## Section: New Results

### Generic cut-elimination for Substructural Logics

Participant : Lutz Straßburger.

We were able (in a joint work with Agata Ciabattoni, TU Wien, and
Kazushige Terui, Kyoto University) to make further progress in the
development of a systematic and algebraic proof theory for
nonclassical logics. Continuing the work
of [33] we defined a hierarchy on Hilbert
axioms in the language of classical linear logic without exponentials,
and gave a systematic procedure for transforming axioms up to the
level P_{3}^{'} of the hierarchy into inference rules in
multiple-conclusion (hyper)sequent calculi, which enjoy
cut-elimination under a certain condition. This allows a systematic
treatment of logics which could not be dealt with in previous
approaches. Our method also works as a heuristic principle for
finding appropriate rules for axioms located at levels higher than
P_{3}^{'} . The work is published in [17] .