Why Phrasal Verbs Are Predicator + Adjunct

Halliday & Matthiessen (2014: 152n):

Note that if the lexical verb is a phrasal one, the non-verbal part, the adverb and/or preposition, serves as Adjunct, thus falling outside the scope of the Predicator. The combination of Predicator + Adjunct corresponds to the Process. This analysis enables us to account for discontinuous Processes realised by phrasal verbs, as in look that one up in the dictionary with look up as Process, and look as Predicator and up as Adjunct: [Predicator:] look [Complement:] that one [Adjunct:] up [Adjunct:] in the dictionary.