Halliday & Matthiessen (2014: 531):
With ‘mental’ process clauses the picture is more complex, since the reference form that tends to be associated with certainty and the substitute so with uncertainty; the principle is actually the same, but it is operating in a different environment (cf. the different senses of thought in quoting and reporting, referred to above). The principle is that a substitute does not refer; it simply harks back. It thus has the general semantic property of implying, and so excluding, possible alternatives; cf. the nominal substitute one as in a big one, meaning ‘there are also small ones, and I don’t mean those’. This is why so, which is a clause substitute, has the general sense of ‘non-real’, by contrast with what is ‘real’; besides (i) projection, where it signifies what is asserted or postulated, it is used in two other contexts: (ii) hypothetical, as opposed to actual, and (iii) possible, as opposed to certain. Hence:
(i) I think so but I know [that] not I know so
(ii) if so but because of that not because so
(iii) perhaps so but certainly not certainly so