We introduce three alternative combinatorial formulations of the theory of evidence (ToE), by proving that both plausibility
and commonality functions share the structure of 'sum function' with belief functions. We compute their Moebius inverses, which we call
basic plausibility and commonality assignments. In the framework of the geometric approach to uncertainty measures the equivalence of the
associated formulations of the ToE is mirrored by the geometric congruence of the related simplices.
We can then describe the point-wise geometry of
these sum functions in terms of rigid transformations mapping them onto each other. Combination rules can be applied to plausibility and
commonality functions through their Moebius inverses, leading to interesting applications of such inverses to the probabilistic transformation problem.