Modals do allow the head of their infinitival complement to occur either right or left of the head:
Example (41a) illustrates normal word order, while (41b) illustrates the construction in which the governed infinitive occurs right of the head. Word orders in which the head of a verbal complement precedes its governor are usually referred to as instances of ``inversion''.
At first blush, we can account for inversions by simply allowing a modal verb to select for its verbal complement either to the right or to the left (that is, the DIR feature is left uninstantiated). We need to impose additional constraints on the [DIR left] option, however, as the possibility of inversion is not always available.
First of all, it is restricted to finite modal governors:
Second, inversion is possible only if the governed verb is not itself a verb-raiser. This is illustrated for modals, perception verbs, and auxiliaries, in the examples below. Note the difference between (42b,c), in which the most deeply embedded verb occurs left of its (infinitival) governor, and (43a,b), in which governed modal occurs left of its (finite) governor.
The second constraint on inversion implies that somehow a distinction between ``verb raisers'' and other verbs must be made. To this end, we introduce the (boolean) feature VR (comparable to the feature AUX in the grammar of English), which has a positive value only if a verb is a ``verb raiser''.
We can now account for modal inversion by adding the following type of lexical entry for finite modals:
One can either consider the lexical entry in (44)
as stipulated, or else, if these finite forms are derived by means of
a lexical rule from an un-inflected root (as are the regular finite
forms), one can attach a constraint to the lexical entries of modal
roots. The constraint is a disjunction, saying that the last element
on SUBCAT is [DIR right], or else the last element is
[DIR left,-VR] and the sign itself is [VFORM fin].
Auxiliaries allow for the same type of inversion as modals, that is, the participle of an auxiliary may often occur either to the right or to the left of the auxiliary.
Auxiliaries differ from modals, however, in that the possibility of inversion exists with non-finite auxiliaries as well:
Note that in these complex inversion cases, the participle has to occur as the first element of the verb sequence, and (normally) cannot occur left-adjacent to the governing auxiliary, as in (46c).6
Auxiliaries are like modals, in that inversion is excluded if the governed verb is a verb-raiser:
Note that the (47) illustrates IPP (infinitivus pro participio, see also section 4), i.e., the governed verb-raiser appears not as a participle but in its infinitival form.
We can account for inversion with a governing auxiliary as follows. First of all, we account for the IPP-effect by simply stipulating two different entries for hebben, one selecting -VR participles, and one selecting +VR infinitives. As inversion is possible for governed participles, but not for governed infinitives, the DIR-value of the last argument can remain unspecified in the first entry, but must be right for the second:
The possibility of inversion with participles now follows if we instantiate DIR as left in (48a). Note that there is no need to restrict this option to finite forms only. As with modals, one might consider the possibility of merging both lexical entries into one entry, subject to a disjunctive constraint.
The interesting aspect of this analysis is that it immediately accounts for the dubious status of (46c). As, under a flat analysis, the participle (including an unspecified value for DIR) is an inherited argument of the finite verb (moet in (46)), the participle must occur either to the right of moet (in which case it must also be right of the auxiliary because of the obliqueness constraint on word order) or to its left. The possibility that gelezen occurs right of the modal but left of the auxiliary is ruled out. Under a binary-branching analysis of the verb-cluster, this fact appears to be much harder to account for. One might pursue the possibility of using the feature FLIP (used by  to account for German AUX-flip) to allow participles to occur left instead of right of the head. Note however, that a binary rule which allows a participle to combine with a following verbal head will also produce the dubious (46c).7