nLab substructural logic

Idea

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

• the contraction rule

• the weakening rule

• the exchange rule

are not necessarily assumed, or only with restrictions.

Among substructural logics are the following:

• linear logic, perhaps the best-known to category theorists, which omits the contraction and weakening rules (if also the exchange rule is omitted, one speaks of noncommutative linear logic);

• affine logic which omits only the contraction rule. (one might call it coaffine logic if also the weakening rule is omitted);

• some forms of relevant logic and paraconsistent logic (often of the coaffine variety).

Related concepts

• bunched logic

• structural rules

References

• Kosta Došen, Peter Schroder-Heister, Substructural Logics, Clarendon Press (1993) [ISBN:9780198537779]