Earthborn said:
If all that is needed to solve the problem is to ask who owns the thing that is poluted, we need to ask the owner of the air, not the owner of the restaurant. So who is it? Who owns the air?
Nonsense. This is a huge misunderstanding.
Basically, property rights can be interpreted as rules that tell people what they may not do.
Consider the following three rules:
1. If a piece of land (house, construction etc.) is designated as mine, I and only I decide what I am allowed to do when on it and what you are allowed to do when on it. If you have a problem with that, don't come. I couldn't care any less if you're Kant and the only place in the world where you can write your masterpiece is my property. If I don't want you to, you don't get to do it. What you want doesn't matter, as long as you're on my land.
2. The same goes for any physical object (including my body). If I own it, I and only I decide what it will be done to it by me or another.
3. You are not allowed to keep people from leaving your property, if they have followed the rules.
Now let's apply the rules to your example: I have a restaurant and you, my client, decide to smoke. If I (for ANY reason whatsoever, including insanity, hate, whim etc) decide you are not allowed to do it, you must stop or leave - rule no.1(please notice how I completely disregard the damage done to the air; of course, if somebody owned the air and he wouldn't like smoke, you, the smoker, would have a serious problem). If another client dies because of your smoking, then you have broken rule no. 2 (tough to prove that, though). Rule no. 1 also tells you nobody except yourself may decide with regard to allowing people to smoke in your restaurant.
Ownership of the air is as relevant in this case as is ownership of the smoke, or the ownership of the stars above your head.