law of double negation

English

Noun

law of double negation

1. (logic) The statement that the negation of the negation of A implies A, for any proposition A. Stated symbolically: $\neg \neg A\to A$.

   The law of double negation is not valid intuitionistically. To show this with Heyting algebra semantics, let $A=(0,1)\cup (1,2)$. Then $\neg A=(-\infty ,0)\cup (2,\infty )$, $\neg \neg A=(0,2)$,  $\neg \neg A\to A=(-\infty ,1)\cup (1,\infty )\neq \mathbb {R}$.