https://sourceforge.net/tracker/?func=detail&aid=3323617&group_id=152762&atid=785194

Add one more status "gray" , which means "part of my children were selected".
ICEfaces have this kind of feature (see Tri State Checkbox )
http://composite-component-showcase.icefaces.org/ee-composite-showcase/showcase.jsf

if this kind of checkbox were build, it could be apply to selectable components, such as Listbox, Tree, Menu.
i create a preview snapshot of listbox as attachment.