A logical characterization of coherence for imprecise probabilities |
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Authors: | Martina Fedel Hykel Hosni Franco Montagna |
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Institution: | aDepartment of Mathematics and Computer Science, University of Siena, Italy;bScuola Normale Superiore, Pisa, Italy |
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Abstract: | Whilst supported by compelling arguments, the representation of uncertainty by means of (subjective) probability does not enjoy a unanimous consensus. 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). |
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Keywords: | Subjective probability Probabilistic logic Coherence Betting framework Imprecise probability Many-valued logic |
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