  Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize
every logic defined by a finite matrix. Having obtained such axiomatizations
for Paraconsistent Weak Kleene and Bochvar-Kleene logics, we modify them by
replacing the multiple-conclusion rules with carefully selected
single-conclusion ones. In this way we manage to introduce the first finite
Hilbert-style single-conclusion axiomatizations for these logics.
