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


Wikimedia Foundation. 2010.

Игры ⚽ Поможем сделать НИР

Look at other dictionaries:

  • Linear logic — In mathematical logic, linear logic is a type of substructural logic that denies the structural rules of weakening and contraction . The interpretation is of hypotheses as resources : every hypothesis must be consumed exactly once in a proof.… …   Wikipedia

  • Outline of logic — The following outline is provided as an overview of and topical guide to logic: Logic – formal science of using reason, considered a branch of both philosophy and mathematics. Logic investigates and classifies the structure of statements and… …   Wikipedia

  • List of mathematical logic topics — Clicking on related changes shows a list of most recent edits of articles to which this page links. This page links to itself in order that recent changes to this page will also be included in related changes. This is a list of mathematical logic …   Wikipedia

  • List of topics in logic — This is a list of topics in logic.See also: List of mathematical logic topicsAlphabetical listAAbacus logic Abduction (logic) Abductive validation Affine logic Affirming the antecedent Affirming the consequent Antecedent Antinomy Argument form… …   Wikipedia

  • List of mathematics articles (A) — NOTOC A A Beautiful Mind A Beautiful Mind (book) A Beautiful Mind (film) A Brief History of Time (film) A Course of Pure Mathematics A curious identity involving binomial coefficients A derivation of the discrete Fourier transform A equivalence A …   Wikipedia

  • Dialectica interpretation — In proof theory, the Dialectica interpretation [1] is a proof interpretation of intuitionistic arithmetic (Heyting arithmetic) into a finite type extension of primitive recursive arithmetic, the so called System T. It was developed by Kurt Gödel… …   Wikipedia

  • List of philosophy topics (A-C) — 110th century philosophy 11th century philosophy 12th century philosophy 13th century philosophy 14th century philosophy 15th century philosophy 16th century philosophy 17th century philosophy 18th century philosophy 19th century philosophy220th… …   Wikipedia

  • Structural rule — In proof theory, a structural rule is an inference rule that does not refer to any logical connective, but instead operates on the judgements or sequents directly. Structural rules often mimic intended meta theoretic properties of the logic.… …   Wikipedia

  • Duality (mathematics) — In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one to one fashion, often (but not always) by means of an involution operation: if the dual… …   Wikipedia

  • Algebraic geometry — This Togliatti surface is an algebraic surface of degree five. Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”