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Justified and common knowledge: Limited conservativity. (English) Zbl 1132.03319
Artemov, Sergei N. (ed.) et al., Logical foundations of computer science. International symposium, LFCS 2007, New York, NY, USA, June 4–7, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-72732-3/pbk). Lecture Notes in Computer Science 4514, 1-11 (2007).
Summary: We consider the relative strengths of three formal approaches to public knowledge: “any fool” knowledge by McCarthy (1970), Common Knowledge by Halpern and Moses (1990), and Justified Knowledge by Artemov (2004). Specifically, we show that epistemic systems with the Common Knowledge modality \(C\) are conservative with respect to Justified Knowledge systems on formulas \(\chi \land C\varphi \rightarrow \psi \), where \(\chi , \varphi \), and \(\psi \) are \(C\)-free.
For the entire collection see [Zbl 1121.03005].
Reviewer: Reviewer (Berlin)

MSC:
03B42 Logics of knowledge and belief (including belief change)
68T27 Logic in artificial intelligence
68T30 Knowledge representation
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