  We introduce the concept of a viable generically toroidal crossing (gtc)
Deligne--Mumford stack $Y$. This generalizes the concept of Gorenstein toroidal
crossing space, which in turn generalizes that of a simple normal crossing
scheme.
  On such a space $Y$, we define by explicit construction a natural sheaf
$\mathcal{LS}_Y$, intrinsic to $Y$. Our main theorem states that the set of
nowhere vanishing sections $\Gamma(Y,\mathcal{LS}_Y^\times)$ is canonically
bijective to the set of isomorphism classes of log structures on $Y$ over
$k^\dagger$ compatible with the gtc structure.
  The definition of $\mathcal{LS}_Y$ by explicit construction permits the
effective construction of log structures on $Y$; it also enables logarithmic
birational geometry, in particular the construction -- in some cases -- of
resolutions of singular log structures.
  Our work generalizes Theorem 3.22 in GS06 and our proof follows closely the
proof of that theorem as given in GS06.
