If we compare Nozick with Chomsky, then Nozick sets out to make the case for minarchism in the form that trained philosophers go about in making the case for anything, but Chomsky doesn't have this background and may not have realized that anyone expected this of him. — Walter B

This is a half-formed thought of mine as I'm about to pass out in bed, but: as a left-libertarian myself who loves to hear Chomsky speak (haven't read anything of his unfortunately), who came to my position by way of right-libertarianism and a formal philosophical education, I love the axiomatic approach, "the form that trained philosophers go about in making the case for anything", and I enjoy framing my own version of left-libertarianism in such a way (even a propertarian way, decomposing ownership via a Hohfeldian analysis of rights into more primitive deontic notions, and then building back up to an anti-capitalist form of propertarianism from there), so I would love to read somewhere a concise and rigorous axiomatic buildup of Chomsky's views like the OP is asking for, if such a thing exists. Links appreciated.

I am not sure that this is the case. While libertarians do indeed hold to self-ownership and the non-aggression principle, they are not simply taken as self-evident axioms. Rothbard, for instance, argues for self-ownership from the impossibility or arbitrariness of the alternatives. One alternative would be that one part of humanity begins by owning another part of humanity, and the other would be that every person in the world is jointly co-owned by everybody. Rothbard argues that the former is arbitrary, since some members of one and the same natural kind are afforded a 'natural right' that others are not, and he argues that the latter is impossible to implement, for all sorts of reasons which I won't rehearse here. Whatever we make of his arguments, the point is that they are not simply stipulated. — Virgo Avalytikh

Why should it be that when I own someone that I am afforded a natural right? Rothbard is already invoking talk of natural rights to describe slavery, and so something of political nature is already assumed when describing slavery. Why not give an account of slavery that is descriptive? Here is an example: when I own slaves it is often against their will.
Or will Rothbard defend his argument without axioms?

There are analytical Marxists that try to do that for Marx. I don't know if you care to read them?

Why should it be that when I own someone that I am afforded a natural right? — Walter B

'Ownership' is a statement about property rights. We are not just talking about de facto possession here; a thief who pinches my purse now physically possesses it, but this does not imply that he has a rightful claim to it (a world in which all de facto possession implies a rightful claim of ownership is praxeologically indistinguishable from a Hobbesian state of nature; we might as well not speak of rights at all, if such a world obtained). To speak of a right as 'natural' is simply to say that the right in question is not 'bestowed' upon one by an institution, such as the State. This is pertinent here, because Rothbard is considering the question of starting points: who starts off as the property of whom?

Why not give an account of slavery that is descriptive? Here is an example: when I own slaves it is often against their will. — Walter B

Well, one problem is that it does not seem possible to define slavery apart from rights (specifically, property rights, which fundamentally are the only kinds of rights there are). The 'account' of slavery you have just given is not a definition. It does not give us a set of necessary and sufficient conditions for distinguishing cases of slavery from cases of non-slavery. Moreover, in the description you have given you have invoked the concept of 'ownership'. This is not a wertfrei description, for it simply throws us back upon the question, 'Who is the rightful owner of the person in question?' Trying to define slavery independently of property rights is like trying to define theft independently of property rights. If I take something from you against your will, is that 'theft'? Not necessarily - maybe it was my property, and you had previously stolen it from me. Distinguishing cases of theft from non-theft requires us to have a system of rights in place, and I would suggest that such is also necessary for distinguishing cases of slavery from non-slavery (e.g. employment).

The closest thing would be Gerry Cohen, especially Self-Ownership, Freedom, and Equality. Like so many works of political philosophy, I disagree with it while also being profoundly appreciative of it.

Also some of the left-libertarians I mentioned above: Hillel Steiner, Michael Otsuka, Peter Vallentyne, Roderick Long. I find these thinkers much more compelling than Chomsky himself, despite their lacking his celebrity status. Steiner's An Essay on Rights is especially brilliant.

