In this section, we present our analysis of German verb clusters. We present a HEAD-COMPLEMENT schema which allows both full and partial verb phrases to be derived. Furthermore, we present our approach to word order, which relies on LINEAR PRECEDENCE statements. 5Linear precedence within phrases is determined by three principles:
The distinction between the verb cluster and other parts of the VP is expressed by means of the distinction between inner and outer zone, and the order of elements within the verb cluster is determined by the direction of government.
We assume the following, general, HEAD-COMPLEMENT schema:
Schema (20) states that a phrase may consist of a lexical head daughter and one or more complement daughters. The requirement that the head daughter must be of type word, while the mother is a phrase rules out recursive rule application, i.e. no phrase derived by means of the HEAD-COMPLEMENT schema can be the head of a larger phrase also derived by means of the HEAD-COMPLEMENT schema. The requirement that there must always be at least one complement means that there can be no non-branching derivations. Both constraints are required to rule out spurious derivations.
The HEAD-COMPLEMENT schema is subject to the VALENCE Principle, which is similar to the Subcategorization Principle of [13, 34]: 6
Note that valence does not distinguish between a case where all complements are selected, and cases where one or more complements are not selected. The latter allows partial phrases to be derived.7This is essential for our account of partial VP fronting and partial extraposition (or third construction) verbs.
The order of complements relative to the head daughter is determined by the feature DIR. A head daughter may specify its complements as either [DIR ], in which case the complement must precede the head, or as [DIR ], in which case it follows the head. In German subordinate clauses, NP complements must precede the head daughter, which means that a ditransitive verb such as geben (to give), can be specified as:
The following two LP statements implement directionality:
Note that directionality only orders complements relative to the head daughter, the order of complements with respect to each other is left open. In previous work on Dutch , we have assumed that obliqueness provides an ordering of complements: if C1 is more oblique than C2 (i.e. the SYNSEM-value of C1 follows the SYNSEM-value of C2 on COMPS), than C1 appears closer to the head daughter than C2. Such a constraint might be too restrictive for German, however.8The order of lexical, verbal, complements is discussed below.
Note finally, that the head daughter of a HEAD-COMPLEMENT phrase is marked [ZONE inner], also referred to as I-ZONE; whereas NP-complements are marked [ZONE outer] (O-ZONE). The relevance of this distinction is explained below.
Following the analysis of , we assume that modals and auxiliaries are complement inheritance verbs, which select for a list of complements consisting of a verb and the complements selected by that verb:
The verbs helfen (to help) and lassen (to let) are analyzed as complement inheritance verbs as well, but these verbs also select for an additional NP object:
Our account of the verb cluster rests on the assumption that complement inheritance verbs select for an I-ZONE verbal complement. The ZONE feature defines whether an element occupies the `inner' or `outer' zone topological field. The inner zone contains the head daughter, along with any complements which are required to appear `close' to this head. Furthermore, we assume that the I-ZONE may only contain daughters of type word. The outer zone is occupied by the other complements. Thus, we make the following assumptions:
The effect of the two LP constraints above is that no O-ZONE daughter can appear in between two I-ZONE daughters. Since head daughters are required to be in the I-ZONE by the HEAD-COMPLEMENT schema, this has the effect of creating a topological field for the head daughter and I-ZONE complements. In verb phrases, the I-ZONE will contain the verb cluster. The interaction of the zone and directionality constraints can be represented schematically as in (27).
The I-ZONE principle ensures that complement inheritance is not just a possibility, but a necessity. Since I-ZONE elements must be words, complement inheritance verbs, which select for an I-ZONE complement, must in fact combine with a lexical verbal complement. Thus, all complements of this lexical verbal complement must be inherited by the higher, complement inheritance, verb.
The effect of the I-ZONE principle is therefore that VPs headed by a complement inheritance verb must be `flat'. For instance, the VPs in the two examples below, are given in (29) and (30). In these examples, an arrow points toward a head daughter.
The `flat' constituent structures shown here are the only ones possible according to the grammar. Furthermore, NP-complements must precede the I-ZONE and all verbs must appear in the I-ZONE. The relative order of the verbs in the cluster is still unconstrained, however.
