 What about voyeurism?

For a stable society, people need assurance that they will not be spied on, so we must slightly extend the concept of private property to include personal space. Otherwise, someone repeatedly coming within a centimeter of you and using the "I'm not touching you" kindergarten taunt would be totally allowed. The extent of this personal space is context dependent, and could be the toilet, changing room, bedroom, underneath a skirt, etc. If someone's personal space is in overlap with your private property, you cannot immediately violate said space, but can ask them to leave, and take measures to remove them only if they don't comply within a reasonable timeframe.