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).

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