1 Contextual domain restriction across languages - Iker - CNRS

45 Pages·2009·0.5 MB·English

by  Anastasia Giannakidou

Contextual domain restriction across languages:
Determiners, quantifiers, and the structure of QP

Urtzi Etxeberria and Anastasia Giannakidou
IKER/CNRS, and University of Chicago
September 2009

Abstract
The question of whether contextual restriction of quantificational determiners (Qs) is done
explicitly (i.e. at LF; von Fintel 1994, Stanley 2002, Stanley and Szabó 2000, Martí 2003,
Giannakidou 2004, Etxeberria 2005, 2008, 2009), or purely pragmatically (via e.g. free
enrichment as in Recanati 2002, 2004, 2007, or a relevance theoretic process) has been a matter
of intense debate in formal semantics and philosophy of language. In this paper, we contribute to
the debate and argue that the domain for quantifiers in certain languages is restricted overtly, i.e.
in the syntax, by a determiner head (D). This strategy of domain restriction via D— D —
DR
happens by applying D to the nominal argument, but we present novel data that show D to
DR DR
also apply to the Q itself, in which case it forms a constituent with it. In both cases, D is a type
DR
preserving function, i.e. a modifier, and supplies the contextual C variable. Evidence for our
analysis is drawn from Greek, Basque and Salish primarily—three different language families—
and we build on our earlier ideas in Giannakidou (2004), and Etxeberria (2005, 2008, 2009).
Our analysis provides support for the program that domain restriction is syntactically
realized, but we propose an important refinement: domain restriction can affect the Q itself (pace
Stanley 2002), and in fact quite systematically in certain languages. Finally, we show that the Q
that is affected by D is typically a strong one, and we ask whether weak Qs can also be
DR
inherently domain restricted (as suggested by Martí 2009). We conclude that they cannot:
indefinites can at most be associated with a felicity condition of specificity (in the sense of Ionin
2006), anchored to the speaker, and is not part of the common ground like domain restriction.

1 Background: Determiners, quantifiers, and contextual domain restriction

One of the most fruitful ideas in formal semantics has been the thesis that quantifier phrases
(QPs) denote generalized quantifiers (GQs; Montague 1974, Barwise & Cooper 1981, Zwarts
1986, Westerståhl 1985, Partee 1987, Keenan 1987, 1996, Keenan & Westerståhl 1997, among
many others). GQ theory initiated an exciting research agenda in the ‘80s, and the decades that
followed featured extensive studies of quantificational structures, with attention to the internal
structure of QPs, their use in discourse, and their scopal properties. For many years the focus of
inquiry was on English, but soon enough crosslinguistic research made obvious a spectacular
variation (see e.g. the works appearing in Bach et al. 1995, Szabolcsi 1997, Matthewson 1998,
2001, 2008, Giannakidou and Rathert 2009) in the patterns of quantification across languages,
suggesting that some fine tuning, or even more radical modifications, of the classical theory are
necessary. Some of the fine tuning concerns the internal composition of quantifier words like
each and every and their equivalents, as will become evident in our dicussion here.
Classical GQ theory posits that there is a natural class of expressions in language, called
quantificational determiners (Qs), which combine with a nominal (NP) constituent (of type et, a
1
first order predicate) to form a quantificational argumental nominal (QP). This QP denotes a GQ,
a set of sets. In a language like English, the syntax of a QP like every woman is as follows:

(1) a. [[every woman]] = λP. ∀x. woman (x) → P(x)
b. [[every]] = λP. λQ. ∀x. P(x) → Q(x)]
c. QP
〈〈e, t〉, t〉

Q NP
〈〈e, t〉, 〈〈e, t〉,t〉〉 〈e, t〉
every woman : λx. woman (x)

