Abstract We propose dynamic extensions to the framework of Social Epistemic Logic introduced in Logic in the Community (Seligman et al., pp. 178–188, 2011). One of them introduces a notion of a semi-public announcement made by an aware agent and only transmitted to this agent’s social connections. Another extension along the epistemic dimension of the framework contains separate ‘sending’ and ‘reading’ modalities that allow for a more realistic asynchronous spreading of messages in a social network. Finally, we briefly discuss an extension along the ‘social’ dimension of the framework, which introduces an operator to break links within an epistemic social network based on information at the agent’s disposal. Completeness and decidability results are provided.

We propose a multi-agent epistemic logic of asynchronous announcements, where truthful announcements are publicly sent but individually received by agents, and in the order in which they were sent. Additional to epistemic modalities the logic contains dynamic modalities for making announcements and for receiving them. What an agent believes is a function of her initial uncertainty and of the announcements she has received. Beliefs need not be truthful, because announcements already made may not yet have been received. As announcements are true when sent, certain message sequences can be ruled out, just like inconsistent cuts in distributed computing. We provide a complete axiomatization for this asynchronous announcement logic ( AA ). It is a reduction system that also demonstrates that any formula in AA is equivalent to one without dynamic modalities, just as for public announcement logic. A detailed example modelling message exchanging processes in distributed computing in AA closes our investigation.

International audience