Proof nets for display logic

Moot & Puite (2002) have introduced proof nets for the multimodal Lambek calculus NL3R. Since then, numerous other connectives have been proposed to deal with different linguistic phenomena, a par — or co-tensor, as some authors prefer to call it— together with the corresponding co-implication (Lambek 1993, Moortgat 2007, Bernardi & Moortgat 2007), Galois and dual-Galois connectives (Areces, Bernardi & Moortgat 2001). We can incorporate these extensions (as well as a few others) into the proof net calculus by simply dropping the restriction that sequents are trees with a unique root node and obtain what are, in effect, proof nets for display logic (Goré 1998). The notion of contraction generalizes to these new connectives without complications. Like for the Lambek calculus, proof nets for display logic have the advantage of collapsing proofs which differ only for trivial reasons. The display rules in particular are compiled away in the proof net representation.