The analysis of cross-serial dependencies in terms of argument inheritance interacts with the analysis of adjuncts presented in section 2.2. If a matrix verb inherits the arguments of the verb it governs, it should be possible to find modifiers of the matrix verb between this verb and one of its inherited arguments. This prediction is borne out (13a). However, we also find structurally similar examples in which the adjunct modifies the governed verb (13b). Finally, there are examples that are ambiguous between a wide and narrow scope reading (13c). We take it that the latter case is actually what needs to be accounted for, i.e. examples such as (13a) and (13b) are cases in which there is a strong preference for a wide and narrow scope reading, respectively, but we will remain silent about the (semantic) factors determining such preferences.
On the assumption that the lexical entries for lijken en ontwijken are as in (14), example (13c) has two possible derivations (() and ()). Procedurally speaking, the rule that adds adjuncts can be applied either to the matrix verb (after division has taken place) or to the governed verb. In the latter case, the adjunct is `inherited' by the matrix verb. Assuming that adjuncts take scope over the verbs introducing them, this accounts for the ambiguity observed above.
The assumption that adjuncts scope over the verbs introducing them can be implemented as follows. We use a unification-based semantics in the spirit of Pereira and Shieber . Furthermore, the semantics is head-driven, i.e. the semantics of a complex constituent is reetrant with the semantics of its head (i.e. the functor). The feature structure for a transitive verb including semantics (taking two NP's of the generalized quantifier type as argument and assigning wide scope to the subject) is:
Thus, a lexical entry for a transitive verb can be defined as follows (where TV refers to the feature structure in 15):
The lexical rule for adding adjuncts can now be extended with a semantics:
Each time an adjunct is added to the subcategorization frame of a verb, the semantics of the adjunct is `applied' to the semantics as it has been built up so far (), and the result () is passed on. The final step in the recursion unifies the semantics that is constructed in this way with the semantics of the `output' category. As an adjunct that appears to the left of an adjunct in the string will be added to the subcategorization frame of the governing verb after is added, this orders the (sentential) scope of adjuncts according to left-to-right word order. Furthermore, since the scope of adjuncts is now part of a verb's lexical semantics, any functor taking such a verb as argument (e.g. verbs selecting for an infinitival complement) will have the semantics of these adjuncts in its scope.
Note that the alternative treatments of adjuncts mentioned in section 2.2 cannot account for the distribution or scope of adjuncts in cross-serial dependency constructions. Multiple (i.e. a finite number of) categorizations cannot account for all possible word orders, since division implies that a trigger for cross-serial word order may have any number of arguments, and thus, that the number of `subcategorization frames' for such verbs is not fixed. The polymorphic solution (assigning adjuncts the category ) does account for word order, but cannot account for narrow scope readings, as the adjunct will always modify the whole verb cluster (i.e the matrix verb) and cannot be made to modify an embedded verb only.