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 a special case of possibility space .
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 .
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and coherent lower and upper previsions
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imprecise probabilities and
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desirability, hence imprecise probabilities ,
imprecise probabilities
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information algebra of coherent sets of gambles
resulting information algebras
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a special case of possibility space
product possibility spaces. Moreover, it is shown that both are atomistic and therefore they can be embedded in set algebras