1 Introduction
This paper explores the interaction of regularity and idiosyncracy in the formation of nominals. For the sake of concreteness, it first focusses on a highly regular type of combination, as exemplified by red box, and then on two combinations that show some degree of idiosyncracy. The first is the Big Mess Construction (bmc), as exemplified in (1).
Special about this construction is the pre-determiner position of the adjectival phrase (ap). This differs from the canonical order, in which aps follow the determiner, as in a very good bargain, and is only possible – or required – if the nominal is introduced by the indefinite article, and if the ap is introduced by one of a small set of degree markers, including so, how, as and that.Footnote [2] Treatments of the bmc are provided, among others, in Bolinger (Reference Bolinger1972), Bresnan (Reference Bresnan1973), Berman (Reference Berman1974), Zwicky (Reference Zwicky1995), Ginzburg & Sag (Reference Ginzburg and Sag2000), Kennedy & Merchant (Reference Kennedy and Merchant2000), Van Eynde (Reference Van Eynde and Müller2007), Troseth (Reference Troseth2009), Kim & Sells (Reference Kim and Sells2011), Kay & Sag (Reference Kay, Sag, Boas and Sag2012) and Arnold & Sadler (Reference Arnold, Sadler, Butt and King2014).
The second is the Binominal Noun Phrase Construction (bnpc), as exemplified in (2).
Special about this construction is the relation between the nominals. In contrast to what we find in an ordinary [np–of–np] sequence, as in an employee of a Japanese company, where the first nominal is the head of the entire np, and where the second nominal is part of its modifier, the bnpc shows a pattern in which the relation between the nominals is a predicative one: her husband is claimed to be a nitwit, and the headache is claimed to be like a skullcracker. Such a paraphrase is nonsensical for an ordinary [np–of–np] sequence: in an employee of a Japanese company the company is not claimed to be (like) an employee. Treatments of the bnpc are provided, among others, in Napoli (Reference Napoli1989), Aarts (Reference Aarts1998), Bennis, Corver & Den Dikken (Reference Bennis, Corver and Den Dikken1998), Den Dikken (Reference Den Dikken, Alexiadou and Wilder1998), Foolen (Reference Foolen, Radden and Panther2004), Keizer (Reference Keizer2007) and Kim & Sells (Reference Kim and Sells2014).Footnote [3]
The bmc and the bnpc are of course not the only nominals with idiosyncratic properties, nor are they particularly similar in their idiosyncracies, but it is precisely the diversity that makes them a good test case for the more general purpose of investigating how the regular and the idiosyncratic interact in the formation of nominals. It would be less revealing to focus on only one or two very similar constructions. For the investigation, we adopt an approach that is close in spirit to one of the tenets of Construction Grammar, as formulated in Kay & Fillmore (Reference Kay and Fillmore1999).
To know what is idiomatic about a phrase one has to know what is nongeneral and to identify something as nongeneral one has to be able to identify the general …The picture that emerges from the consideration of special constructions …is of a grammar in which the particular and the general are knit together seamlessly.
To make this emerging picture sharp, we adopt the framework of constructivist Head-driven Phrase Structure Grammar (hpsg), as pioneered in Sag (Reference Sag1997) and developed more fully in Ginzburg & Sag (Reference Ginzburg and Sag2000). This is arguably the framework that has been most hospitable to ideas from Construction Grammar, providing them with formal underpinnings and an explicitly defined notation. Characteristic of constructivist hpsg is the idea that phrases are organized in terms of a hierarchy of types in which the lower (more specific) types are a blend of properties that are inherited from the higher (less specific) types, on the one hand, and of type-specific (inherent) properties, on the other hand. Ginzburg & Sag (Reference Ginzburg and Sag2000) provide a detailed application of this approach to a range of clausal types. This paper extends it to nominal types.
The paper starts with a presentation of constructivist hpsg in Section 2. It then provides an analysis of the regular nominals in Section 3, of the bmc in Section 4 and of the bnpc in Section 5. The conclusions are given in Section 6.
2 Basic notions of constructivist hpsg
In hpsg, the basic unit of linguistic analysis is the sign, understood in the Saussurean way as a unit of form (signifiant) and meaning (signifié). Employing the notation of typed feature structures, this is expressed in terms of a feature declaration.
The value of the form feature is a list of graphemes,Footnote [4] and the value of the synsem feature is an object of type synsem, which in turn is declared to have a feature for modeling syntactic properties, called category, and a feature for modeling semantic properties, called content.
Signs are organized in a hierarchy. The basic dichotomy is that between lexical signs and phrases.
Since types inherit the properties of their supertypes, the objects of type lexical-sign and phrase have a form and a synsem feature as well. Besides, phrases have a daughters feature, whose value is a list of signs.
The phrase Kim laughed, for instance, has two daughters, and since those daughters are objects of type sign, they each have a form and a synsem feature, as shown in (7).Footnote [5]
This feature structure makes explicit that the phrase Kim laughed is a clause that denotes a proposition, and that its daughters are a proper noun that denotes a scope-object and an intransitive verb that denotes a state-of-affairs.
To model the formation of phrases in general terms, hpsg does not employ rewrite rules and monadic categories, such as np and vp. Instead, it analyzes categories in terms of features and it models their combination in terms of cross-categorial constraints on phrase types. More specifically, syntactic categories are objects of type category, and these are declared to have a head feature, the valence features subject and comp(lement)s and a marking feature.
The value of the head feature is a part-of-speech label, such as verb or noun. The subject value spells out whether and – if so – what kind of subject the category selects, and the comps value does the same for the selection of complements. An intransitive verb, for instance, selects an np as its subject and does not select any complements. The role of the marking feature will be described in Section 3.1.
The combinatorics is modeled in terms of constraints on phrase types. They are organized in a hierarchy, of which (9) provides a first glimpse.
The phrases are partitioned into those that have a head daughter and those that do not. The former have an extra feature, called head-daughter, whose value is of type sign.Footnote [6]
A defining property of the headed phrases is that their part-of-speech is identified with the one of their head daughter. This is expressed in terms of the implicational constraint in (11).Footnote [7]
The boxed integer 
is a typed variable. Recurrence within the same representation expresses token-identity, in much the same way as the recurrence of a variable in a Predicate Logic formula. In this case, the part-of-speech is required to be the same for the mother and its head daughter. This captures the intuition that phrasal categories are projections of lexical categories.Footnote
[8]
Of the various types of headed phrases, there is one that models the combination of a head and its subject. It is defined in (12).
