Realizing public announcements by justifications

Highlights

• We study two dynamic epistemic logics with justifications.

• We prove a realization theorem for the modal logic of public announcements.

• We develop a realization method by translation.

Abstract

Modal public announcement logics study how beliefs change after public announcements. However, these logics cannot express the reason for a new belief. Justification logics fill this gap since they can formally represent evidence and justifications for an agent's belief. We present $\mathsf{OPAL}(\mathsf{K})$ and $\mathsf{JPAL}(\mathsf{K})$, two alternative justification counterparts of Gerbrandy–Groeneveld's public announcement logic $\mathsf{PAL}(\mathsf{K})$. We show that $\mathsf{PAL}(\mathsf{K})$ is the forgetful projection of both $\mathsf{OPAL}(\mathsf{K})$ and $\mathsf{JPAL}(\mathsf{K})$. We also establish that $\mathsf{JPAL}(\mathsf{K})$ partially realizes $\mathsf{PAL}(\mathsf{K})$. The question whether a similar result holds for $\mathsf{OPAL}(\mathsf{K})$ is still open.