A widget has one button. This button performs different functions depending on the widget's mode at the time the button is pressed.
Can this be said to have modality, or a modal design?
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This quote from Jeff Raskin's book, The Humane Interface (courtesy of wikipedia) gives a good definition for "modal" in this context:
An human-machine interface is modal with respect to a given gesture when (1) the current state of the interface is not the user's locus of attention and (2) the interface will execute one among several different responses to the gesture, depending on the system's current state.
In your case, the "gesture" is "clicking on the widget's button", so the word "modal" is applicable here.
In general English usage the word "modality" means "having or related to modes" (for instance one might refer to "the modality of the music" about modal music), so your example would technically be correct. However, since the word "modality" has a specific different meaning within the context of user interface design, you might be advised to express yourself differently avoid confusion.
In my experience, there are only two recognised uses of
modality in computing:
Neither of these fit your scenario. That's not to say it is entirely wrong -
model does mean 'pertaining to mode or form' - but at best, its use in this context might be unclear
Instead, I would say the button on your widget is
mode-sensitive/mode-dependent - I think
mode-sensitive would be my preference.
I prefer to use modal design, even if modality means also modal quality.
The phrase modal dialog, though, could be understood to have a different meaning, as it is normally used to mean a dialog window that blocks its parent window until it is open. If you think that modal design can be confused with that, then I would use modality.