"Ownership' is a statement about property rights"

It doesn't seem that this is necessarily true. If I say that I own someone, then it could be meant that I have engaged in brute force against that person so that they are under my control. There is no need to invoke property rights to make sense of the statement that I own someone else.

"We are not just talking about de facto possession here; a thief who pinches my purse now physically possesses it, but this does not imply that he has a rightful claim to it (a world in which all de facto possession implies a rightful claim of ownership is praxeologically indistinguishable from a Hobbesian state of nature; we might as well not speak of rights at all, if such a world obtained)."

To say that I "stole" an item from you can mean that I have taken something without informing anyone of my action. No need to invoke property rights to describe this action either.

"To speak of a right as 'natural' is simply to say that the right in question is not 'bestowed' upon one by an institution, such as the State. This is pertinent here, because Rothbard is considering the question of starting points: who starts off as the property of whom?"

And why begin with this question? Why not ask the more basic question: are there really such things as natural rights at all?

"Well, one problem is that it does not seem possible to define slavery apart from rights (specifically, property rights, which fundamentally are the only kinds of rights there are)."

Slavery can be described in a politically neutral manner. When brute force is employed to control another, so that that other must obey the whims of the controller under threat of force, then that person is a slave. If someone threatens to torture me unless I do whatever it is that they want, then I am a slave to that person.

"The 'account' of slavery you have just given is not a definition."
Correct, it was a description of slavery. Not a definition of slavery itself.

"It does not give us a set of necessary and sufficient conditions for distinguishing cases of slavery from cases of non-slavery."
I thought it was clear that I was trying to ask for a politically neutral description of slavery that anyone from any political background can agree with. A definition of slavery that is purely descriptive is not necessary, however, since leftists have their own starting principle that hierarchies that find their basis in brute force are illegitimate. Since most have an intuitive believe that actions that justify themselves by brute force are illegitimate, then slavery may be rejected simply based on how the enslaved remains a slave by the slaver. This is why anyone who embraces the non-aggression principle will also reject slavery without having to know the definition of slavery; so even right-libertarians can reject slavery without having to debate the nature of property with the left-libertarian. This is why I find it strange that you think that a definition is truly necessary here.

If I take something from you against your will, is that 'theft'? Not necessarily - maybe it was my property, and you had previously stolen it from me. — Virgo Avalytikh

It looks like you think that if property rights don't exist, then we can't make sense of statements like "he stole my purse." I already noted that these statements can be made sense of without aligning oneself to any political position.

Distinguishing cases of theft from non-theft requires us to have a system of rights in place, and I would suggest that such is also necessary for distinguishing cases of slavery from non-slavery (e.g. employment). — Virgo Avalytikh

You must understand that definitions that are not politically neutral are not going to be accepted by your political opponent and they will charge you with begging the question. If you are debating the definition of property, and your definition of property is biased in favor of individualism, will the left-libertarian agree with you or will he challenge your definition as biased against him?

Think about how Chomsky talks about freedom. When Chomksy describes freedom it is in no way compatible with right libertarianism and while leftists may rejoice upon hearing of it, the right will not be moved at all.

It doesn't seem that this is necessarily true. If I say that I own someone, then it could be meant that I have engaged in brute force against that person so that they are under my control. There is no need to invoke property rights to make sense of the statement that I own someone else. — Walter B

This seems to be largely a linguistic issue, but from my understanding of English, 'property' and 'ownership' are essentially coterminous. To say that something is my property is to say that it is proper to me; i.e. that it is my own. Slavery just is a case where one person is considered to be the property of another; they are considered 'chattel'.

Moreover, the definition you have given seems too permissive. Suppose that I use force against somebody else so as to encourage them into furnishing me with their labour. Suppose that they have previously signed an employment contract, consenting to furnish me with said labour for a price (wage), and suppose that they have neglected to do so. In using force, I am doing nothing more than enforcing our contract. In refusing to work for me, they are defrauding me and violating my property rights as a result. Am I 'enslaving' them? By no means - it is precisely on the basis of consent (contract) that cases of slavery are distinguished from cases of mere employment. So, the fact that I am using force in order to claim some article of property (in this case, my employee's body, so that they may make good on their commitments) is not automatically slavery.

