Auxiliary Selection

The $\langle$mode$\rangle$ feature is also used to state the subcategorizational constraints between an auxiliary verb and its complement. We model the following constraints:
have takes past participial complements
passive be takes past participial complements
active be takes progressive complements
modal verbs, do, and to take VPs headed by verbs in their base form as their complements. An auxiliary verb transmits its own mode to its root and imposes its subcategorizational restrictions on its complement i.e. on its foot node. e.g. the auxiliary have in its infinitival form involves the following equations:

(529)0(529

(530)

VP_r.b:$\langle$mode$\rangle =$ V.t:$\langle$mode$\rangle$   (530)0(530

(531)

V.t:$\langle$mode$\rangle =$ base   (531)0(531

(532)

VP.b:$\langle$mode$\rangle =$ ppart  

$\langle$passive$\rangle$: This feature is used to ensure that passives only have be as their auxiliary. Passive trees start out with their $\langle$passive$\rangle$ feature as +. This feature starts out at the level of the verb and is percolated up to the level of the VP. This ensures that only auxiliary verbs whose foot node has + as their $\langle$passive$\rangle$ feature can adjoin on a passive. Passive trees have ppart as the value of their $\langle$mode$\rangle$ feature. So the only auxiliary trees that we really have to worry about blocking are trees whose foot nodes have ppart as the value of their $\langle$mode$\rangle$ feature. There are two such trees - the be tree and the have tree. The be tree is fine because its foot node has + as its $\langle$passive$\rangle$ feature, so both the $\langle$passive$\rangle$ and $\langle$mode$\rangle$ values unify; the have tree is blocked because its foot node has - as its $\langle$passive$\rangle$ feature.