Affine logic

Affine logic is a substructural logic whose proof Theory rejects the structural rule of contraction. It can also be characterized as linear logic with weakening. the name "affine logic" is associated with linear logic, to which it differs by allowing the weakening rule. Jean-Yves Girard introduced the name as part of the geometry of interaction semantics of linear logic, which characterizes linear logic in terms of linear algebra; here he alludes to affine transformations on vector spaces.