Phrases of this type have two daughters. The second one is the head daughter 
, and requires the other daughter to be an np 
.The subject value of the resulting phrase is the empty list, since that phrase does not require a subject anymore. Application to Kim laughed yields (13).Footnote
[9]
Being an object of type head-subject-phrase, the second daughter is identified as the head daughter 
, the first daughter’s synsem value is token-identical to the subject value of the head daughter 
and the subject value of the combination is the empty list. Moreover, since head-subject-phrase is a subtype of headed-phrase, it is subsumed by the Head Feature Principle, which implies that it shares its head value 
with the head daughter. For expository purposes, representations of phrasal signs are often converted into trees whose nodes are enriched with features, separated by commas, as in (14).
It is a style of notation that we will also use in this paper.
The analysis presented so far is typical of the strictly lexicalist approach of early hpsg, in which properties of phrases are mainly determined by properties of the constituent words and only to a small extent by properties of the combinatory operations as such. Pollard & Sag (Reference Pollard and Sag1994: 391), for instance, employ only seven types of combinatory operations, including the one for combining a head with its subject. Over time, though, the radical lexicalism gave way to an approach in which the properties of the combinatory operations play a larger role. The small inventory of highly abstract phrase types got replaced by a more fine-grained hierarchy in which the types contain more specific and – if need be – idiosyncratic constraints. This development was started by Sag (Reference Sag1997), was elaborated by Ginzburg & Sag (Reference Ginzburg and Sag2000), and gained momentum afterward, leading to what is now known as constructivist hpsg. Characteristic of this approach is the use of a bi-dimensional hierarchy of phrasal signs. In such a hierarchy, the phrases are not only partitioned in terms of headedness, but also in terms of a second dimension, called clausality, as in (15).
At the upper level, the clausality hierarchy differentiates clauses from non-clauses. Just like the types in the headedness hierarchy, they are associated with implicational constraints. Clauses, for instance, are required to denote an object of type message (Ginzburg & Sag Reference Ginzburg and Sag2000: 41).
At a more fine-grained level, the clauses are partitioned into declarative, interrogative, imperative and exclamative clauses, each with their own constraints. Interrogative clauses, for instance, denote a question, while indicative declarative clauses denote a proposition.Footnote [10]
Since the headedness and clausality dimensions are mutually independent, it is possible to define types whose properties are partly inherited from a type in the first dimension and partly from a type in the second dimension. This is called multiple inheritance. It is illustrated in (17).
The type declarative-head-subject-clause inherits the properties of head-subject-phrase, on the one hand, and declarative-clause, on the other hand. Besides, it may have properties of its own, such as the fact that its head daughter is a finite non-inverted verb (Ginzburg & Sag Reference Ginzburg and Sag2000: 43). It is this combination of type-specific implicational constraints and multiple inheritance that we will use to capture the subtle interaction of the regular and the idiosyncratic in the formation of nominal phrases.
3 Regular nominals
This section provides a bi-dimensional treatment of regular nominals. We first situate them in the headedness hierarchy (Section 3.1) and then in the clausality hierarchy (Section 3.2). For the former, we build on the functor treatment of the noun phrase, as pioneered in Van Eynde (Reference Van Eynde, Coppen, van Halteren and Teunissen1998) and Allegranza (Reference Allegranza, Balari and Dini1998) and further developed in Van Eynde (Reference Van Eynde2006) and Allegranza (Reference Allegranza2007).Footnote [11] For the latter, we are breaking new ground. The combination of the two dimensions is modeled in terms of multiple inheritance (Section 3.3).
3.1 A hierarchy of headed phrases
In a first step, we extend the hierarchy of headed phrases that was introduced in Section 2.
Phrases in which the head daughter selects its non-head sister(s) are subsumed by the head-argument-phrase type. It contrasts with the head-nonargument-phrase type which subsumes phrases in which the head daughter does not select its non-head sister(s). The properties of these intermediate types are spelled out in Section 3.1.1. The non-arguments are further partitioned into those that select their head sister (the functors) and those that do not (the independents). They are treated in Section 3.1.2.
3.1.1 Marking
In head-argument combinations, the degree of saturation of a phrase is registered by the valence features. The addition of a subject, for instance, triggers a change of the subject value, as spelled out in (12). In head-nonargument combinations, the values of the valence features remain unchanged. As a consequence, since the head value remains unchanged as well (because of the Head Feature Principle), non-arguments can be added ad libitum. In some cases, this is just what one wants, but there are also cases where one needs to impose constraints. A nominal, for instance, can be combined with any number of adjectives, but with at most one determiner. To model this, we use the marking feature. Its value is shared between mother and non-head daughter, as spelled out in (19).Footnote [12]
As such, it provides the means to differentiate the category value of the mother from that of the head daughter. The marking feature was introduced by Pollard & Sag (Reference Pollard and Sag1994: 45) to differentiate clauses with a complementizer (marked) from clauses without complementizer (unmarked). Its use was extended to the analysis of nominals by Van Eynde (Reference Van Eynde2006) and Allegranza (Reference Allegranza2007) to differentiate nominals with a determiner (marked) from nominals without determiner (unmarked). An illustration is provided in (20).
Bridges is an unmarked common noun and, since it is the head of the nominal projection, it shares its head value 
with the noun phrase.Footnote
[13]
The addition of the adjective does not change the marking value, since prenominal adjectives are unmarked too 
, but the addition of the determiner does, since determiners have the value marked 
. Nouns that do not take a determiner, such as the pronouns and most of the proper nouns, are inherently marked.
