Modifiers indicating the orientation of the located object with respect to the reference object are limited in number; we illustrate this here for the adposition achterbehind, but the results would be the same for the adposition voorin front of. The modifier rechtstraight in (6a) and the modifiers schuindiagonally and links/rechtsto the left/right in the (b)-examples are complementary in a sense: while the former restricts the set of vectors to those where x = 0, the latter exclude them. Note that we have topicalized the modified PPs in (6) to show unambiguously that the modifier and the PP form a constituent; cf. the constituency test.

The orientation modifiers in (7) could be called approximative, because they all express that the x-value of the vectors lies in between specific contextually determined norms. In other words, the vectors in the denotation set stay close to the y-axis; precies/exact emphasize that there is no deviation (x = 0), while the modifiers ongeveerabout and zowat ‘virtually; express that the deviation is negligible or at least small (x ≈ 0).

The examples in (8) show that modifiers of orientation cannot be extracted from the adpositional phrase by wh-movement; we will see in Subsection II that they differ from modifiers of distance in this respect. The number signs are used to indicate that the examples are possible if recht and schuin are used to characterize Marie’s posture (i.e. whether she is sitting upright or not), which is not relevant here.

It seems likely that the impossibility of extracting the modifier of orientation hoe recht/schuin is related to the fact that orientation modifiers, unlike distance modifiers, are not gradable; cf. the primeless examples in (9). Thus, it is the modification by hoehow and not the wh-extraction of the phrase hoe A that is excluded; this is supported by the primed examples in (9), which show that wh-movement of hoe recht/schuin is also excluded when it pied-pipes the whole PP.

The number signs in (9) again indicate that the examples are possible if recht and schuin describe Marie’s posture, in which case they function as supplementives modifying Marie; cf. also the examples in (14) and (15) below. This suggests that it is no coincidence that the adjectives recht and schuin can be used as modifiers of orientation, since they also denote orientations in their attributive and predicative uses. Consider the examples in (10a&b): in the case of rechtupright, the orientation of the tower is parallel to the vertical axis in the three-dimensional space diagram in Figure 4 below, whereas in the case of schuinleaning, the orientation deviates from this axis. Something similar applies to the adjectives links and rechts in (10c), although in these cases a reference object or reference point is always implied, which can be made explicit by adding a modifying van-PP.

Not all locational PPs denoting a set of vectors can be combined with the three types of modifiers in the examples in (6) and (7). Table 1 lists the relevant prepositions and indicates whether modification by orientation modifiers is possible or not. The percentage sign indicates that modification is blocked by pragmatic factors, and the number sign indicates that modification is possible but does not yield the intended reading; this will be discussed in the following discussion.

preposition	translation	recht ‘straight’	precies/ongeveer ‘exactly/approximately’	schuin ‘diagonally’
achter voor	behind in front of	+	+	+
boven onder	above under	+	+	+
naast links/rechts van	next to left/right of	%	%	%
buiten bij	outside near	—	—	—
om rond	around around	—	—	—
tegenover	opposite	+	+	+
langs	along	—	+	—
tussen	between	—	#	—

If we assume the Cartesian-style coordinate system in Figure 4 (cf. Section 32.3.1.2, sub II), we can conclude from Table 1 that at least the modifiers of orientation recht and schuin can only modify prepositions that refer to a single axis, i.e. to a single dimension in space. We will discuss this in more detail below.

The proposed constraint on the use of modifiers of orientation immediately accounts for the fact that voor/achter and onder/boven are amenable to modification because they refer to only a single axis (the z-axis and the y-axis, respectively). We would also expect modification of naast to be possible, but judgments on such examples are less clear. The primed examples in (11) have been given as grammatical in the literature, but for us they are certainly not as felicitous as the primeless examples with voor/achter and onder/boven: the primed examples seem to be unacceptable (11a') or severely marked (11b'&c'); note in passing that the intended meaning of (11c') can be expressed by (onmiddellijk) links/rechts van (immediately) to the left/right of.

We assign a number sign to the primed examples because their unacceptability may be due to pragmatic rather than to syntactic factors. This is especially true for the examples (11b'&c'); the intended meaning of these examples can in principle also be expressed by the corresponding primeless examples. Since the latter are more precise in the sense that they denote a smaller set of vectors, we may be dealing with a pragmatic blocking effect; according to Griceʼs maxim of quantity, the more precise and therefore more informative assertion is preferred to the less informative one.

The proposed constraint on the distribution of modifiers of orientation easily accounts for the fact indicated in Table 1 that modification of buiten and bij is excluded because they involve two axes (dimensions), viz. the x-axis and the y-axis; cf. Figure 21 in Section 32.3. Similarly, modification of om and rond is excluded because these also involve at least two axes; cf. the discussion of Figure 13C&D in Section 32.3.1.2, sub IIA. Modification of tegenover is possible because it refers to a subset of situations in which voor is applicable, and thus involves only a single axis; cf. the discussion of Figure 19 in Section 32.3.

