Agreement, disagreement and the NP vs. DP debate

Of special relevance for the NP vs. DP debate are nominals in which the determiner has other values for number, gender, case and/or person than the noun, for depending on whether such nominals share these values with the noun or with the determiner they provide evidence in favor of either the NP or the DP approach. This paper discusses some nominals of this kind and shows that they share the relevant feature values with the noun. It then develops an NP analysis for these nominals which is cast in the notation of Head-driven Phrase Structure Grammar. It also shows what a DP analysis would look like. A comparison reveals that the NP analyses are less complex, more uniform and less stipulative. Examples are taken from Dutch, English, German, French, Italian, Spanish, Polish and Serbo-Croatian.


Introduction
Using the term in a theory-neutral sense, we assume that the bracketed strings in (1) are all nominals. (1) [the [blue [box]]] is empty For the analysis of nominals there are -broadly speaking-two approaches in generative grammar. One treats the noun as the head all the way through. In that analysis the largest bracketed string in (1) is an NP. The other makes a distinction between a nominal core, consisting of the noun with its complements and modifiers, if any, and a functional outer layer, comprising determiners, quantifiers and numerals. In that analysis the noun is the head of blue box, but the determiner is the head of the blue box, so that the category of the latter is DP. The NP approach prevailed in generative grammar up to and including the Government and Binding model (Chomsky, 1981). It was also adopted in Generalized Phrase Structure Grammar (Gazdar et al., 1985) and has been the dominant approach in Head-driven Phrase Structure Grammar (Pollard & Sag, 1994) till the present day. The DP approach results from an extension of the X-bar principles to the functional categories. Initially intended for the lexical categories N, V and A (Chomsky, 1970), and extended to P in Jackendoff (1977), they got applied to Infl and Comp in the early eighties, and to Det in the mid eighties, see Hellan (1986); Abney (1987); Szabolsci (1987). This style of analysis was taken on board in other frameworks, including Word Grammar (Hudson, 1990) and Lexical-Functional Grammar (Bresnan, 2001).
The choice for one or the other approach mainly depends on which framework one adopts, and the arguments pro and con are often based on theory-internal considerations. It is therefore a welcome initiative of the editors of this volume on New horizons in the These determiners are in complementary distribution with the articles: They cannot be preceded by one, as in *de wat/veel/meer/genoeg soep 'the some/much/more/enough soup', nor can they be added to a nominal that is introduced by an article, as in *wat/veel/ meer/genoeg de soep 'some/much/more/enough the soup'. 2 When the bracketed phrases in (2) are used as subjects, the finite verb must be singular if the nominal contains a singular mass noun, and plural if it contains a bare plural.
(3) a. Er is/*zijn nog [wat/veel/meer/genoeg soep] in de pot. there is/*are still [some/much/more/enough soup.sg] in the pot 'There is still some/much/more/enough soup in the pot.' b. Er zijn/*is nog [wat/veel/meer/genoeg aardappelen] in de pot. there are/*is still [some/many/enough potato.pl] in the pot 'There are still some/many/more/enough potatoes in the pot.' The agreement facts are the same if the determiner is omitted.
(4) a. Er is/*zijn nog soep in de pot. there is/*are still soup.sg in the pot 'There is still soup in the pot.' b. Er zijn/*is nog aardappelen in de pot. there are/*is still potato.pl in the pot 'There are still potatoes in the pot.' By contrast, if the noun is omitted, the finite verb must be singular, as shown in (5).
Er is/*zijn nog wat/veel/meer/genoeg in de pot. there is/*are still some/much/more/enough in the pot 'There is still some/much/more/enough in the pot.' This suggests that the determiners are singular. Confirming evidence is provided by (6), where the subject precedes the finite verb.

