Intuitionistic logic

Computing Dictionary

intuitionistic logic definition

logic, mathematics
Brouwer's foundational theory of mathematics which says that you should not count a proof of (There exists x such that P(x)) valid unless the proof actually gives a method of constructing such an x. Similarly, a proof of (A or B) is valid only if it actually exhibits either a proof of A or a proof of B.
In intuitionism, you cannot in general assert the statement (A or not-A) (the principle of the excluded middle); (A or not-A) is not proven unless you have a proof of A or a proof of not-A. If A happens to be undecidable in your system (some things certainly will be), then there will be no proof of (A or not-A).
This is pretty annoying; some kinds of perfectly healthy-looking examples of proof by contradiction just stop working. Of course, excluded middle is a theorem of classical logic (i.e. non-intuitionistic logic).
History (http://britanica.com/bcom/eb/article/3/0,5716,118173+14+109826,00.html).
(2001-03-18)
The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
Cite This Source
Explore Dictionary.com
Previous Definition: intuitionist logic
More from Thesaurus.com
Synonyms and Antonyms for intuitionistic logic
More from Reference.com
Search for articles containing intuitionistic logic
Dictionary.com Word FAQs

Dictionary.com presents 366 FAQs, incorporating some of the frequently asked questions from the past with newer queries.

Copyright © 2014 Dictionary.com, LLC. All rights reserved.
  • Please Login or Sign Up to use the Recent Searches feature