Limit-Agreeing To Disagree

Bach, CW ORCID: 0000-0003-0187-1820 and Cabessa, J (2017) Limit-Agreeing To Disagree. Journal of Logic and Computation, 27 (4). pp. 1169-1187.

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Abstract

We reconsider Aumann' s seminal impossibility theorem that agents cannot agree to disagree in a topologically extended epistemic model. In such a framework, a possibility result on agreeing to disagree actually ensues. More precisely, agents with a common prior belief satisfying limit knowledge instead of common knowledge of their posterior beliefs may have distinct posterior beliefs. Since limit knowledge is defined as the limit of iterated mutual knowledge, agents can thus be said to limit-agree to disagree. Besides, an example is provided in which limit knowledge coincides with Rubinstein's (1989) notion of almost common knowledge, and the agents have almost common knowledge of posteriors yet distinct posterior beliefs. More generally, an epistemic-topological foundation for almost common knowledge is thus provided.

Item Type:	Article
Uncontrolled Keywords:	Agreeing to disagree, Agreement theorems, Almost common knowledge, Epistemic-topological framework, Interactive epistemology, Limit knowledge
Depositing User:	Symplectic Admin
Date Deposited:	13 Feb 2017 08:19
Last Modified:	19 Jan 2023 07:19
DOI:	10.1093/logcom/exv082
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3005762