  A surface theoretic view of non-perturbative quantum gravity as "spin-foams"
was proposed by Baez. A possibility of constructing such a model was studied
some time ago based on (2+1) dimensional general relativity as a reformulation
of the Ponzano-Regge model in Riemannian spacetime. In the present work, a
model based on (3+1) dimensional general relativity in Riemannian spacetime is
presented. The construction is explicit and calculable in details. For a
physical application, a computation formula for spacetime volume density
correlations is presented. Remarks for further investigations are made.
