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, 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: |
05 Dec 2022 15:11 |
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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