I’m giving a talk entitled “Terms for Classical Sequents: Proof Invariants and Strong Normalisation” at the 2016 Australasian Association for Logic Conference.
Abstract: A proof for a sequent \(\Sigma\vdash\Delta\) shows you how to get from the premises \(\Sigma\) to the conclusion \(\Delta\). It seems very plausible that some valid sequents have different proofs. It also seems plausible that some different derivations for the one sequent don’t represent different proofs, but are merely different ways to present the same proof. These two plausible ideas are hard to make precise, especially in the case of classical logic.
In this paper, I give a new account of a kind of invariant for derivations in the classical sequent calculus, and show how it can formalise a notion of proof identity with pleasing behaviour. In particular, it has a confluent, strongly normalising cut elimination procedure.