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(2018) Jaakko Hintikka on knowledge and game-theoretical semantics, Dordrecht, Springer.
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 (varphi ) to be the "local truth" of (varphi ), semantically rendered via an interior operator. This is closely related to the notion of (varphi ) 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.
Publication details
DOI: 10.1007/978-3-319-62864-6_6
Full citation:
Bjorndahl, A. (2018)., Topological subset space models for public announcements, in H. Van Ditmarsch & P. Sandu (eds.), Jaakko Hintikka on knowledge and game-theoretical semantics, Dordrecht, Springer, pp. 165-186.
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