A Simple Proof That Super-Consistency Implies Cut Elimination

Abstract: We give a simple and direct proof that super-consistency implies the cut elimination property 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. As an application, we compare our work with the cut elimination theorems in higher-order logic that involve V-complexes.