Modality means the speaker’s judgement of the probabilities, or the obligations involved in what he is saying. A proposition may become arguable by being presented as likely or unlikely, desiderable or undesirable – in other words, its relevance specified in modal terms.
- Halliday (1985), a pag.75

POLARITY is the choice between positive and negative, as in 'is / isn’t', 'do / don’t' [...] However, the possibilities are not limited to a choice between yes and no. There are intermediate degrees: various kinds of indeterminacy that fall in between, like ʻsometimesʼ or ʻmaybeʼ. These intermediate degrees, between the positive and negative poles are known collectively as MODALITY.
- Halliday (1985), a pag.85-86

Modality refers to the area of meaning that lies between yes and no – the intermediate ground between positive and negative polarity. What this implies more specifically will depend on the underlying speech function of the clause.
- Halliday (1985), a pag.335