As already explained (Section 2), we take the terms "belief" and "factuality" to refer to the same phenomenon underlyingly (with perhaps different emphases).
in the quote above, Saurí and Pustejovsky (2012) (apart from distinguishing factuality from truth) also make the point that the writer's communicative intention of making the reader believe she has a specific belief state does not mean that she actually has that cognitive state, since she may be lying.