The Q every combines first with the NP argument woman, and this is what we have come to
think of as the standard QP-internal syntax. The NP argument provides the domain of the
quantifier, and the Q expresses a relation between this set and the set denoted by the VP. Qs like
every woman, most women, etc. are known as ‘strong’ (Milsark 1977), and, simplifying
somewhat (see McNally 1992, 2009 for more refined data), their distinctive feature is that they
cannot occur in the so-called existential there construction. By contrast, three women, some
women, several women, etc. are ‘weak’, and occur happily in this structure:

(2) a. #There are most women in the garden.
b. #There is {every/each} woman in the garden.
c. #There is the woman in the garden.
d. There are {three/some/few/several} women in the garden.
e. There is a woman in the garden.

The question of what accounts for this empirical difference in existential structures is still open,
but, for the purposes of this paper, it is sufficient to accept that one of the main functions of the
struture is to assert existence, and weak QPs do just that. The QPs that are excluded, i.e. strong
ones and definites, do not assert existence but rather presuppose it, and are not admitted in the
structure (Zucchi 1995).
In GQ theory, then, “quantificational determiner” refers to the function that creates a
quantificational argument, i.e., a GQ, from a predicate. Syntactically, in a language like English,
and as far as we know in most Indoeuropean languages, this function is hosted in the head we
designated above as Q, and the domain predicate will come in the form of NP or A(djectival)P as
in every tall boy.
Another element that has the ability to combine with an NP or an AP, and give a nominal
argument is the definite determiner the and its equivalents. The definite article is usually
designated as D (Abney 1987; see Alexiadou, Haegeman, and Stavrou 2008 for an extensive
recent overview). The DP has a structure parallel to (1), only in this case the Q is D, and the
constituent is called DP (though some authors call the Q position uniformly D position; cf.
Matthewson 1998, Gillon 2009). As indicated below, the DP produces typically a referential
expression, a (maximal or unique) individual indicated here with iota:

2
(3) DP, e: ι (λx. woman (x))

D NP
〈〈e, t〉, e〉 〈e, t〉
the woman : λx. woman (x)

The DP produces the most basic argument, and indeed there is consensus in the literature
that the D position is associated with argumenthood: an NP, which can otherwise not be used as
an argument because it is a property (et), closes under D and becomes an argument of the basic
type e. The DP can be understood as a GQ in a system that assigns uniform denotations to all
nominal argumental constituents, yet intuitively the DP is thought of as a referring expression as
this widely accepted analysis suggests (drawing on the analyses of definite descriptions since
Frege 1892 and Strawson 1950; for a recent overview see Elbourne 2007). As a referring
expression, it seems more natural to allow the DP to denote in the type e, an individual (singular,
or plural depending on the number), at least as a primary assignment, and lift it only if necessary
(within a type shifting system like Partee 1987). We will have more to say on D in sections 2
and 3; we will just note here that QPs and DPs are distinct in their primary type assignment: the
QPs are quantificational and denote GQs (type et,t), but the DPs are referential and denote
individuals (type e). Both D and Q, are functions that need a domain, and apply to predicates
(NPs) thereby forming an argument out of it.1
It has long been noted that the domain of Qs is usually contextually (explicitely or
implicitely) restricted. For instance, Strawson (1952) talks about presuppositions induced by Qs,
Horn 1992 about existential commitment of universal quantifiers, and Reuland and Ter Meulen
(1987) further state a distinction between weak and strong quantifiers:

“A noteworthy result of this [the Barwise and Cooper; clarification ours] set-theoretic analysis
of determiners is that for a weak determiner the verification of a sentence Det N is/are Pred is
based only on the intersection of the N- and Pred-interpretations, that is, information provided
by the sentence itself, whereas strong determiners require for their verification
consideration of some other set, often a head given in the interpretation or otherwise
available as part of the conversational background or common ground (emphasis ours].”
Reuland and ter Meulen (1987:4).

