Information algebras in the theory of imprecise probabilities

TL;DR

This paper demonstrates that the algebraic structure of information algebras can represent coherent sets of gambles and lower/upper previsions, linking imprecise probabilities to formal structures in computer science.

Contribution

It introduces an algebraic framework embedding imprecise probabilities into information algebras, providing new insights and connections to other formal systems.

Findings

Information algebras can represent imprecise probabilities.

Both domain free and labeled views are atomistic.

Embedded structures can be represented in set algebras.

Abstract

In this paper, we show that coherent sets of gambles and coherent lower and upper previsions can be embedded into the algebraic structure of information algebra. This leads firstly, to a new perspective of the algebraic and logical structure of desirability and imprecise probabilities and secondly, it connects imprecise probabilities to other formalism in computer science sharing the same underlying structure. Both the domain free and the labeled view of the resulting information algebras are presented, considering product possibility spaces. Moreover, it is shown that both are atomistic and therefore they can be embedded in set algebras.