Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 2-coherent and 2-convex Conditional Lower Previsions   In this paper we explore relaxations of (Williams) coherent and convex
conditional previsions that form the families of $n$-coherent and $n$-convex
conditional previsions, at the varying of $n$. We investigate which such
previsions are the most general one may reasonably consider, suggesting
(centered) $2$-convex or, if positive homogeneity and conjugacy is needed,
$2$-coherent lower previsions. Basic properties of these previsions are
studied. In particular, we prove that they satisfy the Generalized Bayes Rule
and always have a $2$-convex or, respectively, $2$-coherent natural extension.
The role of these extensions is analogous to that of the natural extension for
coherent lower previsions. On the contrary, $n$-convex and $n$-coherent
previsions with $n\geq 3$ either are convex or coherent themselves or have no
extension of the same type on large enough sets. Among the uncertainty concepts
that can be modelled by $2$-convexity, we discuss generalizations of capacities
and niveloids to a conditional framework and show that the well-known risk
measure Value-at-Risk only guarantees to be centered $2$-convex. In the final
part, we determine the rationality requirements of $2$-convexity and
$2$-coherence from a desirability perspective, emphasising how they weaken
those of (Williams) coherence.

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The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
16
The categories of this paper are: stat
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The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
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The categories of this paper are: cs
26
The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas