  For general non-classical systems, we study the different classical
representations that fulfill the specific context dependence imposed by the
hidden measurement system formalism introduced in quant-ph/0008061. We show
that the collection of non-equivalent representations has a poset structure. We
also show that in general, there exists no 'smallest' representation, since
this poset is not a semi-lattice. Then we study the possible representations of
quantum-like measurement systems. For example, we show that there exists a
classical representation of finite dimensional quantum mechanics with ${\Bbb
N}$ as a set of states for the measurement context, and we build an explicit
example of such a representation.
