Dilation properties of coherent Nearly-Linear models

Dilation is a puzzling phenomenon within Imprecise Probability theory: when it obtains, our uncertainty evaluation on event $A$ vaguer after conditioning $B$, whatever $B$ in given partition $\mathcal{B}$. In this paper we investigate dilation with coherent Nearly-Linear (NL) models. These are family of neighbourhood models, obtaining lower/upper probabilities by linear affine transformations (with barriers) probability, and encompass several well-known such as the Pari-Mutuel Model, $\varepsilon$-contamination model, Total Variation others. We first recall results recently obtained for NL model standard procedure natural extension separately discuss role alternative regular extension. Then, characterise For their most relevant subfamily, Vertical Barrier Models (VBM), study coarsening property dilation, extent constriction. The generalise existing ones established special VBMs. As an interesting aside, general framework how logical (in)dependence from $\mathcal{B}$ or extreme evaluations influence dilation.