The principle of peace, that people must not force perceptions on each other, is where all concepts of property and ownership come from. This is a very simple rule, but the applications are nuanced and non-obvious enough that I'm going to go through them in as much detail as I can. Even I'm not certain that I have all the details of the system right, but these are what I'm pretty sure are the rules underlying my conscience. All of these principles are predicated on the difference between action and inaction.
Pinning down how much restitution is owed for an aggression is pretty murky. The rules I'm most confident in are:
For an unintentional harm, the amount owed is the minimum of until the harm is fully repaired or until it costs the cuplrit as much as the original harm.
For an intentional but justified (but undeserved) harm, the amount owed is the minimum of until the harm is fully repaired or until it costs the culprit twice as much as the original harm.
For an intentional and unjustified harm, the amount owed is the maximum of the rule for intentional but justified harm and until it costs the culprit as much as the original harm.
Since people are forced to feel what happens to their body, it's wrong to affect another person's body against their will. This is the most obvious instance of ownership. It isn't limited to pain or injury either. It's violence to force any type of perception onto someone, including tickling or continuing to speak to someone who requests to be left alone. Both of those acts force a perception onto someone else.
External property by possession
Possessing something allows you to use it in ways that affect your experience, so taking it away would count as forcing an effect on someone. In light of metaphysics, this is just an extension of bodily autonomy because there's no difference of kind between your limbs and your possessions, only a difference of degree.
But "possession" is an iffy term here, because there's a caveat:
No ownership of power
Ownership by possession only works because power can normally be used in ways that affect its user. So if you were to possess something that allows you to affect the lives of other people in another universe, but you don't get any feedback, even indirect, on what happens over there, then it wouldn't be your property. Someone else who stole the power wouldn't actually be affecting you at all.
External property by investment
If your action changes something, such as if you build something, cut down a tree, or just move something unowned to a new place, then others must not prevent you from enjoying the result of your actions. To do so would be destroying your labor, and would be violence in the same way as punching someone, only less salient.
This stacks with ownership by possession. Violating either one without the other (taking from someone what they possess by luck or collecting the benefits of their labor that they don't possess and not compensating them) is theft; violating both at once (taking from someone what they've created and possess) is double the gravity.
A lot of relatively reasonable people deny the existence of this altogether on the basis that only individuals can own things.
But shared property is inevitable. Imagine two children home alone and a transient opportunity comes up and they have to make a decision about the property (and they're sure the parents wouldn't want nothing to be done); or the parents die. Assuming the parents didn't plan for this and specify who gets to act in their stead, there's only one possibility: shared ownership (or moral conflict I guess but I doubt anyone wants to stand by that here).
Or suppose two adventurers kill a dragon together and find treasure in its lair that can't be split (such as a single gem that provides magical effects).
In situations like this, what you have to do is believe that any decision one of the owners doesn't want is a violation of their rights. You always have to compensate the person who isn't getting their way with something they agree is fair. This should usually be easy due to transitive valuation, but if no agreement can be reached before a decision must be made, the co-owners could unanimously agree to entrust it to randomness or an outside party's arbitration, or engage in moral conflict. And then in either case compensate the loser(s) to the best extent possible without making it not worthwhile for the winner(s) to win.
Most often you can reach a peaceful arrangement here by alternating periods of time where you have complete ownership minus the right to sell the common property or anything else that would prevent you from giving it to your partner when it's their turn, or alternating by amount of use (measured in whatever way applies). But such a deal has to be accepted unanimously by all co-owners.
Given the above, a realization can be had: appopriation of natural resources forces an effect on those who could've had it otherwise. You can see this less deniably with this example: your house is next to a river. Assume you didn't know about the river when you bought the house, but now value it highly. A company from another area sends in trucks that harvest all the water. Even many anarcho-capitalists would agree this is theft, but what's the difference of kind between that and this:
Your hometown is destroyed by a natural disaster, and you move to the nearest other area that has a water source. The river there is monopolized by a company that uses machines to harvest all its water. They've taken resources which, otherwise, you would now have access to. Time can't be the differentiating factor because even the water taken from the river next to your house you weren't already using; they let you keep the water you had already extracted. Both cases only involved potential access to the natural resource, and yet we can't avoid the conclusion that it counted as you "possessing" it for the purposes of property.
Hence natural resources can generally not be claimed as property in the same way as artificial things. To appropriate a natural resource is to deprive others of something they could've had otherwise, so you have to compensate anyone made worse off by your appropriation.
Favors and gifts
When you do something for someone else without negotiating repayment, you consent to not receiving any because you make a voluntary choice to do it and give them the impression that repayment isn't required. If you do communicate that you're only doing it under the assumption of being repaid but nothing is mutually negotiated, then they must repay the minimum of your sacrifice and their benefit from it. That's because you didn't consent to doing it for free, so if they repay less than that they're violating you, but they also didn't consent to anything, so they can't be obliged to give up anything worth more to them than the result of your favor.
Non-scarce goods (freeloading)
The situation that a software vendor makes their software available for download with pay and (against their intention) you have a way of downloading it for free can be exactly rewritten as follows:
Alice makes a substantial personal sacrifice to provide some benefit to Bob, telling him she's doing it under the assumption that he'll do something else in return, although Bob didn't actually get any input in the matter. This is exactly the inaltruistic favor scenario above and the answer is the same: Bob must repay her the minimum of the value of her sacrifice, his benefit, and her requested price (since she consented to that).
