Halliday & Matthiessen (1999: 104n, 105n):
Propositional logic is interpersonally invariable. Unlike natural logic, it is only concerned with statements, or rather — since language is concerned with validity rather than truth — with the philosophical version of what are statements in natural language. […]
Projecting figures of the ‘think’ type — ‘know’, ‘believe’, ‘want’ — have been represented outside standard logic within intensional logic.