‘KNOWABLE’ AS ‘KNOWN AFTER AN ANNOUNCEMENT’
Philippe Balbiani, Alexandru Baltag, Hans van Ditmarsch, Andreas Herzig, Tomohiro Hoshi, Tiago de Lima · The Review of Symbolic Logic · 2008
Public announcement logic is an extension of multiagent 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 there is a truthful announcement ψ after which φ is true. This logic gives a perspective on Fitch's knowability issues: For which formulas φ, does it hold that φ → ⋄Kφ? We give various semantic results and show completeness for a Hilbert-style axiomatization of this logic. There is a natural generalization to a logic for arbitrary events.