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1993•RePEc: Research Papers in EconomicsRequires access

A Non-Minimal but Very Weak Axiomatization of Common Belief

Philippe Mongin

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Abstract

The paper introduces a modal logic system of individual and common belief which is shown to be sound and complete with respect to a version of Neighbourhood semantics. This axiomatization of common belief is the weakest of all those currently available : it dispenses with even the Monotonicity rule of individual belief. It is non-minimal in that it does not use just the Equivalence rule but the conjunction of the latter with the specially devised rule of C-Restricted Monotonicity

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What this paper is about

The paper introduces a modal logic system of individual and common belief which is shown to be sound and complete with respect to a version of Neighbourhood semantics. This axiomatization of common belief is the weakest of all those currently available : it dispenses with even the Monotonicity rule of individual belief. It is non-minimal in that it does not use just the Equivalence rule but the conjunction of the latter with the specially devised rule of C-Restricted Monotonicity

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Available abstract

The paper introduces a modal logic system of individual and common belief which is shown to be sound and complete with respect to a version of Neighbourhood semantics. This axiomatization of common belief is the weakest of all those currently available : it dispenses with even the Monotonicity rule of individual belief. It is non-minimal in that it does not use just the Equivalence rule but the conjunction of the latter with the specially devised rule of C-Restricted Monotonicity

Key concepts: Monotonic function, Belief revision, Equivalence (formal languages), Modal operator, Modal, Mathematics, Non-monotonic logic, Modal logic

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