Since the marking value is shared between mother and non-head daughter, it can be used as a carrier for other syntactic information that a phrase shares with its non-head daughter. For the analysis of nominal projections, for instance, it is useful to capture the distinction between definite and indefinite nominals. To model this, we add a feature to the objects of type marking, called dtype.Footnote [14]
Unmarked common nouns are indefinite, but when they are combined with a determiner, the latter’s marking value is shared with the phrase, so that the nominal becomes definite if the determiner is definite. The distinctions that the dtype feature captures are not only relevant for modelling the external distribution of nps, such as admissibility in existential clauses, but also for modelling certain types of np-internal agreement, such as strong versus weak declension of prenominal adjectives in German and Dutch. Besides, it plays a role in our treatment of the bmc and the bnpc. For that purpose, we will need to make some finer-grained distinctions among the indefinites.
In head-argument phrases, the marking value is shared with the head daughter, just like the head value.
To motivate why the propagation of the marking value is different in head-argument combinations, we take a prenominal adjective with a complement. Since that combination is rare (if not impossible) in English, we choose a German example: mir unbekannte Frauen ‘women unknown to me’.
The nominal shares its head value with the noun Frauen 
and its marking value with the ap
mir unbekannte 
. The latter in turn shares its head value with the adjective 
, and since mir is an argument of the adjective, the ap also shares its marking value with the adjective 
, as required by (22). If we had not differentiated the head-argument from the head-nonargument phrases, the inherently marked pronoun mir would share its marking value with the ap and hence with the nominal, yielding a marked np, which is undesirable since it erroneously predicts that the nominal cannot be preceded by a determiner.
3.1.2 Functors and independents
Functors are nonarguments that lexically select their head sister. To model this, we use the feature select. It is assigned to objects of type part-of-speech, which implies that it forms part of the head values. Its value is of type synsem or none.Footnote [15]
The match of the selection requirements with the properties of the head sister is modeled in the constraint on head-functor phrases.Footnote [16]
The synsem value of the head daughter is identified with the select value of the non-head daughter 
.
In combination with the marking device, the select feature can be used to model co-occurrence restrictions. Determiners, for instance, can be said to select an unmarked nominal as their head sister, thus accounting for the well-formedness of the (long) bridges, as well as for the ill-formedness of *some the bridges and *the those bridges.Footnote [17] It can also be used to model agreement relations. The plural feminine forms of Italian adjectives, for instance, can be said to select a plural feminine nominal, thus accounting for the well-formedness of strade pericolose ‘dangerous streets’, as well as for the ill-formedness of *strada pericolose and *cani pericolose ‘dangerous dogs’, in which the plural feminine adjective is combined with respectively a singular feminine noun and a plural masculine noun.
The reason why the select feature is included in the head value of the non-head daughter is that the selection properties of a phrasal functor are shared with those of its head daughter: the Italian ap molto pericolose ‘very dangerous’, for instance, requires a plural feminine nominal, because pericolose requires a plural feminine nominal.
To illustrate the interaction between marking and selection, we take again the long bridges.
The adjective selects an unmarked nominal 
and shares its marking value 
with the mother, yielding the unmarked nominal long bridges. The determiner then selects an unmarked nominal 
and shares its marking value 
with the phrase, yielding the marked nominal those long bridges. Given the selection requirements of prenominal adjectives and determiners, the latter is not compatible with another adjective or determiner. This correctly blocks the formation of such ill-formed combinations as *wooden the (long) bridges and *our the (long) bridges.
Signs that do not select their head sister have the select value none. This value is assigned to the non-head daughter in head-complement phrases. The np complement of the verb in built a long bridge, for instance, does not select its head sister. Instead, it is the verb that selects the np. The latter’s select value is, hence, none, and given the Head Feature Principle, this value is shared with the noun bridge. The value none is also assigned to the non-head daughter in phrases of type head-independent, a subtype of head-nonargument-phrase.Footnote [18]
In this type of phrase, neither daughter lexically selects the other. It will play a role in our treatment of the bmc and the bnpc.
3.1.3 Summing up
Noun phrases are projections of nouns in which prenominal adjectives and determiners are functors: they lexically select their head sister, as spelled out in the constraint on head-functor phrases (25), and leave their mark on the combination, as spelled out in the constraint on head-nonargument phrases (19). More elaborate analyses along these lines with applications to other languages and with special attention to np-internal agreement are presented by Van Eynde (Reference Van Eynde2006) and Allegranza (Reference Allegranza2007). It should be added, though, that the present analysis differs from the earlier treatments in one important respect: we do not treat the selection and the marking as pertaining to the same phrase type, but separate them, associating the marking with all head-nonargument phrases and the selection with a subtype of them, i.e. the head-functor phrases. The relevance of this differentiation will become clear in Sections 4 and 5.
3.2 A hierarchy of non-clausal phrases
While the headedness types are defined in cross-categorial terms and mainly concern syntactic properties, the clausality types concern category-specific and semantic properties. Taking a cue from the treatment of clausal phrase types in Ginzburg & Sag (Reference Ginzburg and Sag2000), we develop a partial hierarchy for the nominal phrases. As a starting point, we take the hierarchy of semantic objects in (28), an abbreviated version of Ginzburg & Sag (Reference Ginzburg and Sag2000: 386).
Some of these types have already been mentioned in Section 2, such as message, proposition, state-of-affairs and scope-object. For our purpose, it is mainly the latter that matters, since it is the prototypical content value of a nominal. It consists of an index and a set of facts that impose restrictions on the index (Ginzburg & Sag Reference Ginzburg and Sag2000: 122).
The common noun box, for instance, denotes the set of those entities for which it is a fact that they are a box. The type is also relevant for the adjectives. Red, for instance, denotes the set of those entities for which it is a fact that they are red.
At a finer-grained level, Ginzburg & Sag (Reference Ginzburg and Sag2000: 135–136) differentiate between quantified and non-quantified scope-objects. The former are of type quant-rel. They include nps that are introduced by a quantifying determiner, such as every, each or some, and quantifying pronouns, such as everybody and someone. The nominals that lack quantificational force are of type parameter. They include bare nominals, proper nouns, various types of pronouns and nps that are introduced by a non-quantifying determiner. It is not always immediately clear whether a nominal is quantified or not. Ginzburg & Sag (Reference Ginzburg and Sag2000), for instance, devote a whole chapter to the issue of whether interrogative wh-phrases, such as who, what and which table, are quantified, concluding that they are not (Chapter 4). For our purpose, it is the nominal phrases that denote a parameter that matter. They are subsumed by a subtype of the non-clausal phrases, which we call nominal-parameter. Its properties are spelled out in (30).
