  According to a standard view, quantum mechanics (QM) is a contextual theory
and quantum probability does not satisfy Kolmogorov's axioms. We show, by
considering the macroscopic contexts associated with measurement procedures and
the microscopic contexts (mu-contexts) underlying them, that one can interpret
quantum probability as epistemic, despite its non-Kolmogorovian structure. To
attain this result we introduce a predicate language L(x), a classical
probability measure on it and a family of classical probability measures on
sets of mu contexts, each element of the family corresponding to a
(macroscopic) measurement procedure. By using only Kolmogorovian probability
measures we can thus define mean conditional probabilities on the set of
properties of any quantum system that admit an epistemic interpretation but are
not bound to satisfy Kolmogorov's axioms. The generalized probability measures
associated with states in QM can then be seen as special cases of these mean
probabilities, which explains how they can be non-classical and provides them
with an epistemic interpretation. Moreover, the distinction between compatible
and incompatible properties is explained in a natural way, and purely
theoretical classical conditional probabilities coexist with empirically
testable quantum conditional probabilities.
