What can we achieve by arbitrary announcements?: A dynamic take on Fitch's knowability

Public announcement logic is an extension of multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. We propose an extension of public announcement logic with a dynamic modal operator that expresses what is true after any announcement: ϕ expresses that ϕ is true after an arbitrary announcement ψ. As this includes the trivial announcement , one might as well say that ϕ expresses what remains true after any announcement: it therefore corresponds to truth persistence after (definable) relativisation. The dual operation ♦ϕ expresses that there is an announcement after which ϕ. This gives a perspective on Fitch’s knowability issues: for which formulas ϕ does it hold that ϕ → ♦Kϕ? We give various semantic results, and we show completeness for a Hilbert-style axiomatisation of this logic.

• Type: Conference
• Year: 2007
• Where: TARK
• Authors: Philippe Balbiani, Alexandru Baltag, Hans P. van Ditmarsch, Andreas Herzig, T. Hoshi, Tiago De Lima
• Keywords: Arbitrary Announcement ψ, Multi-agent Epistemic Logic, Public Announcement Logic, TARK 2007