  Given a positive integer $n$, we say that two knots are $V_n$-equivalent if
they have the same Vassiliev invariants of order $\le n$. We showed that the
$V_n$-equivalence classes of ribbon knots form a group, the operation being
induced by the connected sums of knots. The group is free abelian and its rank
is equal to the dimension of the space of primitive Vassiliev invariants of
order $\le n$. The $n$-equivalence classes (following Gusarov's notion) of
ribbon knots also constitute a group. As a corollary, any non-ribbon knot whose
Arf invariant istrivial cannot be distinguished from ribbon knots by finitely
many Vassiliev invariants. Furthermore, all additive knot cobordism invariants
are not of finite type. As a bi-product, we prove that the number of
independent Vassiliev invariants of order $n$ is bounded above by $(n-2)!/2$
for $n>5$.
