Determiners and Noun Phrases

In our English XTAG grammar,^18.6 all nouns select the noun phrase (NP) tree structure shown in Figure 18.1. Common nouns do not require determiners in order to form grammatical NPs. Rather than being ungrammatical, singular countable nouns without determiners are restricted in interpretation and can only be interpreted as mass nouns. Allowing all nouns to head determinerless NPs correctly treats the individuation in countable NPs as a property of determiners. Common nouns have negative(``-'') values for determiner features in the lexicon in our analysis and can only acquire a positive(``+'') value for those features if determiners adjoin to them. Other types of NPs such as pronouns and proper nouns have been argued by Abney [#!Abney87!#] to either be determiners or to move to the determiner position because they exhibit determiner-like behavior. We can capture this insight in our system by giving pronouns and proper nouns positive values for determiner features. For example pronouns and proper nouns would be marked as definite, a value that NPs containing common nouns can only obtain by having a definite determiner adjoin. In addition to the determiner features, nouns also have values for features such as reflexive (refl), case, pronoun (pron) and conjunction (conj).

  

Figure 18.1: NP Tree

A single tree structure is selected by simple determiners, an auxiliary tree which adjoins to NP. An example of this determiner tree anchored by the determiner these is shown in Figure 18.2. In addition to the determiner features the tree in Figure 18.2 has noun features such as case (see section 4.4.2), the conj feature to control conjunction (see Chapter 21), rel-clause- (see Chapter 14) and gerund- (see Chapter 17) which prevent determiners from adjoining on top of relative clauses and gerund NPs respectively, and the displ-const feature which is used to simulate multi-component adjunction. Complex determiners such as genitives and partitives also anchor tree structures that adjoin to NP. They differ from the simple determiners in their internal complexity. Details of our treatment of these more complex constructions appear in Sections 18.3 and 18.4. Sequences of determiners, as in the NPs all her dogs or those five dogs are derived by multiple adjunctions of the determiner tree, with each tree anchored by one of the determiners in the sequence. The order in which the determiner trees can adjoin is controlled by features.

  

Figure 18.2: Determiner Trees with Features

This treatment of determiners as adjoining onto NPs is similar to that of [#!Abeille90:TAG!#], and allows us to capture one of the insights of the DP hypothesis, namely that determiners select NPs as complements. In Figure 18.2 the determiner and its NP complement appear in the configuration that is typically used in LTAG to represent selectional relationships. That is, the head serves as the anchor of the tree and it's complement is a sister node in the same elementary tree. The XTAG treatment of determiners uses nine features for representing their properties: definiteness (definite), quantity (quan), cardinality (card), genitive (gen), decreasing (decreas), constancy (const), wh, agreement (agr), and complement (compl). Seven of these features were developed by semanticists for their accounts of semantic phenomena ([#!KeenanStavi86:LP!#], [#!BarwiseCooper81:LP!#], [#!Partee90:BK!#]), another was developed for a semantic account of determiner negation by one of the authors of this determiner analysis ([#!Mateyak97!#]), and the last is the familiar agreement feature. When used together these features also account for a substantial portion of the complex patterns of English determiner sequencing. Although we do not claim to have exhaustively covered the sequencing of determiners in English, we do cover a large subset, both in terms of the phenomena handled and in terms of corpus coverage. The XTAG grammar has also been extended to include complex determiner constructions such as genitives and partitives using these determiner features. Each determiner carries with it a set of values for these features that represents its own properties, and a set of values for the properties of NPs to which can adjoin. The features are crucial to ordering determiners correctly. The semantic definitions underlying the features are given below.

Definiteness:

Possible Values [+/-].
A function f is definite iff f is non-trivial and whenever f(s)  $\neq~\emptyset$ then it is always the intersection of one or more individuals. [#!KeenanStavi86:LP!#]

Quantity:

Possible Values [+/-].
If A and B are sets denoting an NP and associated predicate, respectively; E is a domain in a model M, and F is a bijection from M₁ to M₂, then we say that a determiner satisfies the constraint of quantity if Det_E<<19900>>1AB  $\leftrightarrow$ Det_E<<19901>>2F(A)F(B). [#!Partee90:BK!#]

Cardinality:

Possible Values [+/-].
A determiner D is cardinal iff D $\in$ cardinal numbers $\geq$ 1.