(6)
Veel hangt/*hangen af van hoe er morgen gestemd wordt. much depends/*depend of how there tomorrow voted is 'Much depends on how people will vote tomorrow.' An anonymous reviewer points out that the addition of the quantitative er in (7) triggers the use of a plural form for the verb.
Er zijn/*is er nog wat/veel/meer/genoeg in de pot. there are/*is r still some/many/more/enough in the pot 'There are still some/many/more/enough in the pot.' This, (s)he adds, suggests that the determiner is unspecified for number, rather than singular. The problem with that proposal, though, is that it does not account for the illformedness of the starred combinations in (5) and (6): If the determiner is unspecified for number, it is expected to be compatible with a plural verb. Moreover, the subject in (7) is not a nominal from which the noun is omitted, as in (5), but a nominal from which the noun is extracted, as made explicit in (8).
(8) Er zijn/*is er i nog [wat/veel/meer/genoeg n i ] in de pot. there are/*is r i still [some/many/more/enough n i ] in the pot 'There are still some/many/more/enough in the pot.' Such nominals have other properties than those in (5) and (6), as will be demonstrated in more detail in Section 4.3.2.
Taking stock, the quantifying determiners wat, veel, meer and genoeg are singular, but are compatible with both singular and plural nouns. When combined, the number value of the combination equals that of the noun. This suggests that an analysis along the lines of the NP approach might be more plausible than one which adopts the DP approach.

Nominals with a genitive determiner
Genitive nominals in Dutch typically take the form of a case marked noun preceded by a determiner which shows case, number and gender agreement with it. In 's avonds 'the.gen evening.gen', for instance, the noun has the genitive affix -s and the determiner, which is a reduced variant of des 'the.gen', shows agreement with it: In this case both are genitive, singular and masculine. 3 Such genitives are mainly used as VP adjuncts and postnominal dependents, but they also turn up in prenominal position, as in (9) In this position they are in complementary distribution with the determiners: They cannot be preceded by one, as in *de 's lands grootste kruidenier, nor can they be added to a nominal that is introduced by an article, as in *'s lands de grootste kruidenier. What is interesting now in this context is that the largest bracketed phrases in (9) are not genitive: The one in (9a) is accusative and the one in (9b) is nominative. Besides, the combinations share their number and gender values with the rightmost noun. The one in (9a), for instance, is not neuter like lands 'land.gen', but masculine like kruidenier 'grocer', and the one in (9b) is not singular like werelds 'world.gen', but plural like bergen 'mountains', as confirmed by the agreement with the verb.
In sum, the case, number and gender values of the bracketed NPs in (9) are not shared with the genitive prenominal, but with the rightmost noun. This provides confirming evidence for the assumption that an analysis along the lines of the NP approach might be more straightforward than one which adopts the DP approach.

Two types of (dis)agreement
To pave the way for an analysis of the (dis)agreement data we make a distinction between morpho-syntactic agreement, also known as concord, and index agreement. This distinction was introduced in Head-Driven Phrase Structure Grammar (HPSG) in Pollard & Sag (1994) and further developed in Kathol (1999) and Wechsler & Zlatić (2003). 4 The latter uses the scheme in (10) to define the distinction.
(10) morphology ⇔ concord ⇔ index ⇔ semantics "We recognize two distinct grammaticalization 'portals', one each via semantics and morphology. These two sources of grammaticalization lead to two distinct bundles of agreement features for a given noun. The morphology-related agreement bundle will be called concord (which includes case, number and gender) and the semantics-related agreement bundle will be called index (which includes person, number and gender)." (Wechsler & Zlatić, 2003, 28) An example of concord is the number and gender agreement between the demonstrative and the noun in the Italian (11) An example of index agreement concerns the co-occurrence restrictions between an anaphoric pronoun and its antecedent, as in (13).
The reflexive pronoun and its antecedent refer to the same entity and must share their person, number and gender, in this case 3rd person singular feminine. Case agreement is not required. In (13), for instance, she is nominative, while herself is accusative. The two types of agreement are distinct in the sense that concord includes case and not person, while index agreement includes person and not case, but there is also some overlap since both include number and gender. Notice, though, that the number and gender values which are relevant for concord are not always identical to those which are relevant for index agreement. To illustrate the relevance of the distinction for gender we take the Spanish example in (14), quoted from Corbett (1991, 225), and the Serbo-Croatian example in (15), quoted from Salzmann (2019).   (14) is morpho-syntactically feminine and the adnominal adjective must share this value: Replacing it with the masculine supremo would yield an ill-formed combination. At the same time, if Majestad denotes a male monarch, its index is masculine and it is this value that is shared with the predicative adjective contento 'pleased'. 6 Similar remarks apply to the noun vladike 'bishops' in (15). It is morpho-syntactically feminine and the adnominal adjective stare 'old' shares this value, but if the noun denotes male members of the clergy, the index of vladike is masculine and it is this value that is shared with the determiner ovi 'this' and the participle posetili 'visited'.
To illustrate the relevance of the distinction for number we use the French examples in (16), quoted from Kathol (1999, 248 The pronoun vous 'you' is morpho-syntactically plural and the finite verb must share that value: Replacing êtes with the singular es yields an ill-formed sentence. The number value that matters for index agreement, though, is underspecified. It is resolved to singular if the pronoun is used as a politeness form, as in (16a), and to plural if it denotes an aggregate of persons, as in (16b).
Applying the distinction between concord and index agreement to the [Det + Nom] combinations, we get four possibilities. The determiner and the noun may show both concord and index agreement (A), they may show index agreement but no concord (B), they may show concord but no index agreement (C), and they may show neither concord nor index agreement (D), see Table 1. For our purpose it is mainly the instances of B, C and D that matter. They will be given special attention in Section 4.3.