The analysis of word order in German and Dutch verb clusters in  combines the  analysis of the verb cluster with a non-concatenative approach to word order. Word order is determined by topological fields as well as direction of government. Our account of word order within the verb cluster closely follows Kathol's proposals. The major distinction between the two approaches is that we implement these proposals in a concatenative setting, whereas Kathol presupposes a non-concatenative framework.
An example of the type of word order domains used by Kathol is given in (31).
Such order domains can be derived using binary branching syntax rules if the daughters in a rule are allowed to be combined by means of sequence union , instead of concatenation. This enables Kathol to adopt a constituent structure very similar to that proposed by , while at the same time word order constraints apply to the `flat' domain shown in (31). The labels cf, mf, and vc refer to the topological fields complementizer field, Mittelfeld, and verb cluster. LP-constraints ensure that cf elements must precede mf elements, and that mf elements must precede vc elements.
The vc topological field corresponds exactly to our I-ZONE field. Note also that in both cases, all verbal elements are sisters, and thus constituency does not impose any constraints on word order. We demonstrate below that Kathol's proposals for determining order within the verb cluster therefore carry over to our analysis. First we discuss how the notion of government can be incorporated in HPSG, and how linear precendence statements referring to government can be defined. We then go on to present the various constraints that must be imposed on the direction of government for German verbs.
The distinction between the relative order of a head daughter and its complement (which is constrained by the value of DIR) and the relative order of a governor and governee is relevant especially for complement inheritance verbs. The COMPS-list of a complement inheritance verb in general contains a number of complements for which the verb subcategorizes, as well as complements inherited from one of these complements. Only the first are assumed to be governed by the complement inheritance verb (i.e. inherited complements are not governed by the verb which inherits them). The distinction between complements that are subcategorized-for and inherited complements is reflected on the level of argument structure. Argument structure is a notion which has been introduced recently in HPSG as the level on which the binding constraints are defined. Canonically, it is the append of the valency features SUBJ, SPR, and COMPS. Exceptional cases can arise, for instance, in `pro-drop' or ergative languages (where ARG-S may contain elements not present on any of the valence lists, or where the mapping between valence and ARG-S is not just append) (see  for discussion) or as the result of applying lexical rules such as the COMPLEMENT EXTRACTION rule (see ). In , we argued that binding in Dutch indicates that the ARG-S of complement inheritance verbs contains the complements the verb subcategorizes for, but not the inherited complements. Manning et al.  reach a similar conclusion for Japanese causatives (which they analyse as bound morphemes which inherit the complements of the host-verb). We will assume, therefore, that the same is true for German: complement inheritance has an effect on valency, but not argument structure. The examples below exemplify this distinction.
We assume that a verb V governs a complement C iff C is an element of the argument structure of V.9
The feature GVOR replaces the feature FLIP of , and accounts for the relative order of a governor and governee. This feature takes four values, ( ) (the governee must (immediately) precede its governor), and ( ) (the governee must (immediately) follow its governor). Since a complement is governed by the sign on whose argument structure it appears, this gives rise to the following LP statements (where expresses immediate precendence):
Kathol  assumes that German main (i.e. non-auxiliary and non-modal) verbs come with the specification [GVOR ]. That is, a governed main verb must always precede its governor. This accounts for the fact that auxiliaries or modal verbs cannot precede the main verbs they govern (i.e. main verbs cannot `trigger' auxiliary flip). An example is given in (34):
For complement inheritance verbs, two GVOR-specifications are relevant: that of the verb itself, and that on its verbal complement. Modal verbs in general may act as trigger of auxiliary flip, and therefore are themselves unspecified for GVOR. There is a distinction between the modals of the werden type, and of the können type. The first, in its finite form, may precede its verbal complement (if it is not a main verb) whereas the second must always follow its complement. This distinction implies that finite forms of werden do not impose a constraint on the GVOR value of their verbal complement, whereas können specifies its verbal complement as [GVOR ]:10
Given these lexical entries, we can derive exactly the three word orders given below (an arrow with subscript g illustrates the value of the GVOR feature; an arrow with subscript d illustrates the DIR feature):
The examples above illustrate that our account predicts the possibility of auxiliary flip and Zwischenstellung, if an auxiliary such as werden governs a modal verb. If the auxiliary governs a main verb, flipped word order is ruled out.
