  We present a general formalism to make the Replica-Symmetric and
Replica-Symmetry-Breaking ansatz in the context of Kikuchi's Cluster
Variational Method (CVM). Using replicas and the message-passing formulation of
CVM we obtain a variational expression of the replicated free energy of a
system with quenched disorder, both averaged and on a single sample, and make
the hierarchical ansatz using functionals of functions of fields to represent
the messages. We begin to study the method considering the plaquette
approximation to the averaged free energy of the Edwards-Anderson model in the
paramagnetic Replica-Symmetric phase. In two dimensions we find that the
spurious spin-glass phase transition of the Bethe approximation disappears and
the paramagnetic phase is stable down to zero temperature in all the three
regular 2D lattices. The quantitative estimates of the free energy and of
various other quantities improve those of the Bethe approximation. We provide
the physical interpretation of the beliefs in the replica-symmetric phase as
disorder distributions of the local Hamiltonians. The messages instead do not
admit such an interpretation and indeed they cannot be represented as
populations in the spin-glass phase at variance with the Bethe approximation.