An NP treatment
Starting from the observation in Section 2 that an analysis along the lines of the NP approach seems more promising to deal with the disagreement data than one which adopts the DP approach, we develop an NP treatment in this section. It is cast in the framework of Head-Driven Phrase Structure Grammar. This implies that it is monostratal and surfaceoriented. It also implies that it conforms to the Lexical Integrity Hypothesis: Syntactic atoms are words, rather than -possibly silent-morphemes. Representations take the form of Attribute Value Matrices (AVMs). Their use inevitably renders the presentation some-6 The determiner su is underspecified for gender. what technical, but in order to keep it accessible we only use those bits of notation that are needed for the purpose at hand, and introduce them in a piece-meal and example-based manner. We start with the treatment of single nouns (Section 4.1), show how the addition of adnominal adjectives is modeled (Section 4.2), and then turn to the central issue of the paper, i.e. the combination of the resulting nominals with a determiner (Section 4.3).
For the sake of concreteness we adopt the functor treatment of adnominal dependents. This was first proposed in Van Eynde (1998) and Allegranza (1998) and further developed in Van Eynde (2006) and Allegranza (2006). It has also been taken on board in Sign-Based Construction Grammar (Sag, 2012).

Nouns
As an example let us take the Italian noun scatola 'box'. Its AVM is expected to contain such information as the fact that it is a common noun, that it is singular and feminine, that it requires a determiner to be saturated, and that it denotes entities which can truthfully be called boxes. Given that HPSG is a monostratal framework, phonetic, syntactic and semantic representations do not constitute separate levels of representation, but are integrated in one AVM. The one of scatola is given in (17) Inspired by the Saussurean definition of the sign as a unit of form and meaning (De Saussure, 1916), words are declared to have a phon attribute whose value is a sequence of phonemes, and a synsem attribute whose value is a bundle of syntactic and semantic features. The syntactic ones are modeled by the values of the cat(egory) attribute. They are of type category and are declared to have (amongst others) a head attribute and a marking attribute. The value of head is a type that stands for the part-of-speech, such as noun or verb: The subtypes may have additional attributes. Nouns, for instance, have an agr(eement) attribute whose value is a type that has case, number and gender attributes. 8 The inventories of these values are language specific. Latin, for instance, has six case values (nominative, vocative, genitive, dative, accusative, ablative), while German has four (nominative, genitive, dative, accusative). Similarly, Latin and German have three gender values (masculine, feminine, neuter), while French and Italian have two (masculine, feminine). The value of marking is a type that registers the degree of saturation. In the case of nominals the value is unmarked for those that do not contain a determiner, such as scatola 'box', and marked for those that contain a determiner, such as questa scatola 'this box'. It is also marked for those that are fully saturated by themselves, such as the pronoun she.
The semantic properties are modeled in terms of the content values. They come in a variety of subtypes, some of which are included in (19), which is an abbreviated version of Ginzburg & Sag (2000, 386).
In the case of nouns the relevant type is scope-object. It has an index attribute and a restr(ictions) attribute. The value of the former is of type index. It stands for a discourse referent and is comparable to a Predicate Logic variable, but in contrast to the latter it has person, number and gender attributes. For most nouns, the number and gender values in the index are identical to the number and gender values in the agr feature, as in (17), but there are exceptions, as will be shown in Section 4.3. The value of restr(ictions) is a set of facts. Facts are propositions that are presupposed to be true. Propositions consist of a state-of-affairs whose nucleus is a relation, in this case the relation box-rel. Relations have one or more arguments. In this case there is only one, and its value is identified with the index. The identification is made explicit by the boxed integer: The recurrence of 1 expresses the fact that the values of index and arg(ument) are identical. This is comparable to the recurrence of the Predicate Logic variable in {x | box(x)}, where x stands for any entity for which it is true that it is a box. A conspicuous property of the AVM in (17) is the amount of internal structure that it displays. The various attributes that it contains are not just listed, but organized in terms of a fine-grained hierarchy of types. head features, for instance, are distinct from marking features, and within the head feature the agr features are distinct from other head features. This is motivated by the fact that these distinctions facilitate the formulation of generalizations in the modelling of phrase formation and semantic composition, as will be shown in Section 4.2.

