomatization also employs the auxiliary notion of attention-based relativized common belief.

A gossip protocol is a procedure for spreading secrets among a group of agents, using a connection graph. In each call between a pair of connected agents, the two agents share all the secrets they have learnt. In dynamic gossip problems, dynamic connection graphs are enabled by permitting agents to spread as well the telephone numbers of other agents they know. This paper characterizes different distributed epistemic protocols in terms of the (largest) class of graphs where each protocol is successful, i.e. where the protocol necessarily ends up with all agents knowing all secrets.

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