'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 withdynamic operators to model the informational consequencesof announce-ments to the entire group of agents. We propose an extension of public an-nouncement logic with a dynamic modal operator that expresses what is trueafteranyannouncement:♦φexpresses that there is a truthful announcementψafter whichφis true. This logic gives a perspective on Fitch’s knowabilityissues: for which formulasφdoes it hold thatφ→♦Kφ? We give various se-mantic results, and we show completeness for a Hilbert-style axiomatizationof 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]

Philippe Balbiani, Alexandru Baltag, Hans van Ditmarsch, Andreas Herzig, Tomohiro Hoshi, et al.. 'Knowable' as 'known after an announcement'. The review of symbolic logic, 2008, 1 (3), pp.305--334. ⟨10.1017/S1755020308080210⟩. ⟨hal-00800649⟩