Nominal phrases
Continuing with the Italian example, let us add an adnominal adjective, as in scatola bianca 'white box'. The result is a phrase, and phrases are signs, just like words. This implies that they have phon and synsem attributes. Besides, they also have a daughters attribute. Its value is a list of signs, where the latter can be words or phrases. In this case the daughters are scatola 'box' and bianca 'white', as shown in (20). 9 (20) The phon value of the phrase is the concatenation of the phon values of the daughters. The order on the phon list reflects the surface order, with the adjective following the noun. English has the opposite order. Likewise, the category and content values of phrases are derived from the category and content values of the words which they contain. This is modeled in terms of constraints on phrase formation and semantic composition.

Phrase formation
Phrase formation is modeled in terms of cross-categorial constraints on phrase types. These types are organized in a hierarchy, part of which is given in (21).
The basic distinction is that between headed and non-headed phrases. The former have an extra attribute, called head-daughter, whose value is a sign, i.e. a word or a phrase. 10 A general constraint on headed phrases is that they share the head value of their head daughter. This is known as the Head Feature Principle. (22) concerns the whole of the head value it not only requires the sharing of the part of speech value, but also of all attributes that are declared for it. In the case of scatola bianca 'white box', for instance, the phrase not only shares its nominal nature with scatola, but also its agr value and, hence, its number, case and gender.
Within the class of headed phrases a further distinction is made between those in which the head daughter selects its dependent(s) (head-argument-phrase) and those in which it does not (head-nonargument-phrase). A subtype of the former is head-complement-phrase. It models the combination of a head with its complement, as in eat mushrooms, where the verb selects an NP complement, and wait for me, where the verb selects a PP complement. Another subtype of head-argument-phrase is head-subject-phrase. More relevant in the present context is the head-nonargument-phrase type. It subsumes amongst others the combination of a head with a modifier, as in white box and run quickly. The distinction between the two types of headed phrases is relevant for the constraints which model the sharing of the marking value, as spelled out in the Marking Principle.
What this says is that a head-argument-phrase shares its marking value with the head daughter, while a head-nonargument-phrase shares it with the non-head daughter. The latter makes it possible for a modifier to leave a mark on the resulting phrase. A subtype of headnonargument-phrase is head-functor-phrase. The defining characteristic of that phrase type is that the non-head daughter selects its head sister. The adjective in scatola bianca 'white box', for instance, selects an unmarked nominal as its head and requires it to be singular and feminine. To model this we add an attribute, called select, to the objects of type part-of speech, and require its value to be identical to the synsem value of the head daughter, as in (25).
Another subtype of head-nonargument-phrase is head-independent-phrase. In that combination neither daughter selects the other. An illustration of the functor treatment is the analysis of scatola bianca 'white box' in (26). 11 [HEAD 1 noun , MARKING 2 unmarked] The noun is treated as the head and the adjective as a functor. Technically, the nominal shares its head value with the noun ( 1 ) because of the Head Feature Principle and its marking value with the adjective ( 2 ) because of Marking Principle. Besides, the adjective selects an unmarked nominal ( 3 ) and shares its marking value with that of the noun ( 2 ). Since the resulting phrase is unmarked, it is compatible with another adnominal adjective, as in scatola bianca pesante 'heavy white box'. For languages in which adnominal adjectives show concord with the noun, such as Italian, adjectives are declared to have the agr attribute, just like nouns, and are required to share the value of that attribute with the selected noun, as in (27).
Since the select attribute is part of the head value, its value is shared with the AP if the adjective has dependents of its own. The select value of the AP in scatola molto pesante 'very heavy box', for instance, is identical to that of pesante 'heavy'.

