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).

Fedel, M., Hosnih, ., & Montagna, F. (2011). A logical characterization of coherence for imprecise probabilities. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 52(8), 1147-1170 [10.1016/j.ijar.2011.06.004].

A logical characterization of coherence for imprecise probabilities

MONTAGNA, FRANCO
2011

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).
Fedel, M., Hosnih, ., & Montagna, F. (2011). A logical characterization of coherence for imprecise probabilities. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 52(8), 1147-1170 [10.1016/j.ijar.2011.06.004].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/17555
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