substructural logic

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

- the contraction rule
- the weakening rule
- the exchange rule

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)