Where Halliday (1985) justifies his process types largely on the basis of configurations of Agent, Process and Medium, Hasan additionally draws the Beneficiary role into the picture.
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The system of process types isn't justified on configurations of Agent, Process and Medium. Each of these — process types, on one hand, configurations of Agent, Process and Medium, on the other — represents a distinct complementary perspective on transitivity: the transitive and ergative models, respectively.
The transitive model is concerned with the ways in which processes are different, with each type of process 'characterised by process-participant configurations where the functions are particular to that type' (Halliday & Matthiessen 2004: 280).
The ergative model, on the other hand, is concerned with how the process types are all alike; how 'they all have the same grammar' (Halliday & Matthiessen 2004: 281).