  The graphs induced by partition logics allow a dual probabilistic
interpretation: a classical one for which probabilities lie on the convex hull
of the dispersion-free weights, and another one, suggested independently from
the quantum Born rule, in which probabilities are formed by the (absolute)
square of the inner product of state vectors with the faithful orthogonal
representations of the respective graph. Two immediate consequences are the
demonstration that the logico-empirical structure of observables does not
determine the type of probabilities alone, and that complementarity does not
imply contextuality.