Semantic composition
Semantically, scatola bianca 'white box' is an instance of intersective modification. It denotes entities for which it is true that they are a box and that they are white. In Predicate Logic this is represented by a formula in which both predicates apply to the same variable, as in {x | box(x) & white(x)}. In AVM notation it is represented as a scope-object in which the index is shared with both daughters and in which the restr value is the union of their respective restr values, as spelled out in (28). 12 The sharing of the index between the phrase and the noun is captured in terms of a general constraint on headed phrases, known as the Semantic Inheritance Principle: Notice that this sharing includes the values of the attributes that are declared for the indices, i.e. person, number and gender. If the index is also shared with the non-head daughter, as in scatola bianca, there is index agreement between the daughters.

Determiners
Continuing with the Italian example, let us add a determiner, as in questa scatola bianca 'this white box'. This is the point where the NP and DP approaches diverge. Adopting the former and leaving the latter for discussion in Section 5, the functor treatment analyses the determiner as a functor that selects an unmarked nominal, but that is marked itself. Given the Marking Principle, it shares this value with the phrase, as shown in (30).
[HEAD 1 noun , MARKING 2 marked] The resulting combination is, hence, incompatible with a functor that selects an unmarked nominal, as in * pesante questa scatola bianca 'heavy this white box' and *la questa scatola bianca 'the this white box'. 13 In this example the determiner shows concord with the nominal, just like the adjective. Moreover, it also shares the index of the nominal, since it does not introduce another discourse referent than the one that is introduced by the noun. In terms of the distinctions that were made in Section 3, this determiner shows both concord and index agreement with the noun. It is an instance of type A. For our purpose, though, the interesting combinations are those in which the determiner does not show agreement with the noun. These are the topic of the rest of this section. We first discuss determiners which do not show index agreement -but possibly concord-with the noun (Section 4.3.1) and then determiners which show index agreement but no concord with the noun (Section 4.3.2). The former are instances of types C and D, the latter of type B.

No index agreement
In contrast to articles and demonstrative determiners, possessive determiners do not share the index of the nominal which they select. In my brothers, for instance, the index of my is first person, singular and underspecified for gender, while the one of the noun is third person, plural and masculine. The determiner, hence, introduces another discourse referent than the one that is introduced by the noun. This is made explicit in its synsem value (31).
There are languages in which a noun can have both a demonstrative and a definite article, such as Modern Greek and Hungarian. In such languages the demonstratives have a marking value of type unmarked. There is nothing anomalous about the fact that a word can have another marking value than its equivalents in other languages, since category values and their attributes, including marking, are prone to crosslinguistic variation. Notice, for instance, the different number values of the German Brille and the English glasses, and the different gender values of the German die Sonne 'the sun' and the Italian il sole 'the sun'. What this says is that the determiner selects a nominal whose index i is related to -but different from-its own index j. The relation is one of possession, in a broad sense of the term. Given the Semantic Inheritance Principle, it is the index of the noun that is shared with the phrase. This accounts for the fact that the anaphoric pronoun in (32) must be third person plural rather than first person singular.
(32) [My j brothers i ] i have hurt themselves i /*myself i .
The lack of index agreement does not imply a lack of concord, though. The Italian possessive nostro 'our', for instance, shows the same number and gender agreement with the noun as adnominal adjectives. It is, hence, of type D, showing neither concord nor index agreement. In this case the difference coincides with a part of speech distinction. While loro is a pronoun, the other possessives are adjectives. Confirming evidence is provided by the fact that loro is also used as a personal pronoun, meaning 'them', whereas the other possessive determiners are not used in that way, as shown by the contrast in (35).

