This illustrates the fact that IKL can reproduce assertion patterns which are traditionally described as paradoxical. (= p (that (not (p)))) is a compact IKL version of the ‘liar paradox’, a proposition which asserts its own falsity. There is no such proposition, so this equality statement is self-contradictory, i.e. always false: so its negation is always true. The figure shows this and some other well-known ‘paradoxes’ rendered as IKL forms.

(via the IKL specification document by Pat Hayes and Chris Menzel)