  We present a general approach to construct a class of generalized topological
field theories with constraints by means of generalized differential calculus
and its application to connection theory. It turns out that not only the
ordinary BF formulations of general relativity and Yang-Mills theories, but
also the N=1,2 chiral supergravities can be reformulated as these constrained
generalized topological field theories once the free parameters in the
Lagrangian are specially chosen. We also show that the Chern-Simons action on
the boundary may naturally be induced from the generalized topological action
in the bulk, rather than introduced by hand.
