Indeed, it would applied only to registered belongings.

As for the unnoticeable trespasser, I agree with you, on a practical view.

But do you get the dilemma on a more theoretical view.
To solve this you can only :

1. Impose that a way must exist between people to communicate.
2. Wait for acknowledgement of your notice before taking action.

And both are imperfect cause,

1. I can imagine a nice guy living his peaceful life on his own, but not willing to learn the language of the folks nearby.
   He initiate no harm to anyone, an if he get noticed with something he can't understand, you can't say he willingly trespassed.
2. Some situations could be life or death, and you can't take the time to ask if he get the warning.