  The problem of constructing semi-discrete integrable analogues of the
Liouville type integrable PDE is discussed. We call the semi-discrete equation
a discretization of the Liouville type PDE if these two equations have a common
integral. For the Liouville type integrable equations from the well-known
Goursat list for which the integrals of minimal order are of the order less
than or equal to two we presented a list of corresponding semi-discrete
versions. The list contains new examples of non-autonomous Darboux integrable
chains.