(36)
Luigi ha dato dei fiori a noi/me/te/voi/lui/lei Luigi has given flowers to us/me/you.sg/you.pl/him/her 'Luigi gave flowers to us/me/you/him/her.' Interestingly, the assumption that determiners can be adjectives or pronouns would be an anomaly in an analysis that treats D as a separate part of speech, but in the present treatment no such anomaly arises, since the class of determiners is not defined in part of speech terms, but in terms of their select and marking values. More specifically, they are marked selectors of an unmarked nominal, and this suffices to differentiate them from unmarked adnominal adjectives, such as bianca 'white'. 14 Another [Det + Nom] combination in which the determiner shows neither concord nor index agreement concerns the Dutch genitive NPs in (9), repeated in (37) These genitives have the same kind of relation with the noun as the possessive determiners, and are in complementary distribution with them: *zijn 's lands grootste kruidenier and *'s lands zijn grootste kruidenier. Their structure is more complex, though, since they do not consist of a single word, but of a common noun preceded by the article 's. To model this we adopt a left branching structure, as in (38) The top node shares its head value with the rightmost nominal (1) and its mark(ing) value with the genitive NP ( 2 ). The latter shares its head value and hence its sel(ect) value ( 3 ) with the noun lands 'country.gen' and its marking value with the article ( 2 ). Moreover, the article selects an unmarked nominal ( 4 ). Both combinations are instances of the type head-functor-phrase, but in terms of agreement, they are at opposite ends of the spectre: While the article shows both concord and index agreement with the genitive noun (type A), the prenominal genitive NP shows neither concord nor index agreement with its nominal sister (type D).

Index agreement without concord
An instance of index agreement without concord (type B) is provided by the Serbo-Croatian (15), repeated in (39). While the agr|gender value of vladike 'bishops' is unambiguously feminine, its index|gender value is underspecified: It can be masculine or feminine, depending on whether it refers to a male or female bishop (whether the latter is at all possible is a matter of religion, not of language). This is made explicit in (40).
The adjective stare 'old' shows concord with the noun, while the demonstrative ovi 'these' shows index agreement. Since its index is masculine, its addition resolves the underspecified index|gender value of the noun, and since the noun is the head of the NP, the latter's agr|gender value is feminine while its index|gender value is masculine. As a consequence, since predicative adjectives and participles show index agreement with the subject (Van Eynde, 2015, 184), the choice of a masculine form for the participle is accounted for. Similar remarks apply to the Spanish (14), repeated in (41).
(41) Su Majestad suprema está contento. his majesty supreme.sg.f is pleased.sg.m 'His supreme Majesty is pleased.' Also here, the noun's agr|gender value is unambiguously feminine, while its index|gender value is underspecified, and also here the adjective suprema 'supreme' shows concord, while the predicative adjective shows index agreement, resolving the noun's underspecified index|gender value to masculine. 15 Another instance of determiners that show index agreement but no concord are the Dutch quantifying determiners in (2), repeated in (42) When used adnominally, they share the index of the nominal they select: The discourse referent of wat soep 'some soup', for instance, is not another one than that of soep 'soup'. This implies that they show index agreement. They do not show concord, though, for while they are singular themselves, they do not require their nominal sister to be singular. Their select value, hence, contains a condition on the index of the nominal, but not on its agr value, as in (43).
When combined with a singular noun, as in wat soep 'some soup', the index|number value of the determiner is resolved to singular, so that its agr|number and index|number values match. When combined with a plural noun, as in wat aardappelen 'some potatoes', the index|number value of the determiner is resolved to plural, so that there is a discrepancy between its agr|number and its index|number value. However, since the nominal is the head daughter, the Head Feature Principle ensures that the resulting combination is morpho-syntactically plural, and the Semantic Inheritance Principle ensures that its index is plural too. This accounts for the fact that the finite verb in (44) is plural.
Er zijn/*is nog [wat/veel/meer/genoeg aardappelen] in de pot. there are/*is still [some/many/more/enough potato.pl] in the pot 'There are still some/many/more/enough potatoes in the pot.' For the sake of concreteness, let us inspect the representation of (44) in (45).
The index is shared between the determiner, the noun and the resulting NP (i), but the head value, which includes agr and, hence, the morpho-syntactic number, is only shared between the noun and the NP ( 1 ). The determiner selects an unmarked nominal whose index it shares ( 3 ), but does not require that nominal to share its own agr value. When combined with an extracted nominal, as in (8), repeated in (46), the bracketed string is unambiguously plural.
(46) Er zijn/*is er i nog [wat/veel/meer/genoeg n i ] in de pot. there are/*is r i still [some/many/more/enough n i ] in the pot 'There are still some/many/more/enough in the pot.' To model this we employ a distinction, introduced in Ginzburg & Sag (2000, 40), between canonical and non-canonical synsems. Typical of the latter is that they are not overtly realized: They are not paired with a phon value. They can be used, though, as values of attributes which model selection, and may contain constraints on any of their syntactic or semantic properties. In this case, the quantifying determiners require their nominal sister to be plural if it is of type non-canonical-synsem, as specified in (47). 16 The fact that these determiners require their extracted head to be plural accounts for the incompatibility with the singular form of the verb, as shown in (46).
When the quantifying determiners are used nominally, they do not select a nominal, so that their index|number value remains underspecified. Their agr|number value, though, is unambiguously singular, and this accounts for the agreement with the finite verb in (5) and (6), repeated in (48).
(48) a. Er is/*zijn nog wat/veel/meer/genoeg in de pot. there is/*are still some/much/more/enough in the pot 'There is still some/much/more/enough in the pot.' b. Veel hangt/*hangen af van hoe er morgen gestemd wordt. much depends/*depend of how there tomorrow voted is 'Much depends on how people will vote tomorrow.' An interesting issue, raised independently by two of the reviewers, concerns the use of the quantifying determiners in partitive constructions, such as (49) The verb shows number agreement with the noun, but the latter is rather deeply embedded in the nominal, separated from the determiner by the preposition van 'of'. To model this we start from the observation that the combinations are also well-formed if the determiner is omitted. A peculiar property of the bracketed strings in these examples is that they have the distribution of an NP, rather than of a PP: They are not only used as subjects, as in (50), but also as complements of transitive verbs and prepositions, as in (51) This suggests that the head of the bracketed strings is not the preposition van 'of', but the nominal which follows it, respectively dat lekkere bier and die lekkere taartjes (Van Eynde, 2004, 42-47). Another peculiarity of these combinations is that van 'of' affects the definiteness of the NP: While dat lekkere bier is definite, the addition of van makes it indefinite. This is not only clear from its semantic interpretation, but also from its admissibility in the subject position of existential clauses, as in (50). To account for these peculiarities we assume that van 'of' is not the complement selecting head of a PP in these examples, but rather a functor which selects a marked NP as its head sister and whose own marking value is of type unmarked, as in (52). 17 The net result is that the phrases which are introduced by this van are unmarked nominals whose head and index values are shared with the noun. Such nominals can be combined with a quantifying determiner without further ado: Nothing need be changed or added to the AVMs of the determiners to model their combination with a partitive van-phrase and to account for the agreement facts in (49).

