nested checkbox behavior check/uncheck

I have a hierarchical category tree and checkboxes next to each item that allow to enable/disable the correpsonding category.

I assume it is an expected default behavior that all subategories of natural environment become checked when I check the natural environment category. But what about unchecking it again: Should this automatically uncheck all subcategories or restore the previous state in case some were checked already? Furthermore... Should unchecking one of the subcategories cause the parent category to become unchecked?