|1||The hospital admitted the patient with cancer while the other incoming patients waited|
|2||The hospital admitted the patient with bodyguards while the other incoming patients waited|
|3||The hospital admitted the patient with apologies while the other incoming patients waited|
The syntactic attachment of the underlined PP in 1 and 2 is to the preceding noun patient as both of these PPs specify which patient is being talked about. The PP in 3 attaches to admitted, as it describes an aspect of what was involved when the hospital admitted the patient.
The difference in the thematic roles of the PPs in 1 and 2 is that in 1 the PP is an attribute of the noun it modifies, while in 2 it is an accompaniment. A self-paced reading task showed that the attribute role is preferred over the accompaniment role (i.e. is read more rapidly).
The Minimal Attachment of the PP would be to the verb phrase, as in 3, since the PP attaches directly to the VP, whereas it is argued that to attach the PP to the NP in 1 or 2 requires an extra intervening NP node to be posited (though note that this is specific to certain approaches to the syntactic analysis of these structures). Nevertheless, the sentence in 1, with Non-minimal Attachment, proves to be easier to process than that in 3. This is claimed to reflect plausibility factors, rather than syntactic preferences.