When only one argument is expressed, this argument can appear either prenominally as a genitive noun phrase/possessive pronoun or postnominally as a van-PP. In the former case, the argument is typically interpreted as the agent or possessor of the object referred to; the paintings referred to in example (507a) were either painted by Rembrandt or possessed by him. However, with certain nouns such as portretportrait, the prenominal genitive noun phrase/possessive pronoun can also be interpreted as the theme: the default reading of example (507b) seems to be that in which Peter is the person portrayed, although in certain contexts he could also be the painter or the possessor of the painting.

When the noun is accompanied only by a van-PP, the construction is usually ambiguous in three ways. Thus, the PP van Rembrandt in example (508a) can have the semantic role of agent, theme or possessor. Like the genitive noun phrase in (507b), the PP van Peter in example (508b) is preferably interpreted as a theme.

Once a picture noun selects two arguments, some of the ambiguity that arises in constructions with only one complement is resolved. First, consider cases where one of the arguments is expressed by a prenominal genitive noun phrase/possessive pronoun. When the van-PP is interpreted as the theme, as in the (a)-examples of (509), the prenominal noun phrase can refer to either the agent or the possessor; when the van-PP is interpreted as the agent, as in (509b), the prenominal genitive noun phrase can only be the possessor. Out of context, the choice between agent and possessor depends on the person(s) referred to and their relationship to the medium involved: Rembrandt is usually interpreted as the painter in (509a), while Jan is probably the possessor in (509a'), unless he is known to be a lithographer.

Second, consider cases where both arguments are expressed postnominally as a van-PP. It has been claimed that the outermost PP is to be interpreted as the possessor or agent, with the theme always being closest to the noun (De Wit 1997:29/31). However, the examples in (510) show that the two PPs can actually occur in either order.

Which order appears depends on linguistic as well as extra-linguistic factors, and there are circumstances in which the preferred order is actually the one in which the agent precedes the theme, e.g. when the theme is relatively long, or when there may be ambiguity regarding the role of the van-PP. For these two reasons, (511b) is preferred to (511a): the PP-theme is long and the order in which the PP van Rembrandt precedes the theme precludes a potentially intrusive reading of (511a) that makes Rembrandt the possessor of the meadow (or perhaps even the cows).

When agent, theme, and possessor are expressed simultaneously, the best result is obtained when the possessor appears as a prenominal possessive pronoun/genitive noun phrase, while the theme and agent are realized as postnominal van-PPs.

In (512) the prenominal phrase is always the possessor. The two postnominal van-PPs can occur in either order. Which of the two orders is preferred may depend on linguistic as well as extra-linguistic factors. Consider the examples in (513). The (a)-examples are equally acceptable: the agent and the theme can occur in either order. The (b)-examples are also both acceptable, although due to the length of the PP-themes, the order in (513b') seems to be preferred. The examples in (513) show again that there is no reason to assume that under neutral circumstances the theme should be closer to the head than the agent.

It is possible to turn all three arguments into postnominal van-PPs, although in most cases the result will be awkward as well as confusing, since such constructions are almost inevitably (and often multiply) ambiguous. It seems that the acceptability of the construction correlates with the degree of definiteness. Example (514a) with the indefinite article eena is rather awkward, which may be due to the fact that the addition of the three PPs makes it rather implausible that the denotation of the modified noun is a non-singleton set: the example may imply that there is yet another painting of the Westertoren painted by Rembrandt and owned by my brother. Example (514b) is marked compared to the (a)-examples in (513), but acceptable. Example (514c) is perfectly acceptable, although it has a somewhat special meaning: the determiner dat has no demonstrative meaning, but is used to introduce an entity into the discourse that is presented as familiar to the hearer; cf. Section 19.2.3.2, sub IIB, for discussion.

As mentioned above, the use of more than one van-PP can lead to all kinds of ambiguities. In (514), for example, the PP van Rembrandt could in principle also be construed as the possessor of the Westertoren: it is only our knowledge of the world that prevents this interpretation. But this could also go the other way: although (515) could be interpreted as a painting by Rembrandt or an apprentice, our knowledge of the world will rather force a reading according to which the painting was done by a pupil of Rembrandt, i.e. a reading in which van Rembrandt modifies leerling.

