Halliday And Matthiessen (2014: 676-8):
When the need arises in discourse to attribute information to some source, this can be done logically by means of clause nexus of projection; but it can also be done experientially by means of a circumstance of Angle. …
Projection can also be manifested interpersonally in the form of a modal Adjunct … Unlike the logical and experiential manifestations, the interpersonal manifestation does not represent the Sayer or Senser; rather it enacts the speaker’s opinion – an enactment of his or her degree of commitment to the proposition: the proposition is assessed as being projected by somebody other than the speaker. This type of assessment is known as ‘evidentiality’: the modal Adjunct is used to indicate the evidential status of the proposition. The nearest logical equivalent would be ‘people say/they say that ...’, or ‘I hear that’: evidentiality is related to ‘verbal’ clauses and ‘mental’ clauses of perception.
In Chapter 4, we called this kind of modal assessment presumption; the comment Adjunct is realised by adverbial groups with adverbs as Head such as evidently, supposedly, reportedly, allegedly; arguably; presumably and they may have cognate verbs such as report, allege, argue serving as Process in a ‘verbal’ clause or suppose, presume serving as Process in a ‘mental’ clause. …
Projection is thus manifested interpersonally as modal assessment of the presumption type; but it extends beyond presumption to cover quite a few other types of modal assessment as well.