Since then, much contemporary work agrees that we need to encode contextual restriction in the
QP somehow, but opinions vary as to whether contextual restriction is part of the
syntax/semantics (Partee 1987, von Fintel 1994, Stanley & Szabó 2000, Stanley 2002, Martí
2003, Matthewson 2001, Giannakidou 2004, Etxeberria 2005, 2008, 2009), or not (Recanati
1996, 2004, 2007, and others in the strong contextualism tradition). In the syntax-semantics
approach, it is assumed that the domains of Qs are contextually restricted by covert domain
variables at LF. These variables are usually free, but they can also be bound, and they can be
either atomic, e.g. C, or complex of the form f(x), corresponding to selection functions (Stanley
2002, von Fintel 1998, Martí 2003):

1 It has also been suggested that the structure of DP may be richer than indicated here, e.g. that there may be two D
positions in the DP one above Q one below (see Szabolcsi 2009 and earlier work, Alexiadou, Haegeman and
Stavrou 2008). This discussion becomes relevant in section 3, and we will take it up there.
3
(4) Many people came to the party last night; every student got drunk.
(5) ∀x [student ] got drunk (x).
c

Here, the nominal argument of ∀, student, is not the set of students in the universe, but
intuitively, the set of students who came to the party last night. This is achieved by positing the
domain variable C, which will refer to the salient set of people who came to the party last night.
Every student then will draw values from the intersection of this set with the set student. The
domain variable can also be understood as f(x), i.e. a free function variable and an argumental
variable of type e. Relative to a context c, f maps e, a student who came to the party last night to
the set of students that came to the party last night. This set is, then, the nominal argument of the
Q ‘every’. Stanley (2002) further argues that the domain variable is, syntactically, part of the
nominal argument, and not of the Q itself.
However, empirical evidence suggests, as we will show, that domain restriction can
affect the Q itself. Our claim will be motivated by data like below (from Giannakidou 2004,
Etxeberria 2005, 2008, 2009), where the Q combines with the D element.

(6) Greek (Giannakidou 2004):
a. o kathe fititis
D.sg every student
‘each student’
b. kathe fititis; *kathe o fititis
‘every student’

(7) Basque (Etxeberria 2005, 2009):
a. mutil guzti-ak
boy all-D.pl
‘all of the boys’
b. *mutil guzti; *mutil-ak guzti

These data, largely unknown to the wider literature, will be the main topic of this paper,
and will be taken to indicate that, syntactically, domain restriction can affect Q itself. One other
important aspect of the data is that contextual domain restriction is done via a definite
determiner D, an idea that builds on an earlier proposal by Westerståhl (1984, 1985) that the
main function of the definite article is to supply a context set. Contextual domain restriction in
our analysis is a presupposition contributed by the typical vehicle of presuppositions, the definite
determiner. This conclusion can be cast independently of how we treat presuppositions, e.g. as
preconditions on updates of contexts or information states (Heim 1993), or within van der
Sandt’s (1992) conception of them as propositions whose place in discourse is underdetermined
by syntax—though it seems to favor, we think, Heim’s approach.
The main data for our analysis will come from languages as diverse typologically as
Greek and Basque, and we will bring into the discussion data from Salish that suggested a use of
D as a domain restrictor on the NP (Matthewson 2001, Giannakidou 2004). The main
conclusions of our discussion are three: first, we have indeed evidence for the ‘explicit strategy’
(von Fintel 1998) of domain restriction; second, being contextually restricted is often an inherent
property of the Q; and third, in the family of semantic functions associated with D we must
acknowledge the function of domain restriction. Finally, we find a difference between strong Qs,
4
which can be domain restricted by D, and weak Qs which cannot, thus supporting the difference
mentioned by Reuland and Ter Meulen (1987).
The discussion proceeds as follows. We start in section 2 with some brief background
discussion of St’át’imcets Salish data from Matthewson (1998, 2001) which prompted
Giannakidou (2004) to argue that D crosslinguistically performs the function of providing C
without iota. In section 3, we introduce our analysis that D provides the context set C by
defining the domain restricting function as a type-preserving (i.e. modifier) function D . In
DR
section 4 we discuss how D correlates with the weak-strong distinction. It appears that only
DR
strong Qs can be contextually restricted via D in Basque and Greek, and we explain this by
arguing, following Etxeberria (2005, 2008, 2009), Giannakidou and Merchant (1997), Stavrou
and Terzi (2009), that weak Qs are not Qs (et,ett), but adjectives or cardinality predicates, i.e.
number functions. In section 5, finally, we consider a recent proposal by Martí (2008, 2009) that
the indefinite plural algunos is domain restricted. We present empirical problems with this
claim—a number of asymmetries between the claimed restricted indefinites and our D -ed
DR
quantifiers, as well as unrestricted uses of the alleged weak indefinites— and conclude that we
are not dealing with domain restriction in these cases, but with a specificity felicity condition
(Ionin 2006). The presupposition of D relies on the common ground, but the felicity condition
DR
on just the speaker’s intentions.

