Logic on the n-cube
Logic
2012-07-25 v1
Abstract
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.
Cite
@article{arxiv.1207.5717,
title = {Logic on the n-cube},
author = {Daniele Mundici},
journal= {arXiv preprint arXiv:1207.5717},
year = {2012}
}