群体简单宣告逻辑

Group Simple Announcement Logic

群体宣告逻辑在公开宣告逻辑基础上增加用于刻画群体宣告的算子,其中的"群体宣告"是指群内个体的一阶或高阶知识被同时、公开、真实地宣告。然而,很多场合下通常并不接受个体宣告高阶知识。本文所探讨的群体简单宣告逻辑只允许群内个体宣告一阶知识,这与此前版本在一些性质上存在差别。文章的主要成果是群体简单宣告逻辑的表达能力和公理系统等结论,以及对有穷规则在群体宣告逻辑中不可靠、但在群体简单宣告逻辑中具有可靠性的证明。

Group announcement logic(GAL)extends public announcement logic with group announcement operators,where a“group announcement”is a combination of first-or higher-order knowledge being simultaneously,publicly and truthfully announced by a given group of agents.In real situation,however,group announcements of higher-order knowledge is often not allowed.We introduce a variant of group announcement logic,called Group Simple Announcement Logic(GSAL),which only allows group announcements of first-order knowledge,and differs from GAL in some logical properties.Main achievements of this paper is the expressivity results and complete axiomatization of GSAL,including a proof of the unsoundness of a finitary rule in GAL and its soundness in GSAL.