Source : Free On-Line Dictionary of Computing

intuitionistic logic
     
         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)