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.
(2001-03-18)
Nearby terms:
Intrusive Testing « Intuition « intuitionism « intuitionistic logic » intuitionistic probability » intuitionist logic » invariant
intuitionistic probability definition
<logic> Florentin Smarandache's representation of the
probability of an event occuring, given by T, I, F which are real
subsets representing the truth, indeterminacy, and falsity
percentages respectively, and
n_sup = sup(T) + sup(I) + sup(F) < 100
Related to intuitionistic logic.
[Florentin Smarandache, "A Unifying Field in Logics. /
Neutrosophy: Neutrosophic Probability, Set, and Logic",
American Research Press, Rehoboth 1999].
(2001-03-18)
Nearby terms:
Intuition « intuitionism « intuitionistic logic « intuitionistic probability » intuitionist logic » invariant » inverse
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