To say that I "stole" an item from you can mean that I have taken something without informing anyone of my action. No need to invoke property rights to describe this action either. — Walter B

One ambiguity here is what it means to 'take' something. One possibility is that I have 'taken' something just in case it is physically on my person; in my hand, for instance. But this is obviously too permissive. This would mean that I 'steal' my own coffee cup when I take it from my cupboard without anybody knowing. It is more difficult than you think it is to define 'taking' in such a way that is neutral to property rights, since 'taking' something from somebody else is not always a matter of transferring it from their immediate person to mine. If I hotwire your car while it sits empty in your garage, I am 'taking' it from you, not because it is being transferred physically from you to me (you might not be anywhere near it at the time), but because the car is associated with you according to a principle of ownership.

And why begin with this question? Why not ask the more basic question: are there really such things as natural rights at all? — Walter B

Rothbard does: see The Ethics of Liberty, ch. 1.

I thought it was clear that I was trying to ask for a politically neutral description of slavery that anyone from any political background can agree with. A definition of slavery that is purely descriptive is not necessary, however, since leftists have their own starting principle that hierarchies that find their basis in brute force are illegitimate. Since most have an intuitive believe that actions that justify themselves by brute force are illegitimate, then slavery may be rejected simply based on how the enslaved remains a slave by the slaver. This is why anyone who embraces the non-aggression principle will also reject slavery without having to know the definition of slavery; so even right-libertarians can reject slavery without having to debate the nature of property with the left-libertarian. This is why I find it strange that you think that a definition is truly necessary here. — Walter B

I don't know what you are trying to get at here. As I mentioned above, there are cases in which I am within my rights in using force to compel someone to furnish me with their labour; i.e. when enforcing a contract. So the suggestion that 'slavery' is just any case in which force is used to compel the labour of another is not politically neutral, since the right-libertarian would not consider this to be a case of slavery, but of the enforcement of an employment contract.

A definition of slavery in terms of property rights is necessary. The NAP does not simply oppose 'force'. It opposes the initiation of force (including the invasion of justly held property). It permits the defensive use of force. But, it is not possible to distinguish which acts of force are initiatory and which are defensive, except in reference to a system of property rights.

Suppose, for instance, that I am a rightful self-owner. This means that, if somebody forcefully invades my person and compels me to work for them against my will, this is a rights-violation, and 'slavery' is the term we use to designate this. If I were to use force to resist them, my use of force would be defensive, whereas theirs is initiatory. So they are in violation of the NAP, but I am not. But suppose that I am instead considered the rightful property of some other person. When they put me to work, they are simply exercising their property rights. If I use force to resist them, I am invading their property by acting as though I rightfully own myself, where we have stipulated that I do not. Here, then, I am the aggressor, and they are the victim. Their use of force is now defensive, protecting their property from somebody else (me) who is depriving them of its use.

So, the NAP depends upon a system of property rights in order to distinguish who is or is not an aggressor, and that is why, from the libertarian standpoint, slavery must be understood in these terms.

It looks like you think that if property rights don't exist, then we can't make sense of statements like "he stole my purse." I already noted that these statements can be made sense of without aligning oneself to any political position. — Walter B

Again, no. Your attempt at defining 'theft' in purely physical terms results in a definition that is too permissive for the libertarian to accept, so it is not politically neutral.

You must understand that definitions that are not politically neutral are not going to be accepted by your political opponent and they will charge you with begging the question. If you are debating the definition of property, and your definition of property is biased in favor of individualism, will the left-libertarian agree with you or will he challenge your definition as biased against him? — Walter B

The fact that somebody may charge the libertarian with question-begging does not imply that she really is question-begging. There are good reasons for libertarians to define their terms as they do, as I hope I have already indicated, and as can be discovered further by reading some of these figures.