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2010.101: A logical characterization of coherence for imprecise probabilities

2010.101: Martina Fedel, Hykel Hosni and Franco Montagna (2010) A logical characterization of coherence for imprecise probabilities.

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Whilst supported by compelling arguments, the consensus on representing uncertainty by means of (subjective) probability is not unanimous. A substantial part of the relevant criticisms point to its alleged inadequacy for representing ignorance as opposed to uncertainty. The purpose of this paper is to show how a strong justification for taking belief as probability, namely the Dutch Book argument, can be extended naturally so as to provide a logical characterization of coherence for imprecise probability, a framework which is widely believed to accommodate some fundamental features of reasoning under ignorance. The appropriate logic for our purposes is an algebraizable logic whose equivalent algebraic semantics is a variety of MV-algebras with an additional internal unary operation representing upper probability (these algebras will be called UMV-algebras).

Item Type:MIMS Preprint
Uncontrolled Keywords:Subjective probability, probabilistic logic, coherence, betting framework, imprecise probability, many-valued logic, MV-algebras.
Subjects:MSC 2000 > 03 Mathematical logic and foundations
MSC 2000 > 60 Probability theory and stochastic processes
MSC 2000 > 91 Game theory, economics, social and behavioral sciences
MIMS number:2010.101
Deposited By:Dr Hykel Hosni
Deposited On:02 May 2011

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