Buddhists would tell you the tetralemma (A, ~A, both, neither). Emptiness is other than any of those logical possibilities. This is how Nagarjuna showed that Emptiness was at the heart of Logic. Interestingly enough Aristotle’s metaphysics is basically a rejection of the tetralemma. He formulated the idea of excluded middle and non-contradiction to avoid falling into what he saw as the confusion of the tetralemma. However, we must remember that Aristotle and the greeks used Syllogistic Logic and the Indians in Sanscrit used Pervasion Logic and talked about Masses. So one reason we find emptiness so hard to swallow is that we are thinking in terms of sets rather than masses as what is most basic to our understanding. We have non-count nouns in our language but our math and logic and everything else emphasizes sets.
Another point of interest is that Emptiness is the dual and oposite of Taoist Void, and so that these two nonduals are both dual with respect to each other. Taoists try to reduce everything to nature, and Buddhists do not believe that physical reality exists beyond consciousness. Thus we are in the interesting situation of having two dual non-dual interpretations of existence.
And even more interestingly the four Aspects (Reality, Truth, Identity, Presence) apply to both Being and Existence.
So when you say the truth definition of existence, you are really using an aspect of Existence to define existence which is probably a category mistake.
There is no true definition of existence, for two reasons. First Existence is neither true nor fiction But it is the nondual between them. Second, definitions imply we can understand things with words which is not true of existence because it is something beyond what is expressible in words, which is why the tetralemma results in the Buddha’s pregnant silences, like when he was asked whether there was a god or not.