  We present a clausal resolution-based method for normal multimodal logics of
confluence, whose Kripke semantics are based on frames characterised by
appropriate instances of the Church-Rosser property. Here we restrict attention
to eight families of such logics. We show how the inference rules related to
the normal logics of confluence can be systematically obtained from the
parametrised axioms that characterise such systems. We discuss soundness,
completeness, and termination of the method. In particular, completeness can be
modularly proved by showing that the conclusions of each newly added inference
rule ensures that the corresponding conditions on frames hold. Some examples
are given in order to illustrate the use of the method.
