Halliday & Matthiessen (2014: 177-8):
In a proposal, the meaning of the positive and negative pole is prescribing and proscribing; positive ‘do it’, negative ‘don’t do it’. Here also there are two kinds of intermediate possibilities, in this case depending on the speech function, whether command or offer.
(i) In a command, the intermediate points represent degrees of obligation: ‘allowed to/supposed to/required to’;
(ii) in an offer, they represent degrees of inclination: ‘willing to/anxious to/determined to’.
We shall refer to the scales of obligation and inclination as modulation, to distinguish them from modality in the other sense, that which we are calling modalisation.