## Section: New Results

### Linear rewriting systems for Boolean logic

Participant : Lutz Straßburger.

Last year's result on the nonexistence of a complete linear term rewriting system for propositional logic [53] has been generalized and some applications to proof theory have been invesigated. For example, we have found that the medial rule which plays a central role in deep inference systems is canonical in a strong sense: It is minimal, and every rule that reduce contraction to an atomic form is indeed derivable via medial. This is published in [15] (joint work with Anupam Das).