The Proof Theory of Common Knowledge

Marti, Michel; Studer, Thomas (2018). The Proof Theory of Common Knowledge. In: Ditmarsch, Hans van; Sandu, Gabriel (eds.) Jaakko Hintikka on Knowledge and Game-Theoretical Semantics. Outstanding Contributions to Logic: Vol. 12 (pp. 433-455). Cham: Springer International Publishing 10.1007/978-3-319-62864-6_18

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Common knowledge of a proposition A can be characterized by the following infinitary conjunction: everybody knows A and everybody knows that everybody knows A and everybody knows that everybody knows that everybody knows A and so on. We present a survey of deductive systems for the logic of common knowledge. In particular, we present two different Hilbert-style axiomatizations and two infinitary cut-free sequent systems. Further we discuss the problem of syntactic cut elimination for common knowledge. The paper concludes with a list of open problems.

Item Type:

Book Section (Book Chapter)

Division/Institute:

08 Faculty of Science > Institute of Computer Science (INF) > Logic and Theory Group (LTG)
08 Faculty of Science > Institute of Computer Science (INF)

UniBE Contributor:

Marti, Michel and Studer, Thomas

Subjects:

000 Computer science, knowledge & systems
500 Science > 510 Mathematics

ISBN:

978-3-319-62863-9

Series:

Outstanding Contributions to Logic

Publisher:

Springer International Publishing

Language:

English

Submitter:

Lukas Jaun

Date Deposited:

07 May 2018 10:28

Last Modified:

07 May 2018 10:28

Publisher DOI:

10.1007/978-3-319-62864-6_18

BORIS DOI:

10.7892/boris.112771

URI:

https://boris.unibe.ch/id/eprint/112771

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