  It is known that the Einstein-Hilbert action with a positive cosmological
constant can be represented as a perturbation of the SO(4,1) BF theory by a
symmetry-breaking term quadratic in the B field. Introducing fermionic matter
generates additional terms in the action which are polynomial in the tetrads
and the spin connection. We describe how to construct the generating functional
in the spin foam formalism for a generic BF theory when the sources for the B
and the gauge field are present. This functional can be used to obtain a path
integral for General Relativity with matter as a perturbative series whose the
lowest order term is a path integral for a topological gravity coupled to
matter.
