Logic on the n-cube.

We endow the partially ordered set of nonempty faces of the n-cube with a distinguished 0-dimensional face and two operations that naturally extend the Rota-Metropolis partial operations. Although the structures thus obtained turn out to be termequivalent 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. [ABSTRACT FROM AUTHOR]