  Inclusion logic is a variant of dependence logic that was shown to have the
same expressive power as positive greatest fixed-point logic. Inclusion logic
is not axiomatizable in full, but its first-order consequences can be
axiomatized. In this paper, we provide such an explicit partial axiomatization
by introducing a system of natural deduction for inclusion logic that is sound
and complete for first-order consequences in inclusion logic.

Logic;Logic in Computer Science