  We introduce a definition for a 'hidden measurement system', i.e., a physical
entity for which there exist: (i) 'a set of non-contextual states of the entity
under study' and (ii) 'a set of states of the measurement context', and which
are such that all uncertainties are due to a lack of knowledge on the actual
state of the measurement context. First we identify an explicit criterion that
enables us to verify whether a given hidden measurement system is a
representation of a given couple $\Si,{\cal E}$ consisting of a set of states
$\Si$ and a set of measurements ${\cal E}$ ($=$ measurement system). Then we
prove for every measurement system that there exists at least one
representation as a hidden measurement system with $[0,1]$ as set of states of
the measurement context. Thus, we can apply this definition of a hidden
measurement system to impose an axiomatics for context dependence. We show that
in this way we always find classical representations (hidden measurement
representations) for general non-classical entities (e.g. quantum entities).