Another confusing example is given in (516a). Although it is clear that Vermeer is the painter, it is not the case that Vermeer functions as the agent of the picture noun schilderij. This is due to the fact that the painting is known as “Het melkmeisje van Vermeer” and therefore we are dealing with a single postnominal constituent that functions as the theme of the picture noun schilderijpainting. This explains why the order in (516a') is unacceptable. If the PP van het melkmeisje van Vermeer does indeed function as the theme of the noun, we can expect that it is possible to add another van-PP expressing the agent, e.g. a forger. The (b)-examples show that this expectation is borne out.

Non-derived story nouns like boekbook and filmfilm can readily be used without argument regardless of whether the noun phrase they head refers to the physical object or to its abstract content. As with picture nouns, the agent argument in (517) could also be interpreted as the possessor of the object referred to by the noun phrase. The salience of this ambiguity seems to depend on the interpretation of the story noun in question: it is more likely to arise in (517a), where the noun phrase refers to the physical object, than in (517b), where the abstract content is relevant.

Noun phrases headed by deverbal story nouns like toespraakspeech or lezinglecture usually refer to abstract content and require the presence of at least one argument, which can be either the agent or the theme. Thus, while in (517) the non-derived noun boekbook can be used without a complement, example (518a) would be considered odd without the presence of a complement; however, once the agent is mentioned, all sentences are acceptable.

The (b)-examples in (518) show that the agent can be expressed either as a postnominal van-PP or as a prenominal genitive noun phrase or possessive pronoun. Although story nouns and picture nouns behave alike in this respect, they differ crucially with respect to the form of the postnominal theme: whereas this argument appears as a van-PP with picture nouns, it always takes the form of a PP introduced by over with story nouns. The examples in (519) show that, as a result, the ambiguity between an agent and a theme reading, which often arises with picture nouns, never occurs with story nouns.

When a story noun is accompanied by two arguments, the agent may appear either postnominally as a van-PP or prenominally as a genitive noun phrase. In both cases the theme argument takes the form of a postnominal over-PP.

In postnominal position, the order of the agent and the theme is relatively fixed: whereas the order agent-theme in the primeless examples in (521) is perfectly acceptable, the reversed order in the primed examples is highly marked (and more or less forces an appositive reading of the PP van Chomsky).

The genitive noun phrase in (520) and the postnominal van-PP in (521) are again ambiguous between an agentive and a possessive reading. Whether the resulting ambiguity is salient depends on the interpretation of the story noun in question: given that the contexts in (520) and (521) favor an abstract reading of the story nouns, the most salient reading is the one with Chomsky/Spielberg as the agent. Out of context, however, examples such as (522a) do exhibit this ambiguity. If we restrict ourselves to the possessive reading, it can be observed that the preferred realization is that as a genitive noun phrase or possessive pronoun: (522b) shows that the realization of the possessor as a postnominal van-PP is degraded and only occurs in a natural way with determiners such as diethose in examples like (522b) with the somewhat special function of introducing some entity into the discourse that is presented as familiar to the hearer; cf. Section 19.2.3.2, sub IIB, for discussion.

In (523) we see that the agent argument can also be expressed simultaneously with a possessor: the possessor is usually expressed by a genitive noun phrase or a possessive pronoun, while expressing the agent in this way leads to a severely degraded result. Expressing both the agent and the possessor as postnominal van-PPs, as in the (b)-examples, is only possible with determiners like die under the somewhat special interpretation discussed above. It seems that placing the possessor adjacent to the noun is preferred in neutral contexts.

Since the agent cannot be expressed by a genitive noun phrase or possessive pronoun when a possessor is present, and since the agent preferably precedes the theme, there are only a limited number of ways in which we can express the agent, theme, and possessor simultaneously. Example (524a) gives the order that arises with a prenominal possessor: inverting the two postnominal PPs leads to a highly marked result (and induces an appositive reading of the PP van Chomsky).

If all three arguments occur postnominally, the result is regularly degraded in all word orders; example (525a) may be marginally acceptable, but seems to require that the possessor be interpreted as an apposition. If the determiner is diethose, (525b) seems acceptable in the given order on the somewhat special interpretation discussed in the previous subsection. Placing the possessive or agentive van-PP in the rightmost position seems marginally possible, but only on an appositive reading.