  We investigate the possibility of extending the non-functionally complete
logic of a collection of Boolean connectives by the addition of further Boolean
connectives that make the resulting set of connectives functionally complete.
More precisely, we will be interested in checking whether an axiomatization for
Classical Propositional Logic may be produced by merging Hilbert-style calculi
for two disjoint incomplete fragments of it. We will prove that the answer to
that problem is a negative one, unless one of the components includes only
top-like connectives.
