There's one issue with the principle: how do you define property? Sometimes is not truly clear.
imo this isn't a problem with the principle (qua principle), but a problem with knowing how to implement it in certain situations. This problem applies equally to the 'Non Aggression Principle' too, with the extra disadvantage that the terminology is more confusing.
He made a fortune out of it and I enherited it. I don't own slaves anynore, but is my propery really mine?
My hunch is that it would likely be treated as yours (until someone who can demonstrate a better claim than you shows up. For instance a descendant of one of the slaves. Incidentally all ownership claims are contingent like this: We say 'owner', assuming for now you have the best claim to ownership of this thing, but remaining open to the possibility that someone with a better claim might show up.
Is the non transgression principle appplicable or the sons or the slaves have a right to get back what was potentially theirs?
Both.
I'm not saying that NAP is better than NTP. Both have limitations. Sometimes it's not easy to distinguish what is agression and what is not or what is transgression and what is not.
Nevertheless, I'm still not convinced that NTP is a better option. For instance, if I could only stop an agression from your side by violating your property, what takes precedence from an ethical point of view? It's not really clear to me, although I suspect that putting an end to the agression entitles me to violate your property. But the opposite is true as well. In the end, transgression is a form of aggression. So, not sure this is adding anything meaninful (besides adding a twist to the NAP in order to make it even more appealing for anarcho-capitalists).
That wouldn't be a violation. At least the Rothbardian take, as I understand it, is that the use of defensive force is permitted, and not a transgression or violation (subject to the principle of proportionality). Or another way of looking at it, the (would be) violator of another's rights forfeits a measure of his own property rights when doing so.
I'm in favour of dropping that way of using the term aggression altogether, for the reasons mentioned in this article.
I'd say it makes it's a more accurate as well as more understandable term, with no disadvantages that I can think of that aren't also shared by the NAP term. That's already a big win imo.