Machine intelligence is anthropomorphic in utility, that is it serves as either surrogate or substitute for a human cognitive capability. This permits enumeration of AI utility categories. Broadly we can distinguish between creative, knowledgeable, analytical, judicial, predictive, and directing.
As an example use of this approach, consider the case of the AI trained on all public domain material and optionally having had training access to private matter (think Vatican archives). Such an instance should generally not be afforded creative rights, but we would be remiss to restrict its utility as a knowledge base.
The other parameters noted in terms of dual of public|private can of course have bearing on setting type specific constraints.