Title: Anonymous Public Announcements

Speaker: Thomas Ågotnes (University of Bergen) 

Time: 2025/11/22 (Saturday) 15:00-18:00 

Location:  Room 106, Lee Shau Kee Humanities Buildings No.2 (李兆基人文学苑2号楼), Peking University 

Abstract: 

I formalise the notion of an anonymous public announcement in the tradition of public announcement logic. Such announcements can be seen as in-between a public announcement from "the outside" (an announcement of ϕ) and a public announcement by one of the agents (an announcement of Kaϕ): we get more information than just ϕ, but not (necessarily) about exactly who made it. Even if such an announcement is prima facie anonymous, depending on the background knowledge of the agents it might reveal the identity of the announcer: if I post some thing on a message board, the information might reveal who I am even if I don't sign my name. Furthermore, like in the Russian Cards puzzle, if we assume that the announcer's intention was to stay anonymous, that in fact might reveal more information. In this talk I first look at the case when no assumption about intentions are made, in which case the logic with an anonymous public announcement operator is reducible to epistemic logic. I then look at the case when we assume common knowledge of the intention to stay anonymous, which is both more complex and more interesting: in several ways it boils down to the notion of a "safe" announcement (again, similarly to Russian Cards). Main results include formal expressivity results and axiomatic completeness for key logical languages. The talk is based on joint work with Rustam Galimullin, Ken Satoh and Satoshi Tojo.