  In a recent work we have shown how to construct an information algebra of
coherent sets of gambles defined on general possibility spaces. Here we analyze
the connection of such an algebra with the set algebra of subsets of the
possibility space on which gambles are defined and the set algebra of sets of
its atoms. Set algebras are particularly important information algebras since
they are their prototypical structures. Furthermore, they are the algebraic
counterparts of classical propositional logic. As a consequence, this paper
also details how propositional logic is naturally embedded into the theory of
imprecise probabilities.
