# nLab substructural logic

Substructural logic is a general term for logics in which the structural rules:

are not necessarily allowed, or are only allowed with restrictions.

Some particular substructural logics include:

• linear logic, perhaps the best-known to category theorists, omits the contraction and weakening rules. “Noncommutative linear logic” omits also the exchange rule.
• affine logic? omits only the contraction rule. One might call it “coaffine logic” if we omit only the weakening rule.
• Some forms of relevant logic? and paraconsistent logic can be regarded as substructural logics (often of the coaffine variety).

Revised on September 2, 2012 07:57:36 by Mike Shulman (71.136.235.154)