Positive Announcements
Abstract
Arbitrary public announcement logic (APAL) reasons about how the knowledge of a set of agents changes after true public announcements and after arbitrary announcements of true epistemic formulas. We consider a variant of arbitrary public announcement logic called positive arbitrary public announcement logic (APAL+), which restricts arbitrary public announcements to announcement of positive formulas. Positive formulas prohibit statements about the ignorance of agents. The positive formulas correspond to the universal fragment in first-order logic. As two successive announcements of positive formulas need not correspond to the announcement of a positive formula, APAL+ is rather different from APAL. We show that APAL+ is more expressive than public announcement logic PAL, and that APAL+ is incomparable with APAL. We also provide a sound and complete infinitary axiomatisation.
Keywords
Cite
@article{arxiv.1803.01696,
title = {Positive Announcements},
author = {Hans van Ditmarsch and Tim French and James Hales},
journal= {arXiv preprint arXiv:1803.01696},
year = {2021}
}