Proof theory in the abstract Original Research Article

Categorical proof theory is an approach to understanding the structure of proofs. We illustrate the idea first by analyzing G0̈delʹs Dialectica interpretation and the Diller-Nahm variant in categorical terms. Then we consider the problematic question of the structure of classical proofs. We show how double negation translations apply in the case of the Dialectica interpretations. Finally we formulate a proposal as to how to give a more faithful analysis of proofs in the sequent calculus.