In this paper, we show that coherent sets of gambles 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
secondly, it connects desirability, hence imprecise probabilities, to other
formalism in computer science sharing the same underlying structure. Both the
domain-free and the labeled view of the information algebra of coherent sets of
gambles are presented, considering general possibility spaces.