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Logic on the n-cube

Authors
  • Mundici, Daniele
Type
Preprint
Publication Date
Jul 24, 2012
Submission Date
Jul 24, 2012
Identifiers
arXiv ID: 1207.5717
Source
arXiv
License
Yellow
External links

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.

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