As was discussed in Section 3.2.2, adjuncts have an identifiable, consistent semantic contribution across heads. The implication of this for any treatment of adjuncts is that there should be a single lexical entry which specifies the meaning of the adjunct with respect to a particular type of head. That is, the content of the adjunct combines in a certain general way with the content of the element it modifies (a verb or noun phrase, for example) and this must be specified only once. Since this combination does not change with every type of head, a single specification is much more efficient than incorporation into the lexical entry, into the subcat list, of each verbal head with which an adjunct can appear.
In particular, a single lexical entry can only be realised if adjuncts select the types of heads they modify. Were individual heads to idiosyncratically specify the adjuncts with which they can appear, the semantics of the adjunct could conceivably be incorporated with the content of the head in a different way for each head, and in effect the adjunct need not have any independent meaning. Furthermore, this approach would require that the set of adjuncts which could appear with a particular head be specified in advance, at the level of the lexicon, for every individual element in the lexicon which could potentially be modified by an adjunct. This is clearly not a desirable consequence.
An additional semantic argument for the selection of a head by an adjunct is observed by kasper:93: ``The semantic contribution of a modifier generally must incorporate the semantic contribution of the element that it modifies, whereas the semantic content of the modified element (the syntactic head) does not depend crucially on any of its potential modifiers''.