2 Background: identifying D as domain restrictor

In this section we introduce the data that, in our view, implicate a role of D in syntactically
expressing domain restriction. The idea is present already in Matthewson (2001)—but we will
object to the particular implementation she suggested, namely that, universally, the Q combines
with an e (instead of et) type argument; we refer to the Appendix and Giannakidou (2004) for a
re-consideration of the Salish data within the spirit of our analysis. We also discuss briefly the
analysis of Giannakidou (2004) which initiated the implementation of D providing a context set
in Salish, while adding to the discussion the case of D modifying Q observed in Greek and
Basque. In section 3, we will present our analysis of the data presented here.

2.1 Quantifiers and D in St’át’imcets (Matthewson 1998, 2001)

Matthewson (1998, 2001) notes that Salish equivalents to every, few, many, etc. take DPs
arguments as complements, instead of the expected NP:

(8) a. Léxlex [tákem i smelhmúlhats-a].
intelligent [all D.pl woman(pl)-D]
‘All of the women are intelligent.’
b. * léxlex [tákem smelhmúlhats]
intelligent [all woman(pl)]

(9) a. Úm’-en-lhkan [zi7zeg’ i sk’wemk’úk’wm’it-a] [ku kándi].
give-tr-1sg.subj [each D.pl child(pl)-D] [D candy]
‘I gave each of the children candy.’
b. * Úm’-en-lhkan [zi7zeg’ sk’wemk’úk’wm’it] [ku kándi].
give-tr-1sg.subj [each child(pl)] [D candy]
5
The D consists of “two discontinuous parts, a proclitic (ti for singulars; i for plurals), which
encodes deictic [emphasis ours] and number morphology, and an enclitic …a which attaches to
the first lexical element in the phrase” (Matthewson 2001: 3; cf. Matthewson 1998 for details).
Matthewson (2001) thus suggests a new syntax for the QP: first, D combines with the NP
predicate to create a DP (type e); then, e becomes the argument of Q which is now of type e,ett.
This combination yields a GQ of the usual type ett.

(10) a. [ tákem i smelhmúlhats-a]
QP
[ all D.pl woman (pl)-D]

b. QP 〈〈e, t〉, t〉

Q 〈e, 〈〈e, t〉, t〉〉 DP e
takem
D 〈〈e, t〉, e〉 NP 〈e, t〉
i
smelhmúlhats

The deviation from the standard GQ analysis is obvious: the domain of Q is not a set, but an
individual. D, in Matthewson’s account is an et,e function, in particular a choice function:

(11) [[ smelhmúlhats (pl.) ]] = [[*]] ([[ smúlhats (sg.) ]]) ‘women’
(12) [[ X … a ]] g = λf ∈ D (g(k)) (f) (Matthweson 2001: (18))
k et

The index of the determiner specifies which choice function will be used; g is an assignment
function, from indices to choice functions, thus g(k) is a choice function of type et,e. If the DP is
plural, a pluralization operator * is posited with standard semantics: it takes a one-place
predicate of individuals f and returns all the plural individuals composed of the extension of f.

