Sentence examples for dual negation from inspiring English sources

Due to the failure of bivalence, the logical law of excluded middle fails for the dual negation ~.

The negation ~ is variably referred to as strong negation, dual negation, or game-theoretical negation.[25] It works as one would expect: φ is false in M iff its negation ~φ is true therein (cf. Sandu 1993).

The double negation amounted to affirmation.

The negation algorithm can be made more informative so it can also detect double negations.

Analogously, strong negation may be added to positive dual intuitionistic logic to obtain a system with a connexive co-implication, and to bi-intuitionistic logic to obtain a system with both a connexive implication and a connexive co-implications, see Wansing 2008.

Can a negation be recorded without that recording somehow negating the negation?

In addition to intuitionistic negation, bi-intuitionistic logic contains a so-called co-negation that is in a sense dual to intuitionistic negation.

This suited her, this negation.

Negation may be either mutual negation (of difference) or absence.

Dual exhausts?

Not negation, but negative capability.