Affine logic

Affine logic

Affine logic is 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 ightarrow B as the linear arrow A {-!circ} B otimes op.

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. ' [http://www.seas.upenn.edu/~sweirich/types/archive/1991/msg00083.html affine logic] '. Message to the TYPES mailing list.
* Jean-Yves Girard, 1997. ' [http://www.seas.upenn.edu/~sweirich/types/archive/1997-98/msg00134.html Affine] '. Message to the TYPES mailing list.

ee also

* Strict logic and relevant logic

unref|date=December 2007


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