# Information algebras in the theory of imprecise probabilities

arXiv: https://arxiv.org/abs/2102.13368 · HTML: https://mlsanity.com/paper/2102.13368/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 13 references that are in the map.
- First posted on arXiv 26 Feb 2021.

## Built on by (most cited first, 2 of 2)

- [Information algebras of coherent sets of gambles in general possibility spaces](https://mlsanity.com/paper/2105.12037/) (2021)
- [Algebras of Sets and Coherent Sets of Gambles](https://mlsanity.com/paper/2105.12986/) (2021)

## Abstract (arXiv)

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.