Summing up
This section has presented an NP analysis of nominals, with special attention for combinations in which the determiner shows (partial) disagreement with the noun. It may be worth stressing that the functor treatment, on which it builds, has not been developed specifically to deal with disagreement data. Instead, it has been used to deal with a broad range of phenomena that are relevant for the analysis of nominals, including nominals with idiosyncratic properties. The Big Mess Construction, for instance, as exemplified by that long a bridge, is analyzed along the lines of the functor treatment in Van Eynde (2007), Kim & Sells (2011), Kay & Sag (2012) and Van Eynde (2018). The same is done for the Binominal Noun Phrase Construction, exemplified by her nitwit of a husband, in Kim & Sells (2014) and Van Eynde (2018), for the sort/kind/type of Construction, exemplified by those kind of problems, in Maekawa (2015), for the interaction of determiners with numerals and predeterminers in Italian nominals in Allegranza (2006), and for the Dutch wat voor Construction, as exemplified by wat voor een man is dat? 'what kind of man is that?', in Van Eynde (2004, 47-50). The latter also explores the application of the functor treatment to complementizers, modeling them as words which select an unmarked verbal projection and which share their marking value with the combination.

Comparison with the DP treatment
Having developed an NP treatment for the instances of disagreement that were presented in Section 2, we now turn to the issue of how they are dealt with in the DP treatment. For the quantifying wat 'some' there is a proposal in Barbiers et al. (2010, 6-9). It involves the use of an empty quantifier which takes a nominal as its complement, and wat as its specifier, as in (53). The reason that is given for treating wat as the specifier of Q, rather than as Q itself, is that it can be used as the specifier of an overt quantifier, as in (54).

