We introduce Arbitrary Public Announcement Logic with Memory (APALM), obtained by adding to the models a ‘memory’ of the initial states, representing the information before any communication took place (“the prior”), and adding to the syntax operators that can access this memory. We show that APALM is recursively axiomatizable (in contrast to the original Arbitrary Public Announcement Logic, for which the corresponding question is still open). We present a complete recursive axiomatization, that includes a natural finitary rule, and study this logic’s expressivity and the appropriate notion of bisimulation. We then examine Group Announcement Logic with Memory (GALM), the extension of APALM obtained by adding to its syntax group announcement operators, and provide a complete finitary axiomatization (again in contrast to the original Group Announcement Logic, for which the only known axiomatization is infinitary). We also show that, in the memory-enhanced context, there is a natural reduction of the so-called coalition announcement modality to group announcements (in contrast to the memory-free case, where this natural translation was shown to be invalid).

我们引入了带有记忆的任意公共公告逻辑 (APALM)，它是通过向模型添加初始状态的“记忆”来获得的，表示任何通信发生之前的信息（“先验”），并添加到可以访问此内存。我们证明了 APALM 是递归公理化的（与原始的任意公告逻辑相反，相应的问题仍然悬而未决）。我们提出了一个完整的递归公理化，其中包括一个自然有限规则，并研究这种逻辑的表达性和互模拟的适当概念。然后，我们检查了带内存的组公告逻辑 (GALM)，这是通过添加到其语法组公告运算符获得的 APALM 的扩展，并提供完整的有限公理化（再次与原始的群公告逻辑相反，唯一已知的公理化是无限的）。我们还表明，在记忆增强的情况下，所谓的联合公告模式自然减少为群体公告（与无记忆情况相反，这种自然翻译被证明是无效的）。