(13) [[ * ]] is a function from D into D such that, for any f ∈ D , x: D : [*f] (x) = 1 iff [f(x)
et et et e
≠ 1 ∧ ∃y∃z [ x =y+z ∧ [*(f)] (y) = 1 ∧ [*(f)] (z) =1]]
(Matthweson 2001: (17))

D thus creates an individual out of a set, which could be understood as iota, but Matthewson
insists on a choice function analysis. Demirdache (1997) and Matthewson (1998) further claim
that Salish DPs are always linked to the here and now of current discourse. These DPs are so
deeply tied to the actual context that Demirdache goes as far as to argue that Salish DPs denote
stages of individuals rather that individuals. In the same vein, Matthewson characterizes the D as
deictic and the DP as taking always the highest possible scope, and Gillon (2006, 2009)
generalizes the characterization deictic to other languages of the Salish family.
We will not insist on the Salish data (but see the Appendix), but rather on the syntactic
aspects of Matthewson’s proposal, namely (a) that the domain of Q becomes an individual, and
(b) that the Q thus combines with an individual and not a set. These are proposed as a strong
hypothesis— the strategy employed in all languages. Giannakidou (2004) and Etxeberria (2005)
point out empirical problems with this assumption that we summarize quickly next.
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2.2 Problems with the assumption that the domain of Q is e

The obvious prediction of Matthewson’s proposal is that Qs should be able to combine with DPs
crosslinguistically. However, this prediction is not borne out. We illustrate below with English,
Greek and Spanish, but non-compatibility of Q with DP seems to characterizes generally
languages that possess a distinction between DP and QP.

English:
(14) a. * every the boy f. all the boys
b. * most the boys g. only the boys
c. * many the boys
d. * three the boys
Spanish:
(15) a. * cada los chicos f. todos los chicos
lit.: ‘each the boys’ ‘all the boys’
b. * la majoria los chicos g. sólo los chicos
lit.: ‘most the boys’ ‘only the boys’
c. * muchos los chicos
lit.: ‘many the boys’
d. * tres los chicos
lit.: ‘three the boys’
Greek:
(16) a. * kathe to aghori d. ola ta aghoria
lit.: ‘every the boy’ ‘all the boys’
b. * merika ta aghoria e. mono ta aghoria
lit.: ‘several the boys’ ‘only the boys’
c. * tria ta aghoria
lit.: ‘three the boys’

Here we see that Q cannot combine with the DP. The grammatical examples—which would fit
Matthewson’s structure— are formed with all and only, elements that have been argued not to be
Qs, and which can have alternative analyses as adverbial modifiers of DPs (see Brisson 1998,
2003 for all, von Fintel 1997 for only). Many of the ungrammatical examples above become
grammatical as soon as the partitive of is introduced (e.g. most of the boys, many of the boys,
three of the boys). So, there is a correlation between the partitive of-DP in European languages
and bare DP complements of Q in Salish that is being missed in Matthewson’s account.
A second problem has to do exactly with the analysis of the partitive: if Qs combine
directly with elements of type e, partitive of must be argued to be semantically vacuous—pace
Ladusaw (1982), where of ensures that the Q receives an et input. According to Matthewson
indeed, the partitive preposition of is only employed for case only. But in giving up Ladusaw
(1982), we lose the neat semantic explanation for why we need an of-element in languages that
employ it; for more discussion see Giannakidou 2004, Etxeberria 2005, 2008, 2009.
Finally, and this is the observation we want to focus on, Matthewson’s analysis predicts
that, in the typical case, DPs are complements to Qs: [Q [DP]]. However, languages, including
Salish, show evidence for both [Q DP] and [D Q] orders. Consider the data below:
7
(17) a. tákem i smelhmúlhats-a
all D.pl woman(pl)-D
b. zi7zeg’ i sk’wemk’úk’wm’it-a
each D.pl child(pl)-D

