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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
##### Keywords:
justified knowledge; common knowledge; Artemov; conservative
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