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5.3.1.General introduction
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The examples in (85) show that R-extraction is possible if the adpositional phrase acts as a PP-complement or as a complementive. Example (85a) shows that R-extraction from the complement of the verb wachten'to wait' is possible; witness the fact that the adverbial phrase de hele dag'the whole day' can intervene between the R-pronoun and the preposition op. Example (85b) shows that R-extraction is also possible from PPs that act as complementives, as is clear from the fact that the accusative object het boek'the book' can intervene between the R-pronoun and the preposition in.

85
a. Jan heeft de hele dag op een bericht gewacht.
PP-complement
  Jan has  the whole day  for a message  waited
  'Jan waited for a message the whole day.'
a'. Jan heeft er de hele dag op gewacht.
b. Jan zette het boek in de kast.
complementive
  Jan put  the book  in the bookcase
b'. Jan zette er het boek in.

Adverbially used adpositional phrases, on the other hand, generally do not allow R-extraction, which is illustrated by the examples in (86); the (b)-examples show that, despite the fact that R-pronominalization of the temporal voor-PP is fully acceptable, R-extraction gives rise to an unacceptable result.

86
a. Jan komt waarschijnlijk voor zijn vakantie nog even langs.
adjunct
  Jan comes  probably  before his holiday  prt. briefly  along
  'Jan will probably visit (us) briefly before his holiday.'
b. Jan komt waarschijnlijk ervoor nog even langs.
b'. * Jan komt er waarschijnlijk voor nog even langs.

The examples in (85) and (86) suggest that R-extraction is only possible with PP-complements and complementives. This would be in line with a generalization from the generative literature (which was formulated as part of Huangʼs (1982) Condition on Extraction Domains) according to which adjuncts are islands for extraction. There is, however, a group of adpositional phrases that are traditionally analyzed as adverbial clauses that do nevertheless allow R-extraction. This is illustrated in (87), for an instrumental PP headed by met'with'; see Section 5.2.1, sub IIIA, for more PPs of this sort.

87
a. Jan opende de kist met een breekijzer.
  Jan opened  the box  with a crowbar
b. Jan opende er de kist mee.

This may give rise to two possible conclusions: either we assume the generalization that only PP-complements and complementives can undergo R-extraction is wrong, or we have to assume that instrumental PPs actually function as a kind of complement of the verb, albeit that they differ from PP-arguments like op een bericht in (85a) or predicative complements like in de kast in (85b) in not being obligatorily. Here we will leave the question of which alternative is correct open.
      Besides the requirement that the adpositional phrase must be a complement, a complementive, or involve a specific semantic role (like instrumental met), it must also occupy a certain position in the clause in order to license R-extraction: the stranded preposition must be left-adjacent to the verb(s) in clause-final position (with some qualifications that will follow below). This is illustrated in (88) by means of the pronominalized form of the instrumental PP met een breekijzer from (87); R-extraction is possible if the pronominalized PP daarmee is left-adjacent to the clause-final verbs but not if it precedes the negative adverb niet or if it is placed in a position following the clause-final verbs.

88
a. dat je de kist niet daarmee mag openen.
  that  you  the box  not  with.that  be.allowed  open
  'that you arenʼt allowed to open the box with it.'
a'. dat je daar de kist niet mee mag openen.
b. dat je de kist daarmee niet mag openen.
  that  you  the box  with.that  not  be.allowed  open
  'that you arenʼt allowed to open the box with it.'
b'. * dat je daar de kist mee niet mag openen.
c. dat je de kist niet mag openen daarmee.
  that  you  the box  not  be.allowed  open  with.that
  'that you arenʼt allowed to open the box with it.'
c'. * dat je daar de kist niet mag openen mee.

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References:
  • Huang, Cheng-Teh James1982Logical relations in Chinese and the theory of GrammarCambridge, MAMITThesis
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