Information algebras in the theory of imprecise probabilities, an extension

Abstract

In recent works, we have shown how to construct an information algebra of coherent sets of gambles, considering firstly a particular model to represent questions, called the multivariate model, and then generalizing it. Here we further extend the construction made to the highest level of generality, setting up an associated information algebra of coherent lower previsions, analyzing the connection of both the information algebras constructed with an instance of set algebras and, finally, establishing and inspecting a version of the marginal problem in this framework.Set algebras are particularly important information algebras since they are their prototypical structures. They also represent the algebraic counterparts of classical propositional logic. As a consequence, this paper details as well how propositional logic is naturally embedded into the theory of imprecise probabilities.