A simple proof that super-consistency implies cut elimination

Gilles Dowek (1) , Olivier Hermant (2)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 PPS - Preuves, Programmes et Systèmes

We give a simple and direct proof that super-consistency implies cut elimination in deduction modulo. This proof can be seen as a simplification of the proof that super-consistency implies proof normalization. It also takes ideas from the semantic proofs of cut elimination that proceed by proving the completeness of the cut free calculus. In particular, it gives a generalization, to all super-consistent theories, of the notion of V-complex, introduced in the semantic cut elimination proofs for simple type theory.

Domaines: Logique en informatique [cs.LO]

Gilles Dowek, Olivier Hermant. A simple proof that super-consistency implies cut elimination. 2007. ⟨hal-00150697⟩