The mother shares its index with the head daughter 
, and its restr(iction) value is the union of the restr values of the daughters (
$\unicode[STIX]{x1D6F4}_{\text{1}}$
and
$\unicode[STIX]{x1D6F4}_{\text{2}}$
). In the hierarchy of non-clausal phrases, the nominal parameters contrast among others with the quantified nominals. These have a content value of type quant-rel which is included in the value of the store feature (Ginzburg & Sag Reference Ginzburg and Sag2000:203–205).
A subtype of nominal-parameter is restrictive-modification, as defined in (31).
This constraint requires that the mother share its index with the non-head daughter as well. It captures the intuition that the noun and its non-head sister apply to the same entities. The nominal red box, for instance, denotes the set of entities that are a box and that are red. While most of the nominal parameters are instances of restrictive modification, there are some that have other properties. The Binominal np Construction, for instance, contains a nominal parameter whose daughters stand in a relation of predication rather than of modification. It will be presented in Section 5.1.1.
3.3 Multiple inheritance
Combining the (partial) hierarchy of headed phrases in Section 3.1 with the (partial) hierarchy of non-clausal phrases in Section 3.2, we can spell out the properties of regular nominals in terms of multiple inheritance. Combinations, such as red box, for instance, are subsumed by a type, henceforth called regular-nominal, that inherits the constraints of head-functor-phrase, on the one hand, and restrictive-modification, on the other hand.
Unifying the constraints that it inherits from its supertypes, we get the feature description in (33).
The phrase shares its head value with its head daughter 
because it is a headed phrase, and it shares its valence values with the head daughter 
and 
and its marking value with the non-head daughter 
because it is a head-nonargument phrase. The select value of the non-head daughter is identified with the synsem value of the head daughter 
because it is a head-functor phrase. Semantically, the phrase shares its index with its head daughter 
and collects the restrictions of both daughters (
$\unicode[STIX]{x1D6F4}_{1}$
and
$\unicode[STIX]{x1D6F4}_{2}$
) because it is a nominal parameter. Moreover, it also shares its index with its non-head daughter 
because it is an instance of restrictive modification. Regular nominals are, hence, constrained in many ways. At the same time, some of its features are deliberately left un(der)specified. There is, for instance, no constraint on the part-of-speech of the non-head daughter: It can be a determiner, an adjective, a participle or even a preposition, as will be shown in Section 4.2. There is also no constraint on the size of the daughters: They can be single words or phrases of any length.
A noteworthy property of the regular nominals is that their constraints are all inherited from higher types. In this respect, they differ from nominals with idiosyncratic properties, as will be shown in Sections 4 and 5 on the bmc and the bnpc, respectively.
4 The big mess construction
Some examples of the bmc are given in (1), repeated in (34).
The italicized phrases are nps. Their internal structure is canonically assumed to be binary, as in (35). See, among others, Bresnan (Reference Bresnan1973: 308), Van Eynde (Reference Van Eynde and Müller2007: 425), Kim & Sells (Reference Kim and Sells2011: 353), Kay & Sag (Reference Kay, Sag, Boas and Sag2012: 240) and Arnold & Sadler (Reference Arnold, Sadler, Butt and King2014: 51).
In terms of our bi-dimensional type hierarchy, the lower np is a regular nominal. This implies that it is an instance of the head-functor phrase type, with the article as the functor and the nominal as its head sister. It also implies that it is an instance of restrictive modification, albeit with the proviso that the non-head daughter (the article) does not contribute any restrictions. In terms of (30), its restr value (
$\unicode[STIX]{x1D6F4}_{\text{1}}$
) is the empty set 
. This conforms to the treatment of the indefinite article in Discourse Representation Theory, where its semantic contribution is argued to be the introduction of a new discourse referent, rather than the introduction of an existential quantifier (Kamp & Reyle Reference Kamp and Reyle1993: 74–85). Converted into hpsg terminology, this means that a nominal that is introduced by the indefinite article is of type parameter rather than of type quant-rel.
Following Van Eynde (Reference Van Eynde and Müller2007) and Kim & Sells (Reference Kim and Sells2011), we assume that the pre-determiner ap is also an instance of the head-functor type of combination, with the adverb as the functor and the adjective as its head sister. Moreover, we assume that the adverb has a marking value of type marked, so that the ap is marked as well, as shown in (36).
In combination with the fact that determiners require an unmarked nominal as their sister, this accounts for the ill-formedness of (37).
In contrast, adverbs like very and extremely are unmarked, so that the aps that they introduce are admissible in post-determiner position, as in (38).
Taking stock, the bmc is an np that consists of a marked ap and a marked np, and the internal structures of these two constituents are unexceptional: they are both instances of the head-functor type of combination. What makes the bmc exceptional is the combination of the pre-determiner ap and the indefinite np. This will be discussed and analysed in Section 4.1. The variant of the bmc with of is treated in Section 4.2. A comparison with an alternative treatment is provided in Section 4.3 and a summary in Section 4.4.
4.1 The canonical BMC
To model the combination of the ap and the indefinite np, we add a type to the hierarchy of phrases, called big-mess-phrase, which is a subtype of head-independent-phrase, on the one hand, and restrictive-modification, on the other hand.
Besides the inherited properties, which will be discussed in 4.1.1, the bmc has some properties of its own, to be presented in 4.1.2.
4.1.1 Inherited properties
Being a subtype of head-nonargument-phrase, the bmc has a head daughter with which it shares its head value 
and a non-head daughter with which it shares its marking value 
. These are in turn shared with the head daughter of the np and the functor daughter of the ap, respectively.
In contrast to the regular nominals, the big mess phrase is not a subtype of head-functor-phrase, but of head-independent-phrase. This implies that the non-head daughter (the ap) does not lexically select its head sister. To motivate this, let us check what would happen if the ap were to select its sister. In that case, the ap would have a select value, requiring a marked np. Now, since the select feature is part of the head value, it is shared with that of its head daughter, so that the adjective without degree marker has the same select value. This, however, erroneously licenses ill-formed combinations, such as *good a bargain. To avoid this, we assume that the constraints on the combination of the pre-determiner ap with the marked np do not derive from lexical properties of the adjective, but rather from properties of the construction itself.
