Halliday & Matthiessen (2014: 515):
The uses of this kind of projecting nexus include(i) the representation of the speaker’s thinking in dialogue (often as a way of assessing what is projected, where the projecting clause comes to stand for a modality of probability);
(ii) the representation of the addressee’s thinking in dialogue, often as a way of probing for information;
(iii) the representation of a character’s consciousness in narrative;
(iv) the representation of institutional or expert opinions and beliefs in news reporting and scientific discourse;
(v) the representation of the speaker’s angle in scientific discourse, often as the result of a chain of reasoning.