Information algebras in the theory of imprecise probabilities

In this paper we create a bridge between desirability and information algebras: we show how coherent sets of gambles, as well as coherent lower previsions, induce such structures. This allows us to enforce the view of such imprecise-probability objects as algebraic and logical structures; moreover, it enforces the interpretation of probability as information, and gives tools to manipulate them as such. (c) 2021 The Authors. Published by Elsevier Inc.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Automated summary

In this paper, we establish a connection between desirability and information algebras by showing how coherent sets of gambles and coherent lower previsions induce such structures. This approach allows us to treat imprecise-probability objects as algebraic and logical structures, and provides tools for manipulation.