Prisoners aren't 'slaves'. They are being punished for crimes they committed. Very dofferent than being born into it and bought/sold to the highest bidder.
AMENDMENT XIII
Section 1. Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist within the United States, or any place subject to their jurisdiction.
Section 2. Congress shall have power to enforce this article by appropriate legislation.
The punishment is being locked up in a cell. Being forced to work on top of that is the slavery.
Why is it not part of the punishment?
I think it is dependent upon interpretation. Otherwise arresting and locking up can be interpreted as kidnapping and so on.
I do agree that they should be fairly compensated though.
Indeed it is part of the punishment. As an earlier comment in this thread points out from the 13th amendment:
> "Neither slavery nor involuntary servitude, except as a punishment for crime" (emphasis added by me)
They're not. That's why it's slavery. And slavery of prisoners is permitted by the Constitution, which is the main point here.
And yes indeed you are correct that the sate does commit theft and declare it legal for itself.
Prisoners that are made to perform any useful work that anyone else benefits from are slaves, not merely prisoners.
If you want to invoke the word "logic" you should actually employ it.