Halliday & Matthiessen (1999: 141, 141n):
Both cognition and desideration can come to serve as metaphors for the interpersonal system of modality — for modalisation and modulation respectively — alongside congruent realisations such as modal auxiliaries and adverbs. That is, a number of processes of cognition can stand for probabilities — I think : probably, I suppose : perhaps; and a number of processes of desideration can stand for inclinations and obligations — I want : should, I insist : must. For instance:
I think that in a sense you've had to compromise, haven't you?'in a sense you've probably had to compromise, haven't you'
Neither perceptive nor emotive sensing can serve as metaphors for modalities.³
³ Emotion is related to interpersonal attitude — I rejoice that she's returned : she has, happily, returned. Unlike modality, attitude is not an assessment of the validity of a clause (grammatically it is not a Mood Adjunct). Rather, it is a comment on the information presented in a clause.