Kasper makes several relevant semantic assumptions. First, states of affairs (soas) come in two basic kinds: those that are spatio-temporally located (located-qfsoa) and those that are not (unlocated-qfsoa). Second, the nucleus of a state of affairs is split into a primary quantifier-free soa (qfsoa) and a set of restrictions. Multiple semantic restrictions with respect to the same state of affairs can thereby be specified in the restrictions set. This set plays a role analogous to the restrictions feature on referential indices in the semantic content of nominal objects in standard HPSG. Thus adverbials and adnominals can be treated in a parallel manner.
The head-complement structure of standard HPSG is extended by Kasper to include an adjunct-daughters attribute. This is a list of adjunct signs ordered in terms of a ``semantic obliqueness'' hierarchy, i.e. from widest to narrowest semantic scope.
To handle the syntax and semantics of adjunction, Kasper splits the mod field of the adjuncts into two parts: a syn attribute which indicates the syntactic category of the head with which the adjunct must combine and a sem attribute specifying the semantic value to which the adjunct is applied. Kasper then specifies an Adjunct Syntax Principle requiring the mod:syn attribute of all signs on the adjunct-daughters list of a head-complement structure to be token-identical with the cat value of the head daughter. Furthermore, his Adjunct Semantics Principle forces semantic composition to occur in terms of ``semantic obliqueness'' order: the element with narrowest scope is applied to the head's semantics, then the element with second-narrowest scope is applied to the resulting semantics, and so on down the list.
The relative surface order of complements and adjuncts would then have to be constrained by separate principles of constituent order which constrain the possible combinations of elements from the adjunct-daughters and comp-daughters attributes.
An issue about which Kasper remains vague is how elements are put onto the adjunct-daughters list. Apparently the head-complement and head-subject-complement schemata must be redefined to allow for arbitrary insertion of adjuncts into the adjunct-daughters list of the head-complement structure. What drives this insertion, however, remains unclear. Some mechanism must exist to identify all adjunctive sentence constituents, evaluate their relative ``semantic obliqueness'', and insert them into the list.
Since Kasper opts for a semantic obliqueness order on the adjunct-daughters list rather than an order reflecting surface order, semantic differences which depend on syntactic order may not be appropriately handled. The adjunct insertion mechanism discussed above must be defined in such a way as to take order effects into account. Furthermore, the mechanism must also provide for adjuncts which are not hierarchically related semantically (as in the case of restrictive adjuncts) so as to avoid analysis redundancies deriving from differences in order on the list.
It is observed by vannoord_bouma:94 that Kasper's approach cannot account for interpretation ambiguities in Germanic verb cluster constructions. These ambiguities occur because adjuncts are able to modify any verb within a verb cluster. Thus in the Dutch sentences in d57 (From van Noord and Bouma (1994)) the adjuncts (today, with the telescope) can either be interpreted as having narrow scope and modifying the event introduced by the main verb or as having wide scope and modifying the event introduced by the auxiliary.
that Arie wants to hit Bob today
that Arie saw Bob looking at the women with a telescope
Under the standard treatment of such clusters within a flat structure, the first auxiliary verb is treated as the head of the structure. Kasper's solution thus dictates that any adjuncts must modify this head rather than an embedded verb, not allowing for any narrow-scope readings.