## Section: New Results

### Combinatorial characterization of the medial rule

Participant : Lutz Straßburger.

Geometric or combinatoric correctness criteria are important for studying proofs independently from syntax. In [Oops!] , Lutz Straßburger gives such a criterion for the medial rule which is central in the deep inference presentation for classical logic [28] . This means that there are now two independent approaches towards a notion of proof identification: First, via algebraic considerations, i.e., categories [9] , and second, via combinatorial or graph-theoretical considerations, i.e., proof nets and correctness criteria.