To conclude the discussion of the formal classification of adpositions, we want to discuss the structural relation between the four main classes that we have distinguished. Since this is not a well-studied topic, much of what will be said here is highly speculative and must be seen as no more than a first indication of what the structure of adpositional phrases may look like. Some recent studies attributed to this issue, like Van Riemsdijk (1978/1990), Koopman (1997) and Den Dikken (2003), indicate that the correct analysis may in fact be much more intricate than suggested here.
      We start by discussing the relation between pre- and postpositions. One way of describing the difference between the two is by saying that the first take their nominal complement to their right, whereas the latter take their complement to their left. Since we have seen that the postpositions are a proper subset of the prepositions, this can be formalized by assuming the lexical entries in (149): (149a) expresses that adpositions that can be used as prepositions only take their complement to their right, whereas adpositions that can be used either as pre- or as postpositions can take their complement either to their right or to their left.

A problem for the proposal in (149) is that the pre- and postpositional phrases differ in meaning: the first typically denote a (change of) location, whereas the latter denote a direction. In German, this difference is not expressed by means of word order but by means of case marking: both locational and directional adpositions are prepositional, but the locational adpositions assign dative, whereas the directional ones assign accusative case. Given that German and Dutch are so closely related, this casts doubt on the lexical entry in (149b). It may be the case that in Dutch also, the directional adpositions take their complement to their right, but that, due to the fact that Dutch has no morphological case, the nominal complement must be moved to the left of the adposition in order to signal the directional meaning of the postposition. This gives rise to the movement analysis in (150b).

The proposal in (150) might be supported by the fact that the complement of a preposition cannot be scrambled or topicalized, whereas the complement of a postposition can: this would be surprising if they both occupy the complement position of the adposition but would follow in a natural way if we assume that the base-position of the noun phrase in (150a') is not accessible to these operations, whereas the derived position in (150b') is. The relevant data are given in (151).

      If the movement analysis of postpositional phrases in (150b') is tenable, a similar analysis may be feasible for circumpositional phrases. Instead of assuming that circumpositions are discontinuous heads, as is done in traditional grammar, one may assume that circumpositional phrases actually consist of an adposition which takes a PP as its complement, which (for some reason) must be moved leftwards: see, e.g., Zwart (1993:365ff.) and Claessen & Zwarts (2010}

The analysis in (152) has several potential advantages. First, it may account for the fact that the PP-part in (152) must have a form that can also be used independently as a prepositional phrase. Second, the analysis in (152) leaves open the possibility that not all prepositions can occur as the second member of circumpositional phrases and that there are certain elements that may occur as the second member (= the P-part in (152b)) of a circumpositional phrase but cannot be used as a preposition. This would follow if we assume that, just as in the case of verbs, complementation of adpositions is lexically constrained; adpositions like voor, which can only occur as prepositions, have the categorial frame in (153a), adpositions like heen or vandaan, which can only occur as the second member of a circumposition, have the categorial frame in (153b), and adpositions like aan, which can be used both as a preposition and as the second member of a circumposition, have the categorial frame in (153c).

Third, the movement analysis in (152b) predicts that circumpositional phrases can be split; just like the nominal complement of a postposition, the prepositional complement can be moved further leftwards. This may happen if the prepositional phrase contains a nominal wh-phrase, as in (154), which is taken from Section 1.2.5. The question why topicalization of the prepositional complement generally gives rise to a marked result remains unanswered on this analysis.

Finally, the analysis in (b) may account for the fact that toe occurs both as the second member of circumpositional phrases and as the counterpart of tot in pronominalized PPs like er ... toe in example (155b). All that is needed is to claim that circumpositional phrases and pronominal PPs are both derived by leftward movement of the complements of the adpositions, and that the use of toe (instead of tot) is a morphological reflex of these movements.

      A potential problem for the assumption that circumpositions are the result of leftward PP-movement is that movement is often assumed to give rise to Freezing: the moved phrase becomes an island for extraction. The data concerning R-extraction from circumpositional phrases seem to go against this: the proposal in (152) implies that the PP bij de koffie in (156a) occupies its base position, but nevertheless R-extraction is excluded; the PP over het hek in (156b), on the other hand, is claimed to have moved leftward, but nevertheless R-extraction is possible from circumpositional phrases like over het hek heen; cf. Section 1.2.5 for a more detailed discussion of R-extraction.

However, it has been suggested that Dutch clauses also have an underlying head-complement order. If that is indeed correct, the preverbal position of a PP-complement is also a derived position, so that in this case also, Freezing is expected. The examples in (157) show, however, that R-extraction is possible from the preverbal position; it is instead R-extraction from postverbal PPs that is impossible.

This means that on the assumption that Dutch has underlying head-complement order, the freezing effect cannot be assumed to arise with all types of movement: PP-movement resulting in the PP-V order or the surface order of circumpositional phrases must be assumed not to give rise to it; the (a)- and (b)-patterns in (158) must then receive a similar analysis. We leave this suggestion for further research.

      We conclude with a brief remark about the relation between intransitive adpositions and particles. We have seen that the former probably function as the heads of regular adpositional phrases, and that they are only special in that they do not take a complement, or may leave their complement implicit. This does not hold for particles, however. One difference between particles and all other classes of adpositions is that particles are not able to assign case, as is clear from the fact that their arguments are typically assigned accusative case by the verb or nominative case in the subject position of the clause, just like the logical subjects of other predicatively used adpositional phrases. There are two analyses that seem compatible with this observation. According to the first analysis, particles are just like intransitive adpositions in that they do not take a complement, which of course raises the question why they exhibit behavior different from intransitive adpositions. According to the second analysis, particles are like unaccusative verbs in that they do take a complement but are not able to assign case to it, for which reason it must be moved into the case-assigning domain of the verb. Arguments in favor of the second approach can be found in Den Dikken (1995).