From Public Announcements to Asynchronous Announcements

Philippe Balbiani (1, 2) , Hans van Ditmarsch (3) , Saúl Fernández González (1)

1 IRIT-LILaC - Logique, Interaction, Langue et Calcul
2 CNRS - Centre National de la Recherche Scientifique
3 CELLO - Computational Epistemic Logic in LOrraine

We present a multi-agent logic of belief and announcements wherein the sending of announcements and the reception of announcements by agents are separated, thus straying from the paradigm of Public Announcement Logic (PAL). Both PAL and Asynchronous Announcement Logic (recently proposed in the literature) are special cases in our framework. We provide a history-based semantics for our 'Partially Synchronous Announcement Logic', proposing three different interpretations of the notion of asynchronic-ity. We then show that the logic of our three proposals is the same ('PSAL') and prove soundness and completeness for a Hilbert-style axiomatisation. Finally, we propose a notion of common belief for this framework, of which we give some validities.

Domaines: Logique en informatique [cs.LO]

Philippe Balbiani, Hans van Ditmarsch, Saúl Fernández González. From Public Announcements to Asynchronous Announcements. 24th European Conference on Artificial Intelligence (ECAI 2020), European Association for Artificial Intelligence (EurAI); Spanish AI Society (AEPIA); Intelligent Systems Group (GSI) and the Research Center on Intelligent Technologies of the University of Santiago de Compostela (CiTIUS), Aug 2020, Santiago de Compostela, Spain. pp.75 - 82, ⟨10.3233/FAIA200078⟩. ⟨hal-02936439⟩