  Taking quantum formalism as a point of reference and connection, we explore
the various possibilities that arise in the construction of physical theories.
Analyzing the distinct physical phenomena that each of them may describe, we
introduce the different types of hidden variables theories that correspond to
these physical phenomena. A hierarchical classification of the offered
theories, based on the degree of correlation between dichotomic observables in
bipartite systems, as quantified by a Bell type inequality, is finally
proposed.