Being a subtype of restrictive-modification, the bmc denotes a parameter in which the daughters share their index. In this respect, it resembles regular nominals, such as red box. Evidence for treating the bmc along the same lines is provided by the fact that some of the aps with a degree marker are used both in the idiosyncratic pre-determiner position and in the canonical post-determiner position. This is illustrated for aps with more, less and enough in (41)–(43).Footnote [19]
As a consequence, since the instances with the post-determiner order are instances of restrictive modification, and since there is no difference in truth-conditional meaning with the instances of the pre-determiner order, it is only natural to treat the latter as instances of restrictive modification as well. Notice, incidentally, that this provides further evidence for the drt style treatment of the indefinite article as lacking quantificational force, for if the article were treated as an existential quantifier, the bmc would not comply with the constraints on restrictive-modification, which in turn would necessitate an otherwise unmotivated differentiation between the (a) and (b) examples in (41)–(43).
4.1.2 Inherent properties
Beside the properties that it inherits from its supertypes, the bmc has some properties of its own. They are spelled out in (44).
The head daughter is required to be a marked regular nominal whose dtype value is a, a subtype of indefinite.Footnote [20]
The marking constraint excludes combinations with unmarked nominals, such as *so serious daily trouble and *how good unexpected bargains, and with nominals that are introduced by another type of determiner, as in *so serious some problem(s) and *how good the bargain(s). Since the indefinite article selects a singular count nominal, (44) also accounts for the fact that the head daughter is singular and count. This is, admittedly, a mere description of the facts. A partial explanation, though, might be seen to follow from the assumption that the big mess phrase is an instance of restrictive modification, as this implies that the head daughter’s content value is of type parameter and, hence, that the determiner must be one without quantificational force. This is not a full explanation, since the indefinite article is not the only determiner without quantificational force, but at least it accounts for the exclusion of quantifying determiners.Footnote [21]
The non-head daughter is required to be an adjectival head-functor phrase. Since it does not have a specific dtype value of itself, it can share the one of its head sister 
, and since the latter is shared with the bmc as a whole, it captures the fact that the resulting phrase has the distribution of an indefinite np. The marking value of the ap is required to be of type marked. This licenses aps that are introduced by a marked adverb, as in so good a bargain and how serious a problem, while it excludes unmarked aps, as in *good a bargain and *very big a house.Footnote
[22]
Given the way in which unification works, (44) also licenses aps that contain an adverb with the underspecified value (marking). This is useful to model the combinations with more, less and enough, whose marking value can be resolved to marked, licensing the pre-determiner position, or to unmarked, licensing the post-determiner position, as illustrated in (41)–(43). Whether an adverb is marked, unmarked or underspecified is a matter of lexical stipulation, and may show language internal variation. For many speakers, the adverbs as, too, that, this and however behave in the same way as so and how, which implies that they consider (46) to be well-formed and (47) to be ill-formed.
There are also speakers, though, for whom too and that are not necessarily marked, as demonstrated by the corpus examples in (48), quoted from Kim & Sells (Reference Kim and Sells2011: 339).
There is, hence, some variation in the assignment of the marking value for at least some of the adverbs. Since this variation is not semantically motivated, the marking feature is a more appropriate device to model it than the content feature.
An interesting test case for the treatment are bmcs with a more complex pre-determiner ap, as in (49)–(50).
In (49), the degree marker as is preceded by a modifier of its own. To model this, we assume that nearly shares the marking value of its head sister, as in (51).Footnote [23]
Given that as is marked, this accounts for the well-formedness of nearly as rude a remark as well as for the ill-formedness of *a nearly as rude remark. Moreover, it also accounts for the fact that the combination of nearly with an unmarked adjective, as in nearly empty, yields an unmarked phrase, which in turn accounts for the well-formedness of a nearly empty room and the ill-formedness of *nearly empty a room.
The combinations with far in (50) can be dealt with along the same lines. Assuming that far shares the marking value of its head sister and that too has an underspecified marking value, we account for the well-formedness of both far too big a failure and a far too big failure.
Notice, finally, that a big mess phrase cannot contain another big mess phrase. Iterative application is not licensed, since (44) requires the head daughter to be of type regular nominal, which is incompatible with the type big-mess-phrase.
4.2 The variant with ‘of’
Some examples of the variant with of are given in (52).
This construction is mainly used in American English, as pointed out by Bolinger (Reference Bolinger1972: 136), Zwicky (Reference Zwicky1995: 113–114), Kennedy & Merchant (Reference Kennedy and Merchant2000: 125–126) and Fillmore, Lee-Goldman & Rhomieux (Reference Fillmore, Lee-Goldman, Rhomieux, Boas and Sag2012: 348). It provides an extra challenge, for if we adopt the canonical analysis of a [p–np] sequence, we get a pp that is combined with an ap to yield an np! An analysis along these lines is actually proposed by Zwicky (Reference Zwicky1995: 117) and Kim & Sells (Reference Kim and Sells2011: 357), but it is not the one that we adopt.
Instead, we assume that the [of–np] sequence is headed by the np. The preposition is, hence, not treated as the complement selecting head of a pp but as a head selecting functor, more specifically as a functor that selects an np with the dtype value a. Its own dtype value captures the fact that we are dealing with a use of of in which it is necessarily followed by the indefinite article. We call it ofa for mnemonic reasons. It is a subtype of indefinite, just like a. The synsem value in (53) spells this out in formal terms.
The assignment of the empty set as its restr value captures the semantic vacuity of the preposition.
As a consequence, the combination of the preposition with the np can be treated as an instance of the regular-nominal type: in terms of the headedness dimension, it is an instance of head-functor-phrase, and in terms of the clausality dimension, it is an instance of restrictive-modification, albeit with the proviso that the preposition does not contribute any restrictions.
The resulting nominal matches nearly all of the constraints on the head daughter of the big mess phrase, as spelled out in (44). The only modification we need is to make the dtype value of the head daughter in (44) disjunctive, allowing both a and ofa. This suffices to license combinations as in (54).
Independent evidence for the functor treatment is provided by the stranding test. In languages that allow adposition stranding, such as English and Dutch, adpositions may be stranded if they head a pp, as in (55).