(18) a. i tákem-a smúlhats (Matthewson 2001: fn.5)
D.pl all-D woman
b. i zí7zeg’-a sk’wemk’úk’wm’it (Matthewson 1999: (41c))
D.pl each-D child(pl)

It is unclear to us what structure Matthewson would assign to these examples, but obviously,
they do not fit her suggested universal structure [Q DP]. Importantly, examples where the Q is
preceded by the D can also be found in Greek, as shown below:

(19) a. o kathe fititis (Giannakidou 2004: (32b))
D.sg each student
b. * kathe o fititis

And in Basque (a head final language), we find Qs, and not their nominal arguments, to be
composed directly with the D. It follows Q because Basque D is a suffix: 2

(20) a. mutil guzti-ak (Etxeberria 2005: (37a))
boy all-D.pl
b. mutil bakoitz-a (Etxeberria 2005: (37b))
boy each-D.sg

These data, where a D combines with a Q are unexpected under Matthewson’s proposal where D
universally affects the NP argument and creates an individual; and the fact that we noted earlier
that D in these very same languages does not apply to the NP directly suggests that we cannot
adopt wholesale the idea that the domain of a Q is an individual. If we do, we make many wrong
predictions, and we miss the observed interaction between Q and D, which is also observed in
Salish, as we saw. Giannakidou 2004 proposes to capture this interaction by suggesting that D
provides domain restriction in the form of a context set. This analysis will be our starting point.

2 In Hungarian every NP can be expressed in two ways.

(i) a. minden diák
every student
b. az összes diák
the all student
c. * összes az diák
all the student

The relevant example for us is (ib) where the D combines with the Q, and not with its nominal argument, as shown
by (ic), just as our Basque and Greek examples. Thanks to Aniko Liptak for helping us with Hungarian data.

8
2.3 Giannakidou (2004): D can function as a domain restrictor

Giannakidou takes the deictic nature of the Salish DP to indicate that, as an argument, such a DP
is always contextually restricted. She then takes the embedding of DP under Q to indicate that,
in this language (and others like it; see Gillon 2006), Qs combine only with contextualized
domains, never with unrestricted ones. Giannakidou (2004) suggests the following reanalysis of
the Salish data. D contributes a context set (Westerståhl 1984, 1985). This set is indicated as the
contextual variable C, yielding a GQ with a contextually specified set as its generator.

(21) DP 〈〈e, t〉, t〉

D 〈〈e, t〉, 〈〈e, t〉, t〉〉 NP 〈e, t〉

(22) [[ X... a ]] = λP λQ {x: C(x)=1 & P(x) =1} ⊆ {x: Q(x)=1}
(23) [[ ti smúlhats-a ]] = λP {x: C(x)=1 & woman (x) =1} ⊆ {x: P(x)=1}
‘D woman’

In Giannakidou’s analysis we have the standard GQ denotation expected of a definite, only the
domain argument is now intersected with some property C. Once we get this structure, we can
apply Partee’s (1987) type-shifting BE, and go from the GQ to the predicative type 〈e, t〉.3

(24) BE: 〈〈e, t〉, t〉 → 〈e, t〉: λΡ [λx [{x}∈ P]]
et,t

If we assume, along with Partee (1987), Chierchia (1998), and others, that type shifters can have
some kind of syntactic realization, it follows that BE will be covert in SS. The result will be:

(25) QP 〈〈e, t〉, t〉

Q 〈〈e, t〉, 〈〈e, t〉, t〉〉 PP 〈e, t〉

∅ DP 〈〈e, t〉, t〉
BE

D 〈〈e, t〉, 〈〈e, t〉, t〉〉 NP 〈e, t〉

This analysis renders Salish QPs partitive structures, and, Giannakidou argues, is consistent with
the fact that there are no overt partitives in SS.4 Since overt type-shifters block covert shift

