Affine logic

A substructural logic that denies the structural rule of contraction. It can also be characterized as linear logic with weakening.

Affine logic can be embedded into linear logic by rewriting the affine arrow $A\rightarrow B$ as the linear arrow $A{-\!\circ }B\otimes \top$.

Whereas full linear logic (ie. linear logic with multiplicatives, additives and exponentials) is undecidable, full affine logic is decidable.

Affine logic forms the foundation of ludics.

References

• Gianluigi Bellin, 1991. 'affine logic'. Message to the TYPES mailing list.
• Jean-Yves Girard, 1997. 'Affine'. Message to the TYPES mailing list.

See also

• Linear logic
• Strict logic and relevant logic
• Substructural logic
• Ludics