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28 March 2024
 
  » arxiv » cs.AI/0203013

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Representing and Aggregating Conflicting Beliefs
Pedrito Maynard-Reid II ; Daniel Lehmann ;
Date 12 Mar 2002
Journal Proceedings of the Seventh International Conference on Principles of Knowledge Representation and Reasoning (KR 2000), April 2000, pp. 153-164
Subject Artificial Intelligence; Logic in Computer Science ACM-class: I.2.4; I.2.11 | cs.AI cs.LO
AffiliationMiami University), Daniel Lehmann (Hebrew University
AbstractWe consider the two-fold problem of representing collective beliefs and aggregating these beliefs. We propose modular, transitive relations for collective beliefs. They allow us to represent conflicting opinions and they have a clear semantics. We compare them with the quasi-transitive relations often used in Social Choice. Then, we describe a way to construct the belief state of an agent informed by a set of sources of varying degrees of reliability. This construction circumvents Arrow’s Impossibility Theorem in a satisfactory manner. Finally, we give a simple set-theory-based operator for combining the information of multiple agents. We show that this operator satisfies the desirable invariants of idempotence, commutativity, and associativity, and, thus, is well-behaved when iterated, and we describe a computationally effective way of computing the resulting belief state.
Source arXiv, cs.AI/0203013
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