Of course, the specific nature of the software version of this scenario creates different abilities for the consumer. In particular there's nothing wrong with the consumer pirating it and paying after using it - he can't be obliged to pay more than the software is worth to him and paying before using it means paying before finding out how much it's worth to him.
The obvious difficulty might be: but surely it's always moral to not use the work and pay nothing, and if the only difference between a moral course of action and the one in question is that someone benefits, how can that be considered theft? But here's the insight: if the work isn't worth anything to you, then you wouldn't have been asking this question anyway since the value you're obliged to pay is zero. If the work is worth something to you, then by definition the alternative to freeloading would have been paying that amount to use it, not not using it.
Any other form of non-scarce good would be the same way: using someone's artwork, for example. It's worth noting that using someone's artistic or intellectual property without paying them but with credit and in a way that doesn't devalue the product they're selling (such as posting music from a movie on Youtube) is generally of substantial benefit to the artist, since it gives them publicity at no cost to them. A lot of people who are stingy about copyright of their works overlook that and think they're being stolen from when they're actually being helped.
Trespassing isn't the crime you think it is
Entering someone's home without their permission is forcing your presence on them. (It's also worth considering in the house case that just by opening the door you probably waste some money on air conditioning or heating or let bugs in.) However, since you can only violate someone by causing them an experience, being on someone else's land but not in their house or in their immediate yard is generally not a crime because it won't cause them any disturbance. If it does happen to cause a significant disturbance by some unfortunate combination of circumstances then you can make restitution. There's no need for any hostility because there's no sin.
This consequence may seem instinctively repulsive to many, so I'll give another intuitive reason why you should reconsider: the "encirclement" problem. Suppose you live in a small circle of land, less than an acre, and all the rest of the world is "owned" by other people who don't allow anyone on their land, so you can't leave your area. Would the "owners" of the surrounding land be justified in keeping keep you in the circle? Does your conscience really tell you that you wouldn't have the right to trespass?
Sub-ownership is when a person owns something, but gives control over it to someone else for the foreseeable future. The "child owner" has full ownership of it for the purposes of conflicts with third parties, but the "parent owner" still has full ownership over it when conflicted with the child owner.
Parent and child owner are accurate terms because that is the most common example of this. Children often have "property" or "belongings" that the other children have no right to interfere with, but the parents do, because it's still coming out of their pocket and the child isn't entitled to it.
Restitution after death
A common situation that I've heard a lot of people talk about but never elaborate on because they couldn't resolve it in a way that satisfied them (and it bothered me too for a while) is that A steals from B, then A and/or B dies. There are a few possible cases here, and they're somewhat murky:
The criminal dies and the victim wants restitution from the criminal's descendant. My verdict is yes: the criminal's descendant owes restitution to the victim (but isn't obliged to give up more than they gained). If you reject my verdict here then you seem to end up with the consequence that a criminal can legitimately steal your property by stealing it then giving it to someone else and then killing themselves.
Both the original victim and criminal are dead, and the victim's descendants want restitution from the criminal's descendants. I don't think restitution is owed. I don't think you can pass on something you don't possess, at least not to people who weren't alive at the time of wrongdoing.
The victim dies and their descendant wants restitution from the criminal. This one seems like another yes to me, since the criminal does not have legitimate possession and should do what the original owner would likely have done.
Of course, all that is under the assumption that the criminal and victim will never meet again and so properly resolving the situation is impossible. If we're not to assume that people stop existing when they die, if the criminal and victim were to meet after death in some other world, the debt and/or crime would still be there unless the criminal had been punished or redeemed themself and the victim restituted in the interim. If only one of those is the case, you'd have to balance for example a victim owed restitution from a criminal who does not owe restitution. The whole situation is messed up at that point because a third party got involved and now can't be called in for the resolution, but you can try to reach a compromise. The only reason I advocate resolving through the above methods is because from what we know a reunion between the criminal and victim in such a way that they'll recognize each other is very unlikely.
Misunderstandings are unfortunate but they happen. For example, if you labor on an object not knowing it's owned, you still own your investment, but the object also still needs to be the original owner's property. Time / order of events doesn't actually make a difference if you didn't know about it (I'll explain what does in a minute). Since both people have valid ownership claims, assuming it isn't possible to separate the improvements made from the original object, we go to shared property (see above).
Obviously, if you labor on someone else's property knowing it's someone else's property then you can't claim any ownership at all of the resulting object that conflicts with theirs. (The ideal solution is still to separate out your labor if possible.) If there was a probability of it being owned, you multiply the ownership ratio by that.
Lying as a non-peaceful act
Lying is another act that's commonly defended from the same realm of moral judgement as obvious crimes like theft and assault. But giving someone false information generally affects them and insofar as it does, you're responsible for forcing that effect on them, since you prevented them from making an informed choice. Therefore, lying is a crime with the magnitude of the harm it causes. (This doesn't mean it's okay to tell a 100% harmless lie; just that it's only against the value of Truth and not against Peace.)