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.