## Section: New Results

### Towards a combinatorial proof theory

Participants : Lutz Straßburger, Benjamin Ralph.

The main part of a classical combinatorial proof is a skew fibration, which precisely captures the behavior of weakening and contraction. Relaxing the presence of these two rules leads to certain substructural logics and substructural proof theory. We investigated what happens if we replace the skew fibration by other kinds of graph homomorphism. This leads us to new logics and proof systems that we call combinatorial. This has been presented at the TABLEAUX 2019 conference [22].