# How to read out a double negation in propositional logic

How would one verbally say ~~R where R = my program is correct? The tildes are negation symbols. I'm not sure if it just cancels out and comes out as 'my program is correct' or if it's something else.

Thank you!

One way to pronounce "~" is as "not", so one could pronounce that as "not not R".

But frankly, pronouncing complex logic formulas can be ugly, and often it's better to just write it on a whiteboard or piece of paper and point.

Yes, ~~R is equivalent to R.

The answer by @D.W. is valid in classical logic, however if you are on the intuitionistic side, then you can't eliminate double negation (~~).

I'd read the formula as 'It is not true that my program is not correct'.

• Or, in a more natural English way, "my program is not incorrect" Commented May 11, 2016 at 0:59
• +1 for going beyond classical/binary. the world is definitely not just true and false.
– Lzh
Commented May 11, 2016 at 4:24
• @Mzn the second negation is implicit in the word "incorrect", which means "not correct". Commented May 11, 2016 at 4:37
• @Mzn, if I'm not mistaken, you are misinterpreting Intuitionist logic: it does not posit a third truth value, but rather defers assigning one of two truth values until proof. Commented May 11, 2016 at 15:09
• @Mzn, I don't know enough about intuitionist logic to answer your question, but here's one thing that occurred to me: if we wish to call "~~R" a third state (rather than the absence of a state), then we are likewise forced to call ~~~R a fourth state, ~~~~R a 5th, etc. ad infinitum. Commented May 12, 2016 at 14:23