  We study a class of solutions to the SL(2,R)_k Knizhnik-Zamolodchikov
equation. First, logarithmic solutions which represent four-point correlation
functions describing string scattering processes on three-dimensional Anti-de
Sitter space are discussed. These solutions satisfy the factorization ansatz
and include logarithmic dependence on the SL(2,R)-isospin variables. Different
types of logarithmic singularities arising are classified and the
interpretation of these is discussed. The logarithms found here fit into the
usual pattern of the structure of four-point function of other examples of
AdS/CFT correspondence. Composite states arising in the intermediate channels
can be identified as the phenomena responsible for the appearance of such
singularities in the four-point correlation functions. In addition, logarithmic
solutions which are related to non perturbative (finite k) effects are found.
By means of the relation existing between four-point functions in
Wess-Zumino-Novikov-Witten model formulated on SL(2,R) and certain five-point
functions in Liouville quantum conformal field theory, we show how the
reflection symmetry of Liouville theory induces particular Z_2 symmetry
transformations on the WZNW correlators. This observation allows to find
relations between different logarithmic solutions. This Liouville description
also provides a natural explanation for the appearance of the logarithmic
singularities in terms of the operator product expansion between degenerate and
puncture fields.
