Halliday & Matthiessen (2014: 144):
Finiteness is thus expressed by means of a verbal operator that is either temporal or modal. But there is one further feature that is an essential concomitant of finiteness, and that is polarity. This is the choice between positive and negative. In order for something to be arguable, it has to be specified for polarity: either ‘is’ or ‘isn’t’ (proposition), either ‘do!’ or ‘don’t!’ (proposal). Thus the Finite element, as well as expressing primary tense or modality, also realises either positive or negative polarity. Each of the operators appears in both positive and negative form: did/didn’t, can/can’t, and so on.