The preposition langsalong is special in that the vectors it denotes do not have the same starting point (which actually also holds for the prepositions buiten and bij but in a less conspicuous way). Instead, the vectors are more or less parallel; cf. the discussion of Figure 20 in Section 32.3. Therefore, langs also involves more than one dimension, and modification by recht and schuin is correctly predicted to be excluded in (13a). Nevertheless, the use of the modifiers precies and ongeveer is possible in (13b); the two modifiers differ in that the former expresses that the garbage cans are placed in a neat line along the edge of the sidewalk, whereas the latter expresses that their arrangement is somewhat sloppier.

The preposition tussen deserves special treatment. The PP tussen de twee agentenbetween the two cops in (14a) can be preceded by the adjective recht. However, the meaning of recht differs from the intended meaning in that it does not modify the position of the located object Jan with respect to the reference objects de twee agenten, but refers to Jan’s posture: Jan is said to stand between the two agents and his posture is straight. In other words, recht is predicated of Jan and does not modify the PP; it is equivalent to the supplementive rechtopupright, which is not used as a modifier. That we are dealing with a supplementive and not a modifier is also clear from the fact that the AP can be used when the PP is not present, and from the fact that the AP can be topicalized in isolation, as shown in (14b).

Since the same arguments can be repeated for the adjective schuin in (15), which has a similar function as the supplementive gebogenstooped, we can conclude that the modifiers recht and schuin cannot be used to modify a PP headed by tussen.

Modifying the PP with preciesexactly is possible, but then the modifier expresses that the distances from the located object and the relevant reference objects are all equal. Example (16a) expresses that the distance between the painting and candlestick 1 is equal to the distance between the painting and candlestick 2. Note that it is not necessary for the painting to be on the straight line between the two candlesticks; the painting can hang in the area above the candlesticks. The same is true for ongeveerapproximately; example (16b) only expresses that the distance between the painting and candlestick 1 is approximately the same as the distance between the painting and candlestick 2. We therefore conclude that PPs headed by tussen cannot be modified by modifiers of orientation; this means that the modifiers preciesexactly and ongeveerapproximately must have some other function, which is indicated by the use of the number sign in Table 1.

We will conclude with two brief general remarks. First, example (17b) shows that the modifiers discussed in this subsection do not modify the preposition itself, but the whole PP. This is clear from the fact that, in the case of R-pronominalization, the R-word er can intervene between the modifier and the preposition. Note that the R-word can also precede the modifier, but this is not relevant here; it only shows that the R-word can undergo R-extraction to a PP-external position, as is usually the case with locational complementive PPs.

Second, it can be observed that the degree of appropriateness of the use of two prepositions can be compared; example (18a) expresses that, as far as the orientation of the vector is concerned, both bovenabove and naastnext to seem to be applicable, but that boven is the more accurate term. Note that the set of vectors denoted by the adpositions must partially overlap: (18b) shows that antonymous adpositions, which by definition do not satisfy this condition, cannot be used in this construction. The number sign indicates that (18b) is acceptable if meer is interpreted as a frequency adverb with the same meaning as vakermore often; this is not relevant here.

While modifiers of orientation are always adjectival in nature, modifiers of distance (i.e. the modifiers of the magnitude of the vectors in the denoted set) can be either adjectival or nominal. This is shown in (19), where we have topicalized the modified PP in order to show unambiguously that the modifier and the PP form a constituent; cf. the constituency test. We will discuss the adjectival and nominal modifiers in separate subsections.

The previous subsections have discussed the modification possibilities of locational PPs headed by prepositions denoting vector sets; they have shown that such PPs can be divided into three groups. The first group consists of PPs headed by prepositions that relate to a single axis of the coordinate system in Figure 4; the PPs in this group can be easily modified by modifiers of orientation and modifiers of distance. The second group consists of PPs headed by the prepositions buiten and bij, which can be modified by modifiers of distance (with a possible lexical restriction on the choice between the adverbs vlak and pal; cf. (28c&c')), but not by modifiers of orientation. The remaining locational PPs make up a third group, which can be modified neither for orientation nor for distance; exceptions are PPs headed by tegenover, which can be modified by modifiers of orientation like rechtstraight and schuindiagonally, and PPs headed by langs, which can be modified by adverbial modifiers of distance like vlak and pal. These results are summarized in Table 4.

preposition	translation	orientation	distance
		adjectival modification	adjectival modification	vlak/pal ‘close’	nominal modification
achter voor	behind in front of	+	+	+	+
boven onder	above under	+	+	+	+
naast links van rechts van	next to to the left of to the right of	%	—	+ — —	+
buiten/bij	outside/near	—	+	+	+
om/rond	around	—	—	—	—
tegenover	opposite	+	—	—	—
langs	along	—	—	+	—
tussen	between	—	—	—	—