  Amongst conformal field theories, there exist logarithmic conformal field
theories such as $c_{p,1}$ models. We have investigated $c_{p,q}$ models with a
boundary in search of logarithmic theories and have found logarithmic solutions
of two-point functions in the context of the Coulomb gas picture. We have also
found the relations between coefficients in the two-point functions and
correlation functions of logarithmic boundary operators, and have confirmed the
solutions in [hep-th/0003184]. Other two-point functions and boundary operators
have also been studied in the free boson construction of boundary CFT with
$SU(2)_k$ symmetry in regard to logarithmic theories. This paper is based on a
part of D. Phil. Thesis [hep-th/0312160].
