  In this paper we introduce the \emph{semi-online} model that generalizes the
classical online computational model. The semi-online model postulates that the
unknown future has a predictable part and an adversarial part; these parts can
be arbitrarily interleaved. An algorithm in this model operates as in the
standard online model, i.e., makes an irrevocable decision at each step.
  We consider bipartite matching in the semi-online model, for both integral
and fractional cases. Our main contributions are competitive algorithms for
this problem that are close to or match a hardness bound. The competitive ratio
of the algorithms nicely interpolates between the truly offline setting (no
adversarial part) and the truly online setting (no predictable part).
