Section 5.2.2.1 has shown that the possessive pronouns are in complementary distribution with the articles, and we have used this fact to motivate the claim that possessive pronouns function as determiners of the noun phrase. Another reason to adopt this claim is that possessive pronouns also have certain semantic properties in common with the articles. This is clearest with the referential possessive pronouns, which have more or less the same meaning contribution as the definite articles. Consider Figure 1, in which A represents the set of entities denoted by the subject NP and B represents the set of entities denoted by the verb phrase, where A and B are both contextually determined, that is, dependent on the domain of discourse (domain D). The intersection A ∩ B denotes the set of entities for which the proposition expressed by the clause is claimed to be true.

Section 5.1.1.1 has argued that the core meaning of the definite article is that all entities in domain D that satisfy the description of the subject NP are included in the intersection A ∩ B, that is, that the remainder of set A is empty; cf. (422a'). The referential possessive pronoun zijn'his' in (b) expresses a similar meaning but in addition introduces a partitioning of set A: the assertion is not about all entities that satisfy the description of the NP, but about a subset Asub of it that stands in a certain relation to the referent of the possessive pronoun. The fact that the possessive pronouns imply a partitioning of set A does not, of course, necessarily imply that set A is a non-singleton set. If domain D contains just a single book, the speaker can still use the noun phrase mijn boek'my book'; in this case the evoked alternative referent set is empty.

Note that the relationship in question need not be one of possession but can be of various sorts and is largely determined by the non-linguistic context; see Janssen (1976: Section 3.1) for relevant discussion. The referent of the possessive pronoun in (b) may the author or the publisher of the books but also someone who copy-edited them or made a guess about which books would sell well.
      It is not only the core meaning of the definite articles that is associated with the referential possessive pronouns; other properties of definite noun phrases can also be found with noun phrases containing a referential possessive pronoun. For example, both types of noun phrase normally refer to entities in domain D that are assumed to be uniquely identifiable by the speaker; in a question like (423a), it is presupposed that the listener is able to identify the referent of the noun phrase mijn sleutels. And, just as in the case of the definite article, noun phrases with a referential possessive pronoun may introduce new entities into domain D that are somehow anchored to some known entity in domain D. An example such as (423b) does not presuppose that the listener knows who Janʼs wife is, but that the mention of Jan is sufficient to anchor the referent of the noun phrase zijn vrouw'his wife' to someone related to him.

Noun phrases with a referential possessive pronoun, like definite noun phrases, also exhibit exceptions to the general requirement that the noun phrase be uniquely referring. For example, if the noun phrase refers to a body part, like a leg or a hand, the noun phrase may be singular, thus leaving some vagueness with respect to which of the (two) hands or legs is intended; cf. example (424a). Something similar occurs with kinship nouns; an example such as (424b) does not presuppose that the speaker has only one nephew — apparently, it is not the referent that matters here but the relationship between the speaker and the person referred to. A similar case involving a non-kinship noun is given in (424c), which expresses that the train the speaker took that day was delayed.

      Due to the overlap in meaning between referential possessive pronouns and definite articles, the noun phrases introduced by a possessive pronoun in the primeless examples of (425) are virtually synonymous with the noun phrases in the primed examples, with a definite article and a postnominal possessive van-PP. This suggests that, apart from its reference, the meaning of the referential possessive pronouns in the primeless examples consists of two parts that correspond to, respectively, the meaning of the definite article and the modifying van-phrase in the primed examples: the first part involves definiteness, and the second part involves the partitioning of the set denoted by the head noun into two subsets, namely a subset that is in the relevant semantic relation with the referent of the possessive pronoun and a subset that is not.

      Since referential possessive pronouns are inherently definite, possessed indefinite noun phrases normally involve the presence of an indefinite article and a postnominal possessive van -PP, as in (426). As always, the indefinite article expresses that the intersection A ∩ B has the cardinality 1, without any implication for the remainder of set A, that is, A - (A ∩ B) may or may not be empty.

For completeness’ sake, observe that the complement of the preposition van is a personal object pronoun, and not, as in English, a(n inflected) possessive pronoun like in a book of mine/yours/his/hers.
      Example (427a) shows that indefiniteness can also be inherited from the existentially quantified possessive pronoun iemands'someoneʼs'. That the complete noun phrase is indefinite is clear from the fact that the noun phrase iemands auto can occur in the expletive er-construction. The possessive pronoun in this example again introduces a partitioning of set A, but the speaker leaves open which subset of A is intended. The universally possessive pronoun also introduces a partitioning of set A, but now it is claimed that all subsets of A are subsets of B. As a result (427b) expresses more less the same thing as the simpler sentence De/Alle autoʼs staan verkeerd geparkeerd'The/All cars are wrongly parked', which perhaps accounts for the fact that (427b) feels somewhat marked.

      The reciprocal form elkaars'each otherʼs' and the interrogative and relative form wiens'whose' also introduce a partitioning of set A. In (428a), the cardinality of the antecedent of the possessive pronoun is equal to the cardinality of the partitioning of set A, and the members of the antecedent and the relevant subsets of set A are reciprocally related to each other: set A consists of three essays, each by a different pupil, and each of the pupils admires the essays written by the other pupils. In question (428b), it is assumed that the set of books is divided into subsets defined by, e.g., ownership, and the speakers asks, about a certain subset of books, to whom it belongs. In the relative construction in (428c), a certain partitioning is presupposed and used in order to enable the addressee to pick out the intended referent of the complete noun phrase.

The possessive pronouns owe their name to the fact that, in many cases, they refer to the possessor of the referent of the complete noun phrase; the noun phrase mijn boek'my book' typically refers to a book that is in the possession of the speaker. However, the term possessive pronoun (or possessive noun phrase more generally) is a misnomer since the kind of relation between the referent of the pronoun and the referent of the complete noun phrase is not always restricted to possession; the noun phrase mijn boek may also involve, e.g., a relation of authorship. In the following subsections we briefly discuss two systematic kinds of relation the referent of the possessive pronouns and the referent set of the complete noun phrase may enter into. The discussion in the following subsections does not aim at exhaustivity given that the creative powers of the language users far exceed our descriptive potential.