Some applicatons use checkboxes that allow an indeterminate state in addition to the two provided by a normal checkbox. This third state is shown as a square or dash in the checkbox, and indicates that its state is neither checked nor unchecked. This is most often used when the checkbox is tied to a collection of items in mixed states. The indeterminate state cannot usually be selected by the user, and switches to a checked state when activated.
Unfortunately I don't have a solution, just work arounds.
The checkbox is not laid out to be tri-state and I guess some major hacking would be needed to get this.
I was having a similar requirement and used a select instead. A slider would also work nicely.
Additionally, I used default values for checkboxes in my settings view to get rid of the initial indeterminate state.
Good call on using the select/picker for the three values, wil use that work around until a tri-state chekbox is available. There is code for a tri-state checkbox in the Sencha Ext forum, which does load, but does not give the three states, assuming due to fundamental differences in the underlying Checkbox code for Ext vs. Touch.