  We introduce the notion of a relative log scheme with boundary: a morphism of
log schemes together with a (log schematically) dense open immersion of its
source into a third log scheme. The sheaf of relative log differentials
naturally extends to this compactification and there is a notion of smoothness
for such data. We indicate how this weak sort of compactification may be used
to develop useful de Rham and crystalline cohomology theories for semistable
log schemes over the log point over a field which are not necessarily proper.
