Topological Subset Space Models for Public announcements

Abstract

We reformulate a key definition given by Wáng and Ågotnes [18] to provide semantics for public announcements in subset spaces. More precisely, we interpret the precondition for a public announcement of to be the “local truth” of, semantically rendered via an interior operator. This is closely related to the notion of being “knowable”. We argue that these revised semantics improve on the original and offer several motivating examples to this effect. A key insight that emerges is the crucial role of topological structure in this setting. Finally, we provide a simple axiomatization of the resulting logic and prove completeness.