On the Logic of Common Belief and Common Knowledge
AbstractThe paper surveys the currently available axioma.tizations of common belief (CB) and common knowledge (CK) by means of modal propositionallogic:s. (Throughout, knowledge - whether individual or common - is defined as true belief.) Section 1 introduces the formal method ofaxiomatization followed by epistemic logicians, especially the syntaxe-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while bridly 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 (ormer 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 mono tonicity has thusfar proved indispensable. Section 5 explains another consequence of general releo.-ance: despite the "infinitary" nature of CB, the axiom systems of this paper admit of effecth-e decision procedures, i.e., they are decidable in the logician's sense.
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Bibliographic InfoPaper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 1994005.
Date of creation: 01 Jan 1994
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common belief; common knowledge; Kripke structures; neighbourhood structures; partitional model; modal propositional logic; epistemic logic;
Other versions of this item:
- Lismont, L. & Mongin, P., . "On the logic of common belief and common knowledge," CORE Discussion Papers RP -1104, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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- Bonanno, Giacomo & Nehring, Klaus, 1998. "On the logic and role of Negative Introspection of Common Belief," Mathematical Social Sciences, Elsevier, vol. 35(1), pages 17-36, January.
- Mongin, P., 1998.
"Does Optimization Imply Rationality?,"
9817, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
- Heifetz, Aviad, 1996. "Common belief in monotonic epistemic logic," Mathematical Social Sciences, Elsevier, vol. 32(2), pages 109-123, October.
- LISMONT, Luc & MONGIN, Philippe, 1993.
"Belief Closure : A Semantics of Common Knowledge for Modal Propositional Logic,"
CORE Discussion Papers
1993039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Lismont L. & Mongin, P., 1996. "Belief closure: A semantics of common knowledge for modal propositional logic," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 60-60, February.
- Lismont, Luc & Mongin, Philippe, 1995. "Belief closure: A semantics of common knowledge for modal propositional logic," Mathematical Social Sciences, Elsevier, vol. 30(2), pages 127-153, October.
- Kaneko, Mamoru, 1999. "Epistemic considerations of decision making in games," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 105-137, September.
- Klaus Nehring & Giacomo Bonanno & Massimiliano Marcellino, 2003.
"Varieties of Interpersonal Compatibility of Beliefs,"
992, University of California, Davis, Department of Economics.
- Giacomo Bonanno & Klaus Nehring, . "Varieties of Interpersonal Compatibility of Beliefs," Department of Economics 99-02, California Davis - Department of Economics.
- Olivier Gossner & Elias Tsakas, 2012. "Reasoning-based introspection," Theory and Decision, Springer, vol. 73(4), pages 513-523, October.
- Giacomo Bonanno & Klaus Nehring, .
"Intersubjective Consistency Of Knowledge And Belief,"
Department of Economics
98-03, California Davis - Department of Economics.
- Giacomo Bonanno, 2003. "Intersubjective Consistency Of Knowledge And Belief," Working Papers 983, University of California, Davis, Department of Economics.
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