This is just a regular instance of complement extraction. The preposition in the bmc, by contrast, cannot be stranded.
This meshes well with its functor status, since heads cannot be freely extracted.
Further evidence is provided by the fact that the functor treatment also applies to the use of of in the bnpc. Moreover, it has been argued to apply to certain uses of the Dutch prepositions om, te, van and voor by Van Eynde (Reference Van Eynde2004). Also for certain uses of the French prepositions à and de, it has been argued that they are markers, rather than heads of pps (Abeillé & Godard Reference Abeillé and Godard2000).Footnote [24]
4.3 Comparison with another treatment
Another monostratal analysis of the bmc is provided by Kay & Sag (Reference Kay, Sag, Boas and Sag2012). It is cast in the notation of Sign-Based Construction Grammar, which is very similar to that of constructivist hpsg. It employs the head-functor type of combination to model both the lower and the higher np of the bmc, and resorts to a special type of construction to model the pre-determiner ap. It is called the complex pre-determiner construction and its main idiosyncracy is that it triggers a change in the select value of the adjective: while an adjective such as long selects an unmarked nominal, the combination how long selects a marked nominal that is introduced by a (Kay & Sag Reference Kay, Sag, Boas and Sag2012: 238). In support of this choice, Kay & Sag (Reference Kay, Sag, Boas and Sag2012) point out that it generalizes to other indefinite nps with a pre-determiner, such as what a mess, such a beauty and many a day. Assuming that what, such and many are functors that select an indefinite np and that have some other marking value themselves, it is tempting to analyze the bmc along the same lines.
While we agree that it is never good to miss a generalization, we are not convinced that the bmc is so similar to the combinations with what, such and many that a uniform treatment is called for. In fact, there are at least three differences between them. First, in the combinations with what, such and many, the adjectives (if any) follow rather than precede the determiner.
Second, what and such are not only compatible with nps that are introduced by the indefinite article, but also with unmarked nominals.
Third, the pre-determiners may not be separated from the np by of: what (*of) a mess, such (*of) a beauty and many (*of) a splendid day at the beach. These differences make the adoption of a uniform treatment less appealing.
Conversely, the shift of the idiosyncracy to the internal structure of the ap leads to a loss of generalization in the combination of the degree marker with the adjective, for while the addition of the degree marker changes the select value of the adjective in the bmc, it does not trigger such a change when the ap is used in other positions, such as the postnominal and predicative ones in (61).
Our treatment is more general in this respect, since it treats the internal structure of the ap in a uniform way, no matter whether it is in predicative, postnominal or pre-determiner position.
On balance then, we think that a treatment that locates the idiosyncracy of the bmc in the combination of the pre-determiner ap with the np is preferable to one that locates it in the internal structure of the ap.
4.4 Summing up
This section has provided an analysis of the bmc, both the canonical one and the variant with of. It is based on the assumption that the internal structures of the pre-determiner ap and the indefinite np are unexceptional and that the idiosyncracy resides in their combination. This combination is modeled in terms of a type, called big-mess-phrase, that inherits properties of head-independent-phrase, on the one hand, and restrictive-modification, on the other hand. The result of unifying the inherited constraints with the inherent ones is spelled out in (62).
Comparing this with the description of the regular nominals in Section 3.3, the main difference concerns the proportion of inherited and inherent constraints. While the properties of the regular nominals are all inherited from its supertypes, many of the properties of the bmc concern inherent constraints.
5 The binominal noun phrase construction
Some examples of the bnpc are given in (2), repeated in (63).
For its analysis, we subscribe to the view, argued for at length by Aarts (Reference Aarts1998) and Keizer (Reference Keizer2007: 85–108), that the rightmost np is both the syntactic and semantic head: what she is claimed to have in (63b), for instance, is a headache, rather than a skullcracker. A challenge for that view is that it is not in sync with what the surface structure of the combination suggests: in an [n–of–np] sequence, it is the leftmost nominal that is canonically identified as the head. To solve the mismatch, Aarts (Reference Aarts1998) and Keizer (Reference Keizer2007) treat the first nominal as part of a Modifier Phrase (mp) that also includes of and the indefinite article, as in (64).
To motivate this, the authors point out that the preposition and the article can be incorporated in the noun, as in a helluva job, and that the semantic contribution of the mp can be paraphrased by a prenominal ap, as in a hellish job.
A problem with these arguments is that they do not generalize. Incorporation, for instance, is possible with hell, but not with other nouns: combinations like *her nitwituva husband and *a skullcrackeruva headache do not exist. Similarly, the paraphrase in terms of a prenominal adjective is possible with nouns like hell and fool, but not with nouns like nitwit and skullcracker, at least if one expects a morphological relation between the noun and the adjective.
Besides, and more importantly, it is not clear that incorporation is a good criterion for constituency. The fact, for instance, that the infinitival to can be incorporated in certain verbs, as in wanna and gonna, then becomes an argument for assigning a left branching structure to [v–to–vp] sequences, as in [[like to] swim], contrary to the wide-spread and independently motivated practice of assigning it a right branching structure, as in [like [to swim]]. Similarly, the fact that the definite article is incorporated in certain prepositions, as in the German am, zum and zur and the French du and au, then becomes an argument for assigning a left branching structure to [p–det–nom] sequences, as in [[auf dem] Tisch] ‘on the table’ and [[à la] maison] ‘at home’, contrary to the wide-spread and independently motivated practice of assigning them a right branching structure, as in [auf [dem Tisch]] and [à [la maison]]. Similar questions apply to the relevance of paraphrase relations for determining constituency. The fact, for instance, that the Dutch transitive verb beluisteren is nearly synonymous with luisteren naar ‘listen to’ then becomes an argument for treating the latter as a constituent in [[luisteren naar] Mozarts laatste opera] ‘listen to Mozart’s last opera’, contrary to the wide-spread practice of treating the preposition as part of the pp complement of the verb, as in [luisteren [naar Mozart’s laatste opera]].Footnote [25]
In sum, the arguments in favor of (64) are less than convincing. Besides, there are some arguments against it. Kim & Sells (Reference Kim and Sells2014: 14), for instance, point out that the treatment of the [n–of a] sequence as a constituent complicates the expression of the constraint that the rightmost nominal must be a count noun, since the article is not a sister of that nominal.
