Sequent systems for compact bilinear logic
Wojciech Buszkowski · Mathematical logic quarterly · 2003
Abstract Compact Bilinear Logic (CBL), introduced by Lambek [14], arises from the multiplicative fragment of Noncommutative Linear Logic of Abrusci [1] (also called Bilinear Logic in [13]) by identifying times with par and 0 with 1. In this paper, we present two sequent systems for CBL and prove the cut‐elimination theorem for them. We also discuss a connection between cut‐elimination for CBL and the Switching Lemma from [14].