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).

A logical characterization of coherence for imprecise probabilities / M. Fedel, H. Hosni, F. Montagna. - In: INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. - ISSN 0888-613X. - 52:8(2011), pp. 1147-1170.

A logical characterization of coherence for imprecise probabilities

H. Hosni
;
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).
Subjective probability; Probabilistic logic; Coherence; Betting framework; Imprecise probability; Many-valued logic
Settore M-FIL/02 - Logica e Filosofia della Scienza
2011
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/326233
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