The treatment of adjuncts in Pollard and Sag (1994) centres on the selection of a head by an adjunct. The adjunct specifies the type of head which it modifies via the mod feature of its synsem:loc:category:head field. Semantic integration is specified in the lexical entry of the adjunct, via structure sharing between a substructure of the head's content and the content of the adjunct. Adjuncts differ from complements in that they have a non-null mod value, that they are not subcategorised-for by the element with which they combine, and that they are joined with that element via a different mechanism.
Immediate dominance (ID) schemata govern the permissible configurations of immediate consituency (akin to phrase-structure trees) in HPSG. One such schema creates a head-adjunct-structure, combining a head and an adjunct into one structure, and ensuring that the head of the constituent is an element allowed by the mod feature of the adjunct. The content of the mother in a head-adjunct-structure is required to be token-identical with the content of the adjunct via the Semantics Principle. This guarantees that the appropriately integrated semantics is associated with the phrase as a whole.
The specification of the ID schemata in standard HPSG does not allow
for Mittelfeld phenomena. The schemata handling complements require
that all complements other than the subject must be combined at once
into a phrase. The adjunct attachment schema allows the adjunct to
appear immediately before or after the head it selects,
or before or
after the phrase containing the head and all of its complements, but
does not license the appearance of the adjunct within a group of
complements.
Other characteristics of adjuncts are handled in this approach, however. A single lexical entry specifies the integration of an adjunct's semantics with the element it modifies. The difference between restrictive and operator adjuncts can be accommodated by variances in the definitions in the context field of the adjunct's synsem feature. Redundancy constraints are not explicitly accommodated, but could conceivably be implemented within the mod feature of an adjunct in terms of restrictions on the modified head. How this implementation would be accomplished is not, however, entirely clear.
Surface order and semantic precedence issues remain a stumbling block for the standard HPSG approach. Since linear precedence constraints (constraints defined in terms of obliqueness which control the surface order of elements relative to one another) apply at the level of individual phrases built by the ID schemata, and only one adjunct at a time can be attached to a head via an ID schema, the order of modification is constrained to surface order.