Nets and rewriting.  The multimodal and symmetric calculi of §3.1 and §3.3 pose a challenge to the proof net methods as originally developed for linear logic.  In these systems we typically find one-way structural rules, such as the extraction postulates for overt displacement, or the Grishin distributivity laws in the case of LG: these one-way rules naturally suggest a notion of graph rewriting. A completely general proof net framework for the extended Lambek calculi, with a correctness criterion based on rewriting, has been developed in Moot and Puite 2002 and Moot 2007.