  We address the problem of computing the tachyon correlation functions in
Liouville gravity with generic (non-rational) matter central charge c<1. We
consider two variants of the theory. The first is the conventional one in which
the effective matter interaction is given by the two matter screening charges.
In the second variant the interaction is defined by the Liouville dressings of
the non-trivial vertex operator of zero dimension. This particular deformation,
referred to as "diagonal'', is motivated by the comparison with the discrete
approach, which is the subject of a subsequent paper. In both theories we
determine the ground ring of ghost zero physical operators by computing its OPE
action on the tachyons and derive recurrence relations for the tachyon bulk
correlation functions. We find 3- and 4-point solutions to these functional
equations for various matter spectra. In particular, we find a closed
expression for the 4-point function of order operators in the diagonal theory.
