Semantic A-translation and Super-consistency entail Classical Cut Elimination
Blanqui, Frédéric, Dowek, Gilles, Grienenberger, Émilie, Hondet, Gabriel, Thiré, François · arXiv (Cornell University) · 2014
The λΠ-calculus modulo theory is a logical framework in which many logical systems can be expressed as theories. We present such a theory, the theory {U}, where proofs of several logical systems can be expressed. Moreover, we identify a sub-theory of {U} corresponding to each of these systems, and prove that, when a proof in {U} uses only symbols of a sub-theory, then it is a proof in that sub-theory.