The infinite epistemic regress problem has no unique solution

Meester, Ronald; Kerkvliet, Timber

doi:10.1007/s11229-019-02383-7

Cited by 4 publications

(2 citation statements)

References 15 publications

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“…Among the most recent work in the area, Meester and Kerkvliet have recently proposed to look at the issue from a different perspective [111,110], by redeveloping and rederiving various notions of conditional belief functions, using a relative frequencies stance similar to that of [97]. The authors call the two main forms of conditioning contingent and necessary conditioning, respectively.…”

Section: Other Workmentioning

confidence: 99%

A geometric approach to conditioning belief functions

Cuzzolin

2021

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Conditioning is crucial in applied science when inference involving time series is involved. Belief calculus is an effective way of handling such inference in the presence of epistemic uncertainty -unfortunately, different approaches to conditioning in the belief function framework have been proposed in the past, leaving the matter somewhat unsettled. Inspired by the geometric approach to uncertainty, in this paper we propose an approach to the conditioning of belief functions based on geometrically projecting them onto the simplex associated with the conditioning event in the space of all belief functions. We show here that such a geometric approach to conditioning often produces simple results with straightforward interpretations in terms of degrees of belief. This raises the question of whether classical approaches, such as for instance Dempster's conditioning, can also be reduced to some form of distance minimisation in a suitable space. The study of families of combination rules generated by (geometric) conditioning rules appears to be the natural prosecution of the presented research.

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Section: Other Workmentioning

confidence: 99%

A geometric approach to conditioning belief functions

Cuzzolin

2021

Preprint

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“…For a more sceptical view about the Shafer approach, see for instance(Pearl 1988). 9 For the former, seePeijnenburg (2007) andAtkinson and Peijnenburg (2017); for the latter, seeMeester and Kerkvliet (2019), Sect. 4.…”

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Probability functions, belief functions and infinite regresses

Atkinson

Peijnenburg

2020

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In a recent paper Ronald Meester and Timber Kerkvliet argue by example that infinite epistemic regresses have different solutions depending on whether they are analyzed with probability functions or with belief functions. Meester and Kerkvliet give two examples, each of which aims to show that an analysis based on belief functions yields a different numerical outcome for the agent’s degree of rational belief than one based on probability functions. In the present paper we however show that the outcomes are the same. The only way in which probability functions and belief functions can yield different solutions for the agent’s degree of belief is if they are applied to different examples, i.e. to different situations in which the agent finds himself.

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Infinitism: rival or common ground in answering the epistemic regress?

Murday

2024

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The infinite epistemic regress problem has no unique solution

Cited by 4 publications

References 15 publications

A geometric approach to conditioning belief functions

A geometric approach to conditioning belief functions

Probability functions, belief functions and infinite regresses

Infinitism: rival or common ground in answering the epistemic regress?

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