English Dictionary

law of double negation

noun

(logic) The statement that the negation of the negation of A implies A, for any proposition A. Stated symbolically: ¬¬A→A.

The law of double negation states that a sentence remains unchanged when the negation is applied twice.

意味（1）

(logic) The statement that the negation of the negation of A implies A, for any proposition A. Stated symbolically: ¬¬A→A.

The law of double negation is not valid intuitionistically. To show this with Heyting algebra semantics, let A=(0,1)∪(1,2). Then ¬A=(-∞,0)∪(2,∞), ¬¬A=(0,2), ¬¬A→A=(-∞,1)∪(1,∞) ne ℝ.