On confirmation and rational betting

Lehman, Robert S.

doi:10.2307/2268221

Cited by 94 publications

(48 citation statements)

References 4 publications

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“…0 ), condition (b) easily follows, Suppose now that (b) holds, and take any event E " H3G;Go : then either there exists such that P ? (H)90, and so (since H is union of atoms generated by C) the probability P(E " H) can be determined by formula (24); or the event H is such that P ? (H):0 for every .1, and so we can give to E " H a (coherent) probability…”

Section: Strengthening Coherencementioning

confidence: 99%

Conditioning and inference in intelligent systems

Coletti¹,

Scozzafava²

1999

Soft Computing - A Fusion of Foundations, Methodologies and App

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We maintain that among the research trends concerning the various aspects and methodologies for the management of partial and revisable information in automated reasoning and giving particular emphasis to conditioning and inference, conditional events and conditional probability (in a coherent -in the sense of de Finetti -framework) play a central role: we will review some of our and related results, showing that this approach is able to encompass many of other existing numerical and symbolic methods dealing with the treatment of partial knowledge and uncertainty in Artificial Intelligence.

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Section: Strengthening Coherencementioning

confidence: 99%

Conditioning and inference in intelligent systems

Coletti¹,

Scozzafava²

1999

Soft Computing - A Fusion of Foundations, Methodologies and App

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“…Shortly after, the converse was established by Kemeny in [21], a result proved independently in [24]. The Shimony-Kemeny characterisation is obtained under far more restrictive conditions than those yielding de Finetti's theorem, which 1991 Mathematics Subject Classification.…”

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confidence: 96%

Strict Coherence on Many-Valued Events

Flaminio¹,

Hosni²,

Montagna³

2018

J. symb. log.

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Abstract. We investigate the property of strict coherence in the setting of manyvalued logics. Our main results read as follows: (i) a map from an MV-algebra to [0,1] is strictly coherent if and only if it satisfies Carnap's regularity condition and, (ii) a [0, 1]-valued book on a finite set of many-valued events is strictly coherent if and only if it extends to a faithful state of an MV-algebra that contains them. Remarkably this latter result allows us to relax the rather demanding conditions for the Shimony-Kemeny characterisation of strict coherence put forward in the mid 1950s in this Journal. §1. Introduction and motivation. This paper contributes to the logical foundations of probability by investigating strict coherence on many-valued events. The notion of strict coherence was introduced in this Journal by Abner Shimony and John Kemeny as a logically inspired refinement of the notion of coherence used by Bruno de Finetti to ground his subjective interpretation of probability. Informally, coherence demands that a rational agent avoids the logical possibility of "sure loss" in suitably specified betting situations. Its strict counterpart, in addition, demands that each prospect of losing should be balanced by a prospect of gaining.Interest in the condition of strict coherence was prompted by Carnap's analysis of what he termed "regular" probability functions in [4] (see also [37, Chapter 10 ]). Informally those functions arise by strengthening the usual normalisation axiom of probability in the right-to-left direction. That is to say that 1 (respectively, 0) is assigned only to tautologies (respectively, contradictions). The rationale for Carnap-regular functions is that, however unlikely, possible events may happen.In [38] Shimony proved that imposing strict coherence to a map from finite boolean algebras to [0, 1] was sufficient to single out Carnap-regular functions. Shortly after, the converse was established by Kemeny in [21], a result proved independently in [24]. The Shimony-Kemeny characterisation is obtained under far more restrictive conditions than those yielding de Finetti's theorem, which 1991 Mathematics Subject Classification. Primary 03B48, Secondary 60A05, 06D35, 06F20, 52B11.

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“…Converse Dutch book theorems [51,59] purport to show that any agent who obeys the probability calculus is immune to a Dutch book. Yet other Dutch book theorems purport to show that any agent who violates Conditionalisation, Reflection, etc.…”

Section: Dutch Book Argumentsmentioning

confidence: 99%