## Section: New Results

### Proof complexity

Participant : Lutz Straßburger.

In proof complexity one usually distinguishes between proofs “with extension” and proofs “without extension”, whereas in other areas of proof theory one distinguishes between proofs “with cut” and proofs “without cut”. We have shown that with the use of deep inference it is possible to provide a uniform treatment for both classifications. This allows, in particular, to study cut-free proofs with extension, which is not possible with other formalisms. By using deep inference we could also give a new and simpler proof for the well-known theorem saying that extended Frege-systems p-simulate Frege-systems with substitution, and vice versa.