Symfony2 forms: Render null value as indeterminate checkbox

In my application there are lots of boolean databse fields which can be NULL. NULL means that the value is unknown. Users must know if the value is unknown, "true" or "false". Therefore I'd like to render NULL as checkbox with indeterminate state. Is this possible?

Also I need to find a way to write a change from "false" to "NULL" back to the database. As far as I know, Doctrine just ignores fields with NULL values. Is there a way to change this behavior?