A logical characterization of coherence for imprecise probabilities

Fedel, Martina and Hosni, Hykel and Montagna, Franco (2010) A logical characterization of coherence for imprecise probabilities. [MIMS Preprint]

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Abstract

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 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations
MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
MSC 2010, the AMS's Mathematics Subject Classification > 91 Game theory, economics, social and behavioral sciences
Depositing User: Dr Hykel Hosni
Date Deposited: 21 Nov 2010
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/1546

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