Revision rules for convex sets of probabilities
Mathematical models for handling partial knowledge in artificial intelligence
Artificial Intelligence
Belief models: An order-theoretic investigation
Annals of Mathematics and Artificial Intelligence
Epistemic irrelevance on sets of desirable gambles
Annals of Mathematics and Artificial Intelligence
Notes on conditional previsions
International Journal of Approximate Reasoning
Marginal extension in the theory of coherent lower previsions
International Journal of Approximate Reasoning
Graphical models for imprecise probabilities
International Journal of Approximate Reasoning
Epistemic irrelevance in credal nets: The case of imprecise Markov trees
International Journal of Approximate Reasoning
Artificial Intelligence
Sets of desirable gambles: Conditioning, representation, and precise probabilities
International Journal of Approximate Reasoning
Notes on desirability and conditional lower previsions
Annals of Mathematics and Artificial Intelligence
Independence concepts for convex sets of probabilities
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Exchangeability and sets of desirable gambles
International Journal of Approximate Reasoning
Conglomerable natural extension
International Journal of Approximate Reasoning
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The results in this paper add useful tools to the theory of sets of desirable gambles, a growing toolbox for reasoning with partial probability assessments. We investigate how to combine a number of marginal coherent sets of desirable gambles into a joint set using the properties of epistemic irrelevance and independence. We provide formulas for the smallest such joint, called their independent natural extension, and study its main properties. The independent natural extension of maximal coherent sets of desirable gambles allows us to define the strong product of sets of desirable gambles. Finally, we explore an easy way to generalise these results to also apply for the conditional versions of epistemic irrelevance and independence. Having such a set of tools that are easily implemented in computer programs is clearly beneficial to fields, like AI, with a clear interest in coherent reasoning under uncertainty using general and robust uncertainty models that require no full specification.