  We investigate a formulation of continuum 4d gravity in terms of a
constrained BF theory, in the spirit of the Plebanski formulation, but
involving only linear constraints, of the type used recently in the spin foam
approach to quantum gravity. We identify both the continuum version of the
linear simplicity constraints used in the quantum discrete context and a linear
version of the quadratic volume constraints that are necessary to complete the
reduction from the topological theory to gravity. We illustrate and discuss
also the discrete counterpart of the same continuum linear constraints.
Moreover, we show under which additional conditions the discrete volume
constraints follow from the simplicity constraints, thus playing the role of
secondary constraints.
