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 proof of the cut elimination theorem for super-consistent theories in natural deduction modulo, inspired by proof normalization, but without explicit proofs. It can also be formulated as a completeness proof for the cut free calculus. This formulation involves some kind of V-complexes. We then discuss application to simple types theory and the links, in this case, with the normalization and purely semantical methods, in particular those using V-complexes.

Domaines: Logique en informatique [cs.LO]; Théorie et langage formel [cs.FL]

Gilles Dowek, Olivier Hermant. A simple proof that super consistency implies cut elimination. 18th International Conference, RTA 2007, Jun 2007, Paris, France. pp.Pages 93-106, ⟨10.1007/978-3-540-73449-9_9⟩. ⟨hal-00743256⟩