In order to avoid the problems with (64) without giving up the intuition that the rightmost nominal is the head, we adopt a structure that is isomorphic to the canonical structure of an [n–of–np] sequence, as in (65), but with the stipulation that the preposition is a functor, rather than the head of a pp.
In fact, the properties of the preposition in the bnpc are the same as those of the preposition in the bmc, as spelled out in (53).Footnote [26] Corroborating evidence for the functor treatment is provided by the contrast in (66).
(66a) is well-formed since the stranded preposition is the head of a pp, but (66b) is not, since the stranded preposition is a functor.
Given its functor status, the combination of the preposition with its np sister is a straightforward instance of the regular-nominal type. What is truly idiosyncratic about the bnpc is the combination of this [of–np] sequence with the first nominal, as in [nitwit [of a husband]]. Its properties are discussed and analyzed in Section 5.1. A variant of the bnpc with a bare plural, as in jewels of villages, is treated in Section 5.2. A comparison with another monostratal treatment is provided in Section 5.3 and a summary in Section 5.4.
5.1 The canonical BNPC
To model the combination of the first nominal with the [of–np] sequence, we add a type to the hierarchy of phrases, called binominal-np, which is a subtype of head-independent-phrase, on the one hand, and inverted-predication, on the other hand.
Just as in the treatment of the bmc, we differentiate the properties that the bnpc inherits from its supertypes (Section 5.1.1) from its inherent properties (Section 5.1.2).
5.1.1 Inherited properties
Sharing the assumption of Aarts (Reference Aarts1998) and Keizer (Reference Keizer2007) that the first nominal is a prenominal adjunct, we treat the bnpc as a head-nonargument-phrase in which the first daughter is the non-head daughter. Since it shares its marking value with the mother, the addition of the first nominal has the effect of turning a marked np into an unmarked one, as shown in (68).
This accounts for the fact that the resulting combination is compatible with a determiner, as in her nitwit of a husband.
Just like in the bmc, the nonhead daughter is not a functor. We, hence, assume that it does not lexically select its sister. Assuming otherwise would lead to the rather far-fetched claim that nouns like nitwit, hell and skullcracker lexically select an np sister that is introduced by of a. In fact, since they only combine with such nps when they are part of the bnpc, the proper place to model this is in the definition of the bnpc itself, rather than in the lexical entries of the nouns.
Turning to the clausality dimension, we assume that the relation between the two nominals is not one of restrictive modification, but of predication, as suggested by the paraphrases in (69).
We call it more specifically inverted predication, since the order of the predicate and the predicand in the bnpc differs from the canonical order in the paraphrase. This captures the same intuition as the one that underlies the transformational analysis of Bennis et al. (Reference Bennis, Corver and Den Dikken1998) and Den Dikken (Reference Den Dikken, Alexiadou and Wilder1998), where the bnpc is treated as a result of predicate inversion. It is also in line with the observation that ‘N1 and N2 are in a reverse subject-predicate relation’ (Kim & Sells Reference Kim and Sells2014: 6).
To model this, we build on the hpsg treatment of predicative constructions by Van Eynde (Reference Van Eynde2015). In that treatment, predication is a relation of type attribute-rel between a theme denoting nominal and an attribute denoting predicate.Footnote [27] In ordinary predicative constructions, this relation is expressed by the verb, usually the copula, but in the bnpc there is no verb: the theme denoting nominal and the predicate are part of one complex np. Rather than postulating an empty verb or some newly minted functional category, we include the relevant relation in the definition of the construction itself. More specifically, we add a type to the hierarchy of non-clausal phrases, called inverted-predication, which is a subtype of nominal-parameter and whose inherent properties are spelled out in (70).
The predicative relation between the daughters is made explicit in the restr value of the phrase, which contains a fact whose nucleus is a relation of type attribute-rel in which the theme role is assigned to the head daughter 
and the attribute role to the non-head daughter 
. The head daughter does not share its index with its sister. In this respect, it differs from phrases of type restrictive-modification, in which the daughters share their index. This has some empirical bite, since indices in hpsg are used to model agreement. More specifically, the objects of type index are declared to have person, number and gender features.
Signs that share their index are, hence, required to have the same person, number and gender. This type of agreement obtains a.o. between an anaphoric pronoun and its antecedent, and is distinct from morpho-syntactic concord, as argued by Pollard & Sag (Reference Pollard and Sag1994), Kathol (Reference Kathol, Levine and Green1999) and Wechsler & Zlatić (Reference Wechsler and Zlatić2003).
The fact that the daughters in (70) do not share their index, therefore, implies that they do not necessarily show agreement for person, number and gender. This may at first seem undesirable since the first nominal is canonically required to show number agreement with the second one, as illustrated by the ill-formedness of *her nitwits of a husband. Yet, a requirement of index sharing would be too strong, since mismatches are not necessarily ill-formed, as illustrated by those prejudiced fools of a jury, quoted from Keizer (Reference Keizer2007: 101). Unsurprisingly, the situation resembles the agreement between predicate nominals and subjects in copular constructions. A recent corpus-based study of that agreement is provided by Van Eynde, Augustinus & Vandeghinste (Reference Van Eynde, Augustinus and Vandeghinste2016). It reports that there is an agreement effect (with 89.48% matches versus 10.52% mismatches in a one million word sample), but it also shows that index sharing is not appropriate to model that effect. As an alternative, it develops an analysis that involves a distinction between collective and distributive interpretations. The details of that treatment need not detain us here. What matters in this context is that index sharing is not the appropriate way to handle the agreement effect, and that the assignment of different indices to the nominals in the bnpc is, hence, justified.
Compared with the restrictive-modification type, which subsumes a wide variety of nominal phrases, the inverted-predication type has a smaller range, but we expect it to include more members than the bnpc alone. Another plausible candidate is the appositive of-construction, as exemplified by the city of Rome, where the relation between city and Rome can be treated as an instance of inverted predication: Rome is claimed to be a city.
5.1.2 Inherent properties
Besides the properties that it inherits from its supertypes, the bnpc has some properties of its own. They are spelled out in (72).
