Information algebras in the theory of imprecise probabilities
This work offers a theoretical unification for researchers in imprecise probabilities and related fields, but it is incremental as it builds on existing algebraic frameworks.
The paper embeds coherent sets of gambles and coherent lower/upper previsions into information algebras, providing a new algebraic and logical perspective on desirability and imprecise probabilities, and connects these to other computer science formalisms.
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.