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.

中文翻译：

---

正面公告

任意公告逻辑 (APAL) 推理一组代理的知识在真实公告之后和任意公告真实认知公式之后如何变化。我们考虑任意公告逻辑的一种变体，称为正任意公告逻辑（APAL+），它将任意公告限制为正公式公告。正公式禁止关于代理人无知的陈述。正公式对应于一阶逻辑中的通用片段。由于连续两次肯定公式的公告不需要与肯定公式的公告相对应，因此APAL+与APAL有很大不同。我们证明 APAL+ 比公告逻辑 PAL 更具表现力，而且 APAL+ 与 APAL 无法比拟。