The Foundations of Property
If others have any legitimate claim to the products of your labor, you are, to that degree, a slave. This implies that all of the products of your efforts must be owned by you and no one else (relies on the proof that men cannot be slaves). But what if you're mixing your efforts with other resources?
Property Disputes
Using the above principle, if you're mixing your labor with someone else's property, it does not help appropriate their property for you - but at the same time, it does not give them ownership over the products of your labor. An agreement between the owner and producer should be reached before labor is performed. In the absence of that agreement, any modification or denial of access to the owner's property violates his property rights.
Acquiring Unowned Resources
If you're mixing your labor with unowned resources, the resources become yours if the two are not trivially divorced. The reason the unowned resources become yours is because to allow anyone access to them once again retroactively coerces your previous labor. However, if allowing someone else to use (not own) those resources does not measurably impact the new product, then they are considered trivially divorced and only the new product is owned. An example of this would be the use of "air" in respiration while producing a chair. Even though the air was effectively used to produce the chair, it is not included in ownership because the two are trivially divorced. Allowing others access to air does not measurably impact the chair.