Bilattice logic of epistemic actions and knowledge

Zeinab Bakhtiari (1) , Hans van Ditmarsch (1) , Umberto Rivieccio (2)

1 CELLO - Computational Epistemic Logic in LOrraine
2 DIMAp - Departamento de Informática e Matemática Aplicada [Natal]

Baltag, Moss, and Solecki proposed an expansion of classical modal logic, called logic of epistemic actions and knowledge (EAK), in which one can reason about knowledge and change of knowledge. Kurz and Palmigiano showed how duality theory provides a flexible framework for modeling such epistemic changes, allowing one to develop dynamic epistemic logics on a weaker propositional basis than classical logic (for example an intuitionistic basis). In this paper we show how the techniques of Kurz and Palmigiano can be further extended to define and axiomatize a bilattice logic of epistemic actions and knowledge (BEAK). Our propositional basis is a modal expansion of the well-known four-valued logic of Belnap and Dunn, which is a system designed for handling inconsistent as well as potentially conflicting information. These features, we believe, make our framework particularly promising from a computer science perspective.

Mots clés: Dynamic epistemic logic; Duality; Algebraic models; Modal logic; Bilattices; bilattices; modal logic; algebraic models; duality

Domaines: Informatique [cs]

Zeinab Bakhtiari, Hans van Ditmarsch, Umberto Rivieccio. Bilattice logic of epistemic actions and knowledge. Annals of Pure and Applied Logic, 2020, 171 (6), pp.102790. ⟨10.1016/j.apal.2020.102790⟩. ⟨hal-03014096⟩