Irrelevant and independent natural extension for sets of desirable
  gambles
  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.