For those speakers that do not allow the Zwischenstellung order (38), we assume, following Kathol, that the GVOR specification on main verbs is [GVOR ] instead of [GVOR ]. The restriction that the governor of a main verb must be right-adjacent rules out the derivation in (38), but not the derivations in (36) and (37).
The final issue to be discussed concerns Ersatzinfinitiv and the auxiliary haben. If haben governs a modal verb, this verb will appear in its infinitival form, instead of its participle form. Following , we will assume that the infinitive form of a modal may be marked [VFORM psp]. Furthermore, since haben must obligatorily precede the modal verb in this case (40), it is specified as [GVOR ]:
The status of the auxiliary haben itself as a trigger for `flipped' word order, depends on the question whether it governs a main verb or a modal. The two cases are illustrated below.
As in the analysis of , we may assume that the status of haben as a trigger for `flipped' word order is determined by the verbal complement it governs. That is, there is a reentrancy between the value of GVOR (FLIP in the analysis of Hinrichs and Nakazawa) on the complement of haben and haben itself:11
The most important difference between the proposal of  and our own is that Hinrichs and Nakazawa employ two rule schemata which explicitly distinguish between the derivation of verbal complexes and other verbal projections. Our HEAD-COMPLEMENT schema, on the other hand, is general, and applies to all HEAD-COMPLEMENT structures in the grammar.12The feature NPCOMPS, which distinguishes the verbal complex from other verbal projections, is replaced by a distinction between I-ZONE and O-ZONE in our account. Note, however, that since this distinction applies to sister nodes in a `flat' VP, we can account for a stricktly larger set of word order possibilities. The FLIP feature of Hinrichs and Nakazawa, finally, is replaced by GVOR. Whereas Hinrichs and Nakazawa use FLIP only to determine the order of a lexical head and its complement, the LP-statements for GVOR must be more sophisticated, as they must order a complement relative to its governor without the aid of phrase structure (see also ).
The I-ZONE principle (26)b says that all I-ZONE daughters in a HEAD-COMPLEMENT structure must be of type word. One reason for stating this requirement as a constraint on rule schemata is that it allows us to refer to the distinction between phrasal and lexical signs without having to introduce a SYNSEM feature such as LEX or NPCOMPS. A more important reason for associating this constraint with the HEAD-COMPLEMENT schema is that it leads to a monotonic account of partial VP fronting. 13
As we pointed out in , one advantage of allowing the HEAD-COMPLEMENT schema to build partial VPs is that it can be used to derive the partial VPs which may be found in fronted position in main clauses. The fronted VP lesen können in (44), for instance, can be assigned the structure in (45).
The use of one rule schema which allows both partial and full VPs to be derived, without having to accept spurious ambiguity, is an improvement of the analysis of , who had to introduce a special rule to account for the derivation of partial VPs in fronted position.
The present set-up has an important additional benefit. To account for the fact that a partial VP in fronted position could be selected by an auxiliary or modal verb that normally would require a lexical (i.e. [LEX +]) verbal complement, Nerbonne introduced a complement extraction rule that moved an element from the COMPS-list of a verb to SLASH, and removed any specification for LEX in the process. In our account, the complication in the complement extraction rule disappears. Since we do not state in the lexical entries of argument-inheritance verbs that they select for a lexical verbal complement, we can simply assume that the canonical complement extraction lexical rule (as given in [13, chpt. 9]) applies:
This rule can be applied to the lexical entry for wird as follows:14
Example (44) is now derived as follows: 15
Note that the element on SLASH of S is [ZONE INNER], but is not constrained to be of type word. The fronted partial VP can therefore be combined with the S/VP as a HEAD-FILLER structure without problem. In particular, the I-ZONE principle (which requires i-zone elements in HEAD-COMPLEMENT structures to be of type word) does not apply to this construction.
The elimination of a special rule schema to build partial VPs together with the elimination of the complication of Nerbonne's complement extraction rule is a significant improvement.
It should be noted, however, that fronting of a single modal (as in (49)) can only be excluded by means of a special constraint.
These examples are seen as problematic by  and , for instance, and are one of the reasons why Kathol does want to maintain the Hinrichs and Nakazawa analysis as far as constituent structure is concerned. In terms of the fragment developed here, these cases can be ruled out by requiring that a filler may not have any I-ZONE elements on its COMPS-list: