Halliday & Matthiessen (2014: 173-4):
… not does not get reduced if the verb is non-finite; and this reflects the systemic association of polarity and mood. What carries the polarity feature, positive or negative, is the speech functional component of the proposition or proposal; hence when the speaker adds a mood tag, meaning ‘please check!’, the unmarked form of the tag is the one which reverses the polarity … If the polarity in the tag remains constant, the meaning is assertive rather than seeking corroboration. It is this reversal of polarity in the tag which enables us to identify the polarity of clauses containing other negative expressions, such as no, never, no one, nowhere, seldom … if the negative word is part of some element in the Residue, the clause itself may be positive …