'Knowable' as 'known after an announcement'

Philippe Balbiani (1, 2) , Alexandru Baltag (3) , Hans van Ditmarsch (1, 4) , Andreas Herzig (1, 2) , Tomohiro Hoshi (5) , Tiago De Lima (6)

1 IRIT-LILaC - Logique, Interaction, Langue et Calcul
2 CNRS - Centre National de la Recherche Scientifique
3 University of Oxford
4 University of Otago [Dunedin, Nouvelle-Zélande]
5 Stanford University
6 TU/e - Eindhoven University of Technology [Eindhoven]

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 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 we show completeness for a Hilbert-style axiomatization of this logic. There is a natural generalization to a logic for arbitrary events.

Mots clés: modal logic; logic of actions; epistemic logic; multi-agent systems.

Domaines: Intelligence artificielle [cs.AI]; Logique en informatique [cs.LO]; Système multi-agents [cs.MA]

Philippe Balbiani, Alexandru Baltag, Hans van Ditmarsch, Andreas Herzig, Tomohiro Hoshi, et al.. 'Knowable' as 'known after an announcement'. [Research Report] IRIT/RR–2008-2–FR, IRIT : Institut de recherche en informatique de Toulouse. 2008. ⟨hal-00872316⟩