In Hinrichs and Nakazawa's account of auxiliary flip, a (head) feature FLIP controls the position of a complement relative to its head. [FLIP -] complements must precede the head, whereas [FLIP +] complements must follow it.9 Given a binary branching analysis of the verb cluster and the assumption that modals are unspecified for FLIP, Hinrichs and Nakazawa predict that both [lesen können] wird and wird [lesen können] are possible word orders. For an analysis in which the verb cluster word order domain has no internal structure, such as Kathol's and ours, ordering with respect to the head only will not be sufficient. Note for instance that if we require lesen to precede the head and do not impose any restriction on the position of können, we predict the following word orders:
Of these, (25b) is clearly ungrammatical, while (25c) is only acceptable to some speakers. What is more, the grammaticality of wird lesen können is unpredicted.
To solve this problem, Kathol proposes a word order constraint that determines the position of a complement relative to its governor, instead of relative to the head. Below, we assume that A governs B iff B is an element of the argument-structure of A.10The notion argument-structure (and the corresponding list-valued feature ARG-S) is introduced in  and . In the canonical case, ARG-S is the append of the values of valence-feature COMPS, SUBJ and SPR (and thus is equivalent to what used to be SUBCAT). Exceptions to the canonical case are possible, however. For instance, in pro-drop languages, ARG-S may contain arguments that do not occur on any of the valence lists. Manning and Sag  describe ARG-S as "an attribute of only lexical signs, used to explain properties such as binding and `deep' subcategorization". In  we used ARG-S in this sense. The ARG-S of argument-inheritance verbs contains only elements for which the verb `really' subcategorizes and not those inherited from its verbal complement. This allowed us to propose a version of the HPSG-binding theory formulated on ARG-S, instead of the valence-features COMPS, SUBJ and SPR. Similarly, we now define the governor of a complement as the sign on whose ARG-S-list it appears.
There is a distinction between the notion governor and head in constructions headed by an argument-inheritance verb, as in these cases not all complements are governed by the same head. Following Kathol, we use the feature GVOR to specify the position of a complement relative to its governor. The specification [GVOR ] means that the element has to precede its governor and [GVOR ] means that it has to follow its governor. The specifications [GVOR ] and [GVOR ] mean that an element has to immediately precede or follow its governor. We can now state the following word order constraints:11