Positive Announcements

TL;DR

This paper introduces positive arbitrary public announcement logic (APAL+), a variant of APAL that restricts announcements to positive formulas, and explores its expressiveness and axiomatization.

Contribution

It defines APAL+, analyzes its expressiveness compared to PAL and APAL, and provides a sound and complete infinitary axiomatisation.

Findings

APAL+ is more expressive than PAL.

APAL+ is incomparable with APAL.

A sound and complete infinitary axiomatisation for APAL+ is provided.

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.