Stable logarithmic maps to Deligne--Faltings pairs II
  We make an observation which enables one to deduce the existence of an algebraic stack of log maps for all generalized Deligne--Faltings log structures (in particular simple normal crossings divisor) from the simplest case with log structures given by a Cartier divisor (essentially the smooth divisor case). 
Dan Abramovich and Qile Chen
math.AG