In this paper we extend our correlation functions to the open/closed case.
This gives rise to actions of an open/closed version of the Sullivan PROP as
well as an action of the relevant moduli space. There are several unexpected
structures and conditions that arise in this extension which are forced upon us
by considering the open sector. For string topology type operations, one cannot
just consider graphs, but has to take punctures into account and one has to
restrict the underlying Frobenius algebras. In the moduli space, one first has
to pass to a smaller moduli space which is closed under open/closed duality and
then consider covers in order to account for the punctures