  We endow the partially ordered set of nonempty faces of the n-cube with a
distinguished 0-dimensional face and three operations that naturally extend the
Rota-Metropolis partial operations. While the structures thus obtained turn out
to be term-equivalent to Post algebras of order 3, the inclusion order between
faces coincides with the De Luca-Termini sharpening order, and yields a compact
coNP-complete logic that tolerates a modicum of inconsistency and
nonmonotonicity.
