About: Common knowledge (logic)

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Common knowledge is a special kind of knowledge for a group of agents. There is common knowledge of p in a group of agents G when all the agents in G know p, they all know that they know p, they all know that they all know that they know p, and so on ad infinitum. It can be denoted as .

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rdf:type	Thing
rdfs:label	Common knowledge (logic) (en)
rdfs:comment	Common knowledge is a special kind of knowledge for a group of agents. There is common knowledge of p in a group of agents G when all the agents in G know p, they all know that they know p, they all know that they all know that they know p, and so on ad infinitum. It can be denoted as . (en)
differentFrom	Common knowledge
sameAs	Common knowledge (logic) Common knowledge (logic)
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Cite_journal dbt:Distinguish dbt:ISBN dbt:Note dbt:Portal dbt:Ref dbt:Reflist dbt:Short_description dbt:Cite_SEP dbt:Game_theory
Subject	Concepts in logic Social epistemology Fixed points (mathematics) Formal epistemology Game theory Knowledge
Link from a Wikipage to an external page	http://twofoldgaze.wordpress.com/2009/11/12/in-the-long-run-we-are-all-dead-ii/ http://terrytao.wordpress.com/2008/02/05/the-blue-eyed-islanders-puzzle/ https://www.physics.harvard.edu/uploads/files/undergrad/probweek/prob2.pdf https://www.physics.harvard.edu/uploads/files/undergrad/probweek/sol2.pdf http://twofoldgaze.wordpress.com/2009/11/07/in-the-long-run-we-are-all-dead/ http://www.masfoundations.org http://www.masfoundations.org/download.html
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prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Common_knowledge_(logic)?oldid=1074349041&ns=0
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Wikipage revision ID	1074349041 (xsd:integer)
Link from a Wikipage to another Wikipage	Logic puzzle Prior probability Propositional calculus Robert Aumann Well-formed formula Ad infinitum Agent-based model Aleph number Aumann's agreement theorem Axiom Stephen Schiffer Two Generals' Problem University of Pittsburgh Press Cambridge University Press Concepts in logic Social epistemology Global game Journal of the ACM Fixed points (mathematics) Formal epistemology Game theory Knowledge David Lewis (philosopher) Mutual knowledge (logic) Nash equilibrium Posterior probability Set theory The Stuff of Thought Truth value Computer science Econometrica Herbert Gintis John Horton Conway Partition of a set Epistemic modal logic Game theory Induction puzzles Kripke semantics Kripke structure (model checking) Transitive closure Steven Pinker Strategy (game theory) Knowledge MIT Press Multimodal logic Reflexive closure
has abstract	Common knowledge is a special kind of knowledge for a group of agents. There is common knowledge of p in a group of agents G when all the agents in G know p, they all know that they know p, they all know that they all know that they know p, and so on ad infinitum. It can be denoted as . The concept was first introduced in the philosophical literature by David Kellogg Lewis in his study Convention (1969). The sociologist Morris Friedell defined common knowledge in a 1969 paper. It was first given a mathematical formulation in a set-theoretical framework by Robert Aumann (1976). Computer scientists grew an interest in the subject of epistemic logic in general – and of common knowledge in particular – starting in the 1980s. There are numerous puzzles based upon the concept which have been extensively investigated by mathematicians such as John Conway. The philosopher Stephen Schiffer, in his 1972 book Meaning, independently developed a notion he called "mutual knowledge" which functions quite similarly to Lewis's and Friedel's 1969 "common knowledge". If a trustworthy announcement is made in public, then it becomes common knowledge; However, if it is trasmitted to each agent in private, it becomes mutual knowledge but not common knowledge. Even if the fact that "every agent in the group knows p" is trasmitted to each agent in private, it still isn't common knowledge: . But, if any agent publicly announces his knowledge of p, then it becomes common knowledge that he knows p (viz. ). If every agent publicly announces their knowledge of p, p becomes common knowledge . (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Common_knowledge_(logic)
is Wikipage redirect of	Blue-eyed islanders
is Link from a Wikipage to another Wikipage of	Grounding in communication Abraham Neyman Aumann's agreement theorem Backward induction Bayesian game Blue-eyed islanders David Lewis (philosopher) Doxastic logic Drama theory Mutual knowledge Mutual knowledge (logic) Nash equilibrium Criticism of Facebook List of important publications in concurrent, parallel, and distributed computing Common ground (linguistics) Common knowledge

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