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  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 P3' 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 P3' . The work is published in  .