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Common knowledge (logic) : ウィキペディア英語版 | Common knowledge (logic)
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.〔Osborne, Martin J., and Ariel Rubinstein. ''A Course in Game Theory''. Cambridge, MA: MIT, 1994. Print.〕 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 〔 Morris Friedell, "On the Structure of Shared Awareness," Behavioral Science 14 (1969): 28-39.〕. 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 book ''Meaning'', independently developed a notion he called "mutual knowledge" which functions quite similarly to Lewis's "common knowledge".〔Stephen Schiffer, ''Meaning'', 2nd edition, Oxford University Press, 1988. The first edition was published by OUP in 1972. For a discussion of both Lewis's and Schiffer's notions, see Russell Dale, ''(The Theory of Meaning )'' (1996).〕 ==Example==
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