Topological Subset Space Models for Public Announcements

Adam Bjorndahl

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arXiv · 1302.4009

Topological Subset Space Models for Public Announcements

Adam Bjorndahl

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Abstract

We reformulate a key definition given by Wang and Agotnes (2013) to provide semantics for public announcements in subset spaces. More precisely, we interpret the precondition for a public announcement of {\phi} to be the "local truth" of {\phi}, semantically rendered via an interior operator. This is closely related to the notion of {\phi} 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.

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BibTeX RIS

Adam Bjorndahl. 2013-02-16. Topological Subset Space Models for Public Announcements. https://arxiv.org/abs/1302.4009

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