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.
|Titolo:||A logical characterization of coherence for imprecise probabilities|
HOSNI, HYKEL (Corresponding)
|Parole Chiave:||Subjective probability; Probabilistic logic; Coherence; Betting framework; Imprecise probability; Many-valued logic|
|Settore Scientifico Disciplinare:||Settore M-FIL/02 - Logica e Filosofia della Scienza|
|Data di pubblicazione:||2011|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1016/j.ijar.2011.06.004|
|Appare nelle tipologie:||01 - Articolo su periodico|
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