The head daughter is required to be a marked regular nominal with the dtype value ofa. The non-head daughter is required to be an unmarked nominal. It may be a single word, as in (63), or a phrase, as in (73).
The former’s structure is spelled out in (74).
Since absolute nitwit is a head-functor phrase, its marking value is shared with the adjective 
, and since its combination with of a husband is a binominal np and, hence, a subtype of head-nonargument-phrase, that marking value is also shared with the mother, yielding an unmarked nominal, which is headed by the rightmost np 
. The resulting nominal can in turn be combined with a determiner, as in her absolute nitwit of a husband. Since this combination is a regular nominal, iterative application is not excluded. It is, hence, not impossible for a binominal np to contain another binominal np. A relevant example is the following quote from the preface of Moby-Dick.
The lower bnpc poor devil of a Sub-Sub is contained in the higher bnpc painstaking burrower and grubworm of a poor devil of a Sub-Sub. Semantically, the Sub-Sub is claimed to be a poor devil, as well as a painstaking burrower and grubworm.
5.2 The variant with a bare plural
The variant with a bare plural is exemplified by the following fragments from the British National Corpus, quoted by Kim & Sells (Reference Kim and Sells2014: 5).
This variant is not accepted by all speakers: Foolen (Reference Foolen, Radden and Panther2004: 85) claims that English does not allow it, Quirk, Greenbaum, Leech & Svartvik (Reference Quirk, Greenbaum, Leech and Svartvik1985: 1285) call it marginal and Napoli (Reference Napoli1989: 212) claims that it is acceptable in British English but not in American English.
To model the grammar of speakers who use this variant, we add a second lexical entry for the functor of, in which it selects an unmarked (bare) plural and in which it has the marking value ofbpl, another subtype of indefinite. Its synsem value is spelled out in (77).
Besides, we slightly modify the definition of the bnpc in (72), allowing the dtype value of the head daughter to be either ofa or ofbpl.
5.3 Comparison with another treatment
There are many analyses with which our treatment could be compared, but we will limit the discussion here to one that is sufficiently similar to our treatment to make a comparison feasible and fruitful, i.e. the one of Kim & Sells (Reference Kim and Sells2014). It is cast in the notation of Sign-Based Construction Grammar, just like the analysis of the bmc in Kay & Sag (Reference Kay, Sag, Boas and Sag2012). The intuition that underlies the analysis is basically the same as that of Aarts (Reference Aarts1998) and Keizer (Reference Keizer2007), and our treatment: ‘we assume that the second element np2/n2 functions as the syntactic as well as semantic head while the first one serves as the modifier’ (Kim & Sells Reference Kim and Sells2014: 29). The way in which this is made explicit is rather different, though. For a start, the bnpc is assigned a flat structure, as in (78).
Second, the construction that licenses this flat structure is claimed to be headed and non-headed at the same time. It is headed in the sense that the first nominal denotes a property of the entities (i) that are denoted by the second nominal, and it is also non-headed in the sense that ‘the bnp has sequences of nominals fulfilling the same grammatical function, neither of which is syntactically dependent on the other’ (Kim & Sells Reference Kim and Sells2014: 22). To make sense of this somewhat paradoxical situation, the authors introduce a type, called head-mod-juxtaposition, that is a subtype of coordination, on the one hand, and head-mod-cx, on the other hand, as in (79).
Being a subtype of head-mod-juxtaposition, the bnpc ‘inherits only some syntactic properties from coordination and some semantic properties from subordination’ (Kim & Sells Reference Kim and Sells2014: 30).Footnote [28] This begs the question of which constraints are inherited from which of the supertypes, but on that point the authors remain vague: ‘we leave it open for future research how to filter these partial properties correctly, and ensure their inheritance in the bnp’ (Kim & Sells Reference Kim and Sells2014: 30). In this respect, the treatment that we propose is more detailed: both the bnpc itself and its supertypes are defined explicitly and the inheritance is strictly monotonic, in the sense that subtypes inherit all properties of their supertypes.
5.4 Summing up
This section has provided an analysis of the bnpc, both the canonical one and the variant with the bare plural. Its properties are modeled in terms of a phrase type that inherits the constraints of head-independent-phrase, on the one hand, and inverted-predication, on the other hand. The result of unifying the inherited constraints with the inherent ones is spelled out in (80).
Comparing this avm to that of the bmc, we observe both similarities and differences. The main similarity concerns the fact that they are both subtypes of head-independent-phrase. Another similarity concerns the functor status of the preposition of. The main difference concerns their place in the clausality hierarchy: while the bmc is an instance of restrictive modification, just like the regular nominals, the bnpc is an instance of inverted predication, a less common type of combination. It appears then that the bnpc has less in common with the regular nominals than the bmc. In that sense, it shows a higher degree of idiosyncracy.
6 Conclusion
This paper has provided a sign-based treatment of both regular nominals and two types of idiosyncratic nominals, i.e. the bmc and the bnpc. Special attention has been paid to the interaction of the regular and the exceptional in the idiosyncratic nominals. To model that interaction, we have exploited the potential of constructivist hpsg, as laid out in Ginzburg & Sag (Reference Ginzburg and Sag2000). The core of the analysis is a bi-dimensional hierarchy of phrase types in which the properties of the nominals are partly inherited from their supertypes and partly spelled out in construction-specific constraints. Example (81) presents the part of the hierarchy that we have focused on.
The resulting treatment is one ‘in which the particular and the general are knit together seamlessly’ (Kay & Fillmore Reference Kay and Fillmore1999). Besides, it chimes well with one of the tenets of Construction Grammar that ‘a linguistic structure is motivated to the extent that it is related to other structures in the language’ (Taylor Reference Taylor, Radden and Panther2004). This relatedness is made fully explicit in the phrase type hierarchy and in the constraints that are associated with the various types.
In future work, we want to explore the potential of this approach for dealing with other types of complex nominals with idiosyncratic properties, such as appositions with and without of (the city of Berlin versus the poet Burns), and partitive and pseudo-partitive nps. This, we believe, will ultimately yield a fine-grained hierarchy of nominal phrase types that charts their mutual similarities and differences in a fully explicit manner and that makes it possible to measure the degree of idiosyncracy of their formation.
stand for lists of objects.