(54)
Ik heb wat veel boeken gelezen. I have some many books read 'I have read quite a bit too many books.' Barbiers et al. (2010) does not address the issue of how the number value of the higher QP in (53) is determined, but an anonymous reviewer points out that Q can be made to share the number value of its NP complement. On that analysis the number value of wat itself does not matter. It matters, though, when there is no NP complement, as in (5), repeated in (55).
(55) Er is/*zijn nog wat in de pot. there is/*are still some in the pot 'There is still some in the pot.' To deal with this the authors "assume a privative system with the features [plural], [non-neuter] and [definite]. For an item to bear no specification for these features means that this item is not endowed with the relative features." (Barbiers et al., 2010, 7-8) Wat is claimed to lack all three of them, and in order to account for the illformedness of the starred combination in (55) the authors add: "If wat is not combined with anything and appears on its own, it is interpreted by default rules: singular in the absence of [plural]." (Barbiers et al., 2010, 8) Given the structure in (53) this implies that the higher QP shares the number value of the lower QP, and (by projection) of the empty Q.
For the prenominal genitive, as in 's lands hoogste bergen 'the.gen country.gen highest mountains', an anonymous reviewer suggests to treat it along the same lines as the English Saxon genitive in the country's highest mountains. To model the latter Adger(2003: 256-258) employs an empty D that takes an NP as its complement and a DP as its specifier. When applied to the Dutch genitive, this yields the structure in (56). The reason that is given for treating the genitive as a specifier of D, rather than as D itself, is that heads are required to be X 0 rather than XP. Another reason is that the position of D may be filled, as in (57), where every takes the D position.

(57)
The Emperor's every wish was immediately carried out.
The issue of how the case and number values of the higher DP are identified is not addressed in Adger (2003), but an anonymous reviewer suggests that D "possibly inherits agreement properties from the noun (via feature sharing)." Having shown how the DP approach can be made to deal with the [Det + Nom] combinations that were discussed in Section 2, it is time now for a comparison with the NP approach. This reveals various differences. One concerns the structures themselves. The NP analyses do not employ empty Ds or Qs, and treat the unmarked nominal (which corresponds to the NP in (53) and (56)) as a daughter -rather than as a granddaughter-of the top node.
Another difference concerns the feature sharing. In the NP analyses the sharing of the agr values between the nominal and the top node follows from the Head Feature Principle and the sharing of the indices follows from the Semantic Inheritance Principle, both of which are independently motivated. In the DP analyses the relevant features are first shared between the empty D (or Q) and its NP complement, and then projected to DP (or QP). This sharing is not only more complex, it also lacks independent motivation, since heads normally do not share the case, number and gender of their NP complement. The verb in eats potatoes, for instance, does not share the number value of its NP complement, and the noun in the German die Vernichtung des Abendlandes 'the annihilation the.gen evening. country.gen' does not share the case of its genitive NP complement, nor its gender.
A third difference concerns the definition of syntactic categories. In the NP analyses categories are decomposed and represented as Attribute Value Matrices. Part of speech is one of the relevant attributes, but the select and marking values are relevant as well, and provide the possibility to differentiate categories in other terms than part of speech distinctions. Determiners, for instance, are defined as marked selectors of an unmarked nominal, and not as members of a separate part of speech. This not only facilitates the capturing of finer-grained distinctions, as that between adjectival and pronominal determiners, it also provides the means to generalize where appropriate. Nominal phrases, for instance, are uniformly treated as NPs, rather than as a disjunction of DP and QP.
In sum, while the DP approach can be made to fit the facts, the NP approach does so in a way that is simpler (no empty Ds or Qs), less stipulative (no sharing of feature values between head and complement), and more uniform (no disjunctive statement for referring to nominal phrases).

Conclusion
An interesting case for the NP vs. DP debate is the treatment of [Det + Nom] combinations in which the determiner does not show agreement with the noun. We have identified a number of such combinations and demonstrated that they share their case, number, gender and/or person values with the noun (Section 2). Paving the way for an analysis we have made a distinction between morpho-syntactic agreement, also known as concord, and index agreement. In terms of that distinction we have differentiated four types of [Det + Nom] combinations, depending on whether or not they show concord and whether or not they show index agreement (Section 3). In a next step, we have developed an NP analysis of the [Det + Nom] combinations. It is cast in the notation of Head-driven Phrase Structure Grammar and adopts the functor treatment of adnominal dependents, as proposed in amongst others Van Eynde (2006) and Allegranza (2006). Special attention was paid to combinations which show (partial) disagreement (Section 4). In a last step we have shown how these combinations are dealt with in the DP approach. A comparison Van Eynde: Agreement, disagreement and the NP vs. DP debate Art. 65, page 21 of 23 with the analyses in the NP approach shows that the latter are simpler, less stipulative and more uniform (Section 5).