On the logic of common belief and common knowledge

Theory and Decision 37 (1):75-106 (1994)
Download Edit this record How to cite View on PhilPapers
The paper surveys the currently available axiomatizations of common belief (CB) and common knowledge (CK) by means of modal propositional logics. (Throughout, knowledge- whether individual or common- is defined as true belief.) Section 1 introduces the formal method of axiomatization followed by epistemic logicians, especially the syntax-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while briefly discussing their motivations. Two standard semantic constructions, Kripke structures and neighbourhood structures, are introduced in Sections 3 and 4, respectively. It is recalled that Aumann's partitional model of CK is a particular case of a definition in terms of Kripke structures. The paper also restates the well-known fact that Kripke structures can be regarded as particular cases of neighbourhood structures. Section 3 reviews the soundness and completeness theorems proved w.r.t. the former structures by Fagin, Halpern, Moses and Vardi, as well as related results by Lismont. Section 4 reviews the corresponding theorems derived w.r.t. the latter structures by Lismont and Mongin. A general conclusion of the paper is that the axiomatization of CB does not require as strong systems of individual belief as was originally thought- only monotonicity has thusfar proved indispensable. Section 5 explains another consequence of general relevance: despite the "infinitary" nature of CB, the axiom systems of this paper admit of effective decision procedures, i.e., they are decidable in the logician's sense.
PhilPapers/Archive ID
Revision history
Archival date: 2017-10-05
View upload history
References found in this work BETA
Relevance.Sperber, D. & Wilson, D.
Computability and Logic.Boolos, George; Burgess, John; P., Richard & Jeffrey, C.

View all 19 references / Add more references

Citations of this work BETA
Awareness and Partitional Information Structures.Modica, Salvatore & Rustichini, Aldo
Game Logic and its Applications I.Kaneko, Mamoru & Nagashima, Takashi

View all 11 citations / Add more citations

Added to PP index

Total downloads
182 ( #13,987 of 37,125 )

Recent downloads (6 months)
59 ( #5,838 of 37,125 )

How can I increase my downloads?

Monthly downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.