3 Matthewson (to appear) argues against the possibility of having the covert type-shifter BE in SS because, it is
claimed, there is no language-internal evidence for it; assuming that BE exists in the language, she notes, would
make incorrect predictions, e.g. that main predicates could have Ds on them, which they cannot. However, claiming
that BE doesn't apply in SS would be a strange gap in the language. The type shifting approach (including the
modifications by Chierchia in terms of covert versus overt type shifters) would allow BE and block it only if there is
an overt element doing what BE does. The question to answer then is: do we have evidence that perhaps D, or
something else, does this in SS? This is our perspective here; cf. §3.
4 Lisa Matthewson (p.c.) mentions that in SS there is a preposition that may perform (along side other functions;
there are only four prepositions in this language) the function that a designated preposition (of) or a case-marker
assumes in other languages. However, this preposition is not required (as of is in English, or de ‘of’ in Spanish). The
9
(Chierchia 1998), the prediction is that languages with overt partitive prepositions -of- or
partitive case (English, Greek, Spanish, Basque, etc.) will block the covert shift. What we saw in
the previous section, i.e. that in these languages the DP does not combine directly with Q, as
well as the contrast between these languages and Salish, are thus readily explained.

To sum up, the upshot of Giannakidou’s reanalysis is the following. First, the structures
where a Q embeds a DP valuable not because they force a syntactic characterization of the
domain argument as an individual, but because they show that contextual domain restriction is
syntactic via D. This idea is further expanded in Gillon (2006, 2009), where she argues that
conveying domain restriction is the main function of D crosslinguistically. As a thesis, the claim
that D conveys domain restriction is an important contribution to the debate of whether domain
restriction is done purely pragmatically or goes through the grammar, pointing in the latter
direction. And the fact that we find D applying to the Q directly (Greek, Basque, and probably
Hungarian as we noted in fn. 2), suggests that the domain restricting function of D can affect
syntactically the Q itself.

3 New proposal: Domain restricting D as a modifier

3.1 Two ways of domain restricting via D: on the NP, or the Q

We will now preserve Giannakidou’s insight, but propose a somewhat simpler analysis, where D
functions not as an individual or GQ forming function, but as a modifier: a function that
preserves the type of its argument, and modifies it by supplying the contextual restriction C.
When D modifies the NP argument and restricts it, we have the following:

(26) [[ D ]] =λP λx P(x) ∩ C(x)
DR et

The D in Salish exhibits typically this case of domain restriction—a type-preserving function,
yielding a contextually salient set of individuals characterized by the NP (P) property.5

(27) Modifier semantics for i…a
[[ i... a ]] =λP λx P(x) ∩ C(x)
et

Salish D applies directly to the nominal domain to restrict it; but European D won’t be able to
restrict the NP—when D is fed an NP it functions referentially in these languages, hence the
need for the partitive preposition to give back the right input (et) for composition with Q. The
application of D on the NP in Salish is consistent with the idea of a lower DP layer (see
DR
especially Szabolcsi 1987, 2009, and more works cited in Alexiadou et al 2008).

examples that are cited in the literature as SS partitives (see Matthewson 1998, 2001) resort to the familiar
structures ‘D weak NP’. Hence, it seems safe to continue to assume that SS lacks a partitive of element (and a
partitive structure) of the English, Romance, Greek, Basque type.
5 A similar result could be achieved by using Chung and Ladusaw’s (2003) Restrict operation:

(i) Contextual Restrict ([λx NP(x)], C) = λx NP(x) ∧ C(x) (Giannakidou 2004: (31))

However, and this is important especially for Greek and Basque, D can also apply to the Q itself, for which a mere
Restrict would not suffice.
10