  A general method is established to derive a ground-complete axiomatization
for a weak semantics from such an axiomatization for its concrete counterpart,
in the context of the process algebra BCCS. This transformation moreover
preserves omega-completeness. It is applicable to semantics at least as coarse
as impossible futures semantics. As an application, ground- and omega-complete
axiomatizations are derived for weak failures, completed trace and trace
semantics. We then present a finite, sound, ground-complete axiomatization for
the concrete impossible futures preorder, which implies a finite, sound,
ground-complete axiomatization for the weak impossible futures preorder. In
contrast, we prove that no finite, sound axiomatization for BCCS modulo
concrete and weak impossible futures equivalence is ground-complete. If the
alphabet of actions is infinite, then the aforementioned ground-complete
axiomatizations are shown to be omega-complete. If the alphabet is finite, we
prove that the inequational theories of BCCS modulo the concrete and weak
impossible futures preorder lack such a finite basis.

Logic in Computer Science