Section: New Results
Cut-elimination in classical logic
Participant : Stefan Hetzl.
A central research topic of the team are the connections between proof theory and computation. A proof-theoretic method which is often used for modeling computational systems is cut-elimination. The computational aspects of this procedure are rather well understood for intuitionistic and linear logic while the situation in classical logic is less satisfactory.  shows that in the general case the number of possible computational interpretations of a classical proof increases as strongly as its computational power and thus provides a lower bound on the set computations encoded by proof.  on the other hand considers proof in classical first-order logic and Peano arithmetic and derives an upper bound which is characterized by a regular tree grammar. This grammar can be used as alternative algorithm for computing cut-free proofs and is therefore a contribution to the reduction of syntax in proof theory.