Editing Noncommutative logic (section)

===Cyclic linear logic===

David N. Yetter proposed a weaker structural rule in place of the exchange rule of linear logic, yielding cyclic linear logic.<ref>{{Cite journal| doi = 10.2307/2274953| issn = 0022-4812| volume = 55| issue = 1| pages = 41–64| last = Yetter| first = David N.| title = Quantales and (Noncommutative) Linear Logic| journal = [[The Journal of Symbolic Logic]]| date = 1990| jstor = 2274953| hdl = 10338.dmlcz/140417| s2cid = 30626492}}</ref>  Sequents of cyclic linear logic form a cycle, and so are invariant under rotation, where multipremise rules glue their cycles together at the formulas described in the rules.  The calculus supports three structural modalities, a self-dual modality allowing exchange, but still linear, and the usual exponentials (? and !) of linear logic, allowing nonlinear structural rules to be used together with exchange.