Property and Community. The very nature of procedural justice (as opposed to distributive justice) is connected to issues of property. Because just like analytic knowledge is about following the correct steps in sequence from the assigned meaning of words, so too procedural justice is about following the correct steps in sequence from the assigned rights that who has over what, which is identical to the concept of ownership, i.e. to have rights over something is what it means to own it.
When we assign ownership of certain things to certain people, which is to say that the will of those people controls what it is permissible to do to or with those things, we enter the realm of property rights, things that are right or wrong just in virtue of who owns what and what they do or don't want done with it, regardless of whether it actually inflicts hedonic suffering or not. This is a matter of perfect duties, of things being obligatory or forbidden, not just about merely supererogatory goods.
But that kind of justice in turn depends on the assignment of ownership of the things in question, and that is not something that is itself a matter of perfect duty, but only imperfect duty. Nobody inherently owns anything but themselves. Rather, sociopolitical communities arbitrarily assign ownership of property to people, and could assign it differently. Like words mean whatever the linguistic community agrees that they mean, people own what other people agree that they own, and so long as everyone involved agrees on who owns what, that is all that is necessary for that ownership to be legitimate.
But when people disagree about who rightly owns what, we must have some method of deciding who is correct, if we are to salvage the possibility of any procedural justice at all; for if, for example, two people each claim ownership of a tract of land and are each wanting to deny the other the use of it, they will find no agreement on who is morally in the right to do so because they disagree about who owns it and so who has any rights over it at all. Such a conflict could be resolved in a creative and cooperative way by dividing up the land into two parcels, one owned by each person, that would permit both people to get the use that they want out of it without hindering the other's use of it. Or the same property can have multiple owners, so long as the uses of the property by those multiple owners do not conflict in context.
(Initially, all property is owned by everyone, and in doing so effectively owned by no one; it is the division of the world into those people who own the property and those who don't that constitutes the assignment of ownership to it.)
But if no such cooperative resolution is to be found, and an answer must be found as to which party to the conflict actually has the correct claim to the property in question, I propose that that answer be found by looking back through the history of the property's usage until the most recent uncontested usage can be found: the most recent claim to ownership that was accepted by the entire community. That is then to be held as the correct assignment of ownership.
(NB that this means just taking or enclosing something by force doesn't make it rightfully yours, if everyone else protests but just can't do anything about it. If later on they get the force together to take it back from you, they have every right to do so; "hey I stole that first fair and square" is no retort).
From these two types of procedural justice, the perfect duties of respecting ownership and the imperfect duties of assigning ownership, we can derive a set of rights, which can be formulated in terms of obligations and their negations. Rights have been categorized, following the work of authors such as Wesley Newcomb Hohfeld, into four groups organized across two different distinctions: the distinction between active and passive rights (not to be confused with positive and negative rights; either an active or a passive right can be either positive or negative), and the distinction between first-order and second-order rights. Active first-order rights are also termed "liberties", while passive first-order rights are "claims", passive second-order rights are "immunities", and active second-order rights are "powers".
A liberty is something that you are not prohibited from doing. It is the negation of the obligation of a negation, and so it is equivalent to a permission. Something you have the liberty to do may nevertheless be bad, but you are not forbidden from doing so; it is an action that you are within your rights to do. A claim, conversely, is a limit on others' liberty: it is something that it is forbidden to deny you, which is just to say that it is obligatory.
I, like most libertarians (at least nominally) do, hold that people have maximal liberty, limited only by the claim to non-aggression: the only things forbidden to do are things that flatly contradict the will of the owner of the thing you are acting upon, such as the body of a person.
But there is in turn an exception to that claim: there is still liberty to contradict the will of the owner of the thing you are acting upon when that someone was already contradicting the will of the owner of the thing they were acting upon. There is a liberty to defend against aggression, which constitutes an exception to the claim to non-aggression: an aggressor cannot invoke the claim to non-aggression to bar you from acting upon him or his property as necessary to stop him from aggressing upon someone else, or to undo the effects of his aggression upon someone else.
For example, someone trying to punch you has no claim against you punching him as necessary to stop him from punching you; and someone who destroys something of yours has no claim against being forced to repair or replace it. But that qualifier "as necessary" is very important: unnecessary violence, in excess of what is necessary to prevent or reverse other violence, constitutes an act of aggression itself, no longer merely an exception to the claim to non-aggression.
And that all depends, of course, on who rightfully owns what, which is where the second-order rights come in to play, which have to do with changing what is or isn't obligatory, by changing the assignment of ownership. A power is the liberty to do so, to change who has what rights, which is equivalent to changing who owns what, as ownership consists entirely of having rights over something. An immunity, conversely, is a limit on others' power, just as a claim is a limit on others' liberty.
I, like most libertarians again, hold that people have maximal immunity — nobody gets to change who has rights over what out from under them, things continue belonging to whoever they belonged to before — limited only by the power to contract, to mutually agree upon an exchange of rights (and consequently permissions and obligations), which power is how that ownership was initially assigned to begin with.
But that power, in turn, has its own exception, in the reflexive case just as with the exception to the claim to non-aggression above: nobody has the power to agree to agree (or not) to any change of rights or ownership, such as by agreeing not to enter into other contracts (as in non-compete agreements), or agreeing to accept whatever terms the other party later dictates (as in selling oneself into slavery, or as in the "social contract" sometimes held to justify a state's right to rule), or agreeing to grant someone a temporary liberty upon certain conditions ("selling" someone the temporary use of your property, as in contracts of rent or interest; letting someone do something is not itself doing something).
In short, the power to contract is limited to the simple trade of goods and services, and cannot create second-order obligations between people that place one person in a position of ongoing power over another person.
The implications of that limitation on rental contracts is especially important to my view on governance. And the limitations on both slavery and rental contracts by the same principle is no coincidence, for just as vandalism is an abstraction of battery (the latter regarding one's body and the former regarding one's other property), and theft is an abstraction of abduction (the latter regarding one's body and the former regarding one's other property), I hold that rent is likewise an abstraction of slavery (again, the latter regarding one's body and the former regarding one's other property).
At first glance, one would think a maximally libertarian society would be one in which there were no claims at all (because every claim is a limit on someone else's liberty), and no powers at all (because powers at that point could only serve to increase claims, and so to limit liberties).
But that would leave nobody with any claims against others using violence to establish authority in practice even if not in the abstract rules of justice, and no claims to hold anybody to their promises either making reliable cooperation nigh impossible.
So it is necessary that liberties be limited at least by claims against such violence, and that people not be immune from the power to establish mutually agreed-upon obligations between each other in contracts.
But those claims and powers could themselves be abused, with those who violate the claim against such violence using that claim to protect themselves from those who would stop them, and those who would like for contracts not to require mutual agreement to leverage practical power over others to establish broader deontic power over them.
So too those claims to property and powers to contract, which limit the unrestricted liberty and immunity that one would at first think would prevail in a maximally libertarian society, must themselves be limited as described above in order to better preserve that liberty.