Genitive:

Possible Values [+/-].
Possessive pronouns and the possessive morpheme ('s) are marked gen+; all other nouns are gen-.

Decreasing:

Possible Values [+/-].
A set of Q properties is decreasing iff whenever s$\leq$t and t$\in$Q then s$\in$Q. A function f is decreasing iff for all properties f(s) is a decreasing set. A non-trivial NP (one with a Det) is decreasing iff its denotation in any model is decreasing. [#!KeenanStavi86:LP!#]

Constancy:

Possible Values [+/-].
If A and B are sets denoting an NP and associated predicate, respectively, and E is a domain, then we say that a determiner displays constancy if (A$\cup$B) $\subseteq$ E $\subseteq$ E$^{\prime}$ then Det_EAB  $\leftrightarrow$ Det $_{E^{\prime}}$AB. Modified from [#!Partee90:BK!#]

Complement:

Possible Values [+/-].
A determiner Q is positive complement if and only if for every set X, there exists a continuous set of possible values for the size of the negated determined set, NOT(QX), and the cardinality of QX is the only aspect of QX that can be negated. (adapted from [#!Mateyak97!#])

The wh-feature has been discussed in the linguistics literature mainly in relation to wh-movement and with respect to NPs and nouns as well as determiners. We give a shallow but useful working definition of the wh-feature below:

Wh:

Possible Values [+/-].
Interrogative determiners are wh+; all other determiners are wh-.

The agr feature is inherently a noun feature. While determiners are not morphologically marked for agreement in English many of them are sensitive to number. Many determiners are semantically either singular or plural and must adjoin to nouns which are the same. For example, a can only adjoin to singular nouns (a dog vs $\ast$a dogs while many must have plurals (many dogs vs $\ast$many dog). Other determiners such as some are unspecified for agreement in our analysis because they are compatible with either singulars or plurals (some dog, some dogs). The possible values of agreement for determiners are: [3sg, 3pl, 3]. The determiner tree in Figure 18.2 shows the appropriate feature values for the determiner these, while Table 18.1 shows the corresponding feature values of several other common determiners.

 

Table 18.1: Determiner Features associated with D anchors

Det	definite	quan	card	gen	wh	decreas	const	agr	compl
all	-	+	-	-	-	-	+	3pl	+
both	+	-	-	-	-	-	+	3pl	+
this	+	-	-	-	-	-	+	3sg	-
these	+	-	-	-	-	-	+	3pl	-
that	+	-	-	-	-	-	+	3sg	-
those	+	-	-	-	-	-	+	3pl	-
what	-	-	-	-	+	-	+	3	-
whatever	-	-	-	-	-	-	+	3	-
which	-	-	-	-	+	-	+	3	-
whichever	-	-	-	-	-	-	+	3	-
the	+	-	-	-	-	-	+	3	-
each	-	+	-	-	-	-	+	3sg	-
every	-	+	-	-	-	-	+	3sg	+
a/an	-	+	-	-	-	-	+	3sg	+
some1	-	+	-	-	-	-	+	3	-
some2	-	+	-	-	-	-	-	3pl	-
any	-	+	-	-	-	-	+	3sg	+
another	-	+	-	-	-	-	+	3sg	+
few	-	+	-	-	-	+	-	3pl	-
a few	-	+	-	-	-	-	+	3pl	-
many	-	+	-	-	-	-	-	3pl	+
many a/an	-	+	-	-	-	-	-	3sg	+
several	-	+	-	-	-	-	+	3pl	-
various	-	-	-	-	-	-	+	3pl	-
sundry	-	-	-	-	-	-	+	3pl	-
no	-	+	-	-	-	+	+	3	-
neither	-	-	-	-	-	+	+	3	-
either	-	-	-	-	-	-	+	3	-
GENITIVE	+	-	-	+	-	-	+	UN18.1	-
CARDINAL	-	+	+	-	-	-	+	3pl18.2	-18.3
PARTITIVE	-	+/-18.4	-	-	-	-	+	UN	+/-

 

In addition to the features that represent their own properties, determiners also have features to represent the selectional restrictions they impose on the NPs they take as complements. The selectional restriction features of a determiner appear on the NP footnode of the auxiliary tree that the determiner anchors. The NP_f node in Figure 18.2 shows the selectional feature restriction imposed by these^18.7, while Table 18.2 shows the corresponding selectional feature restrictions of several other determiners.

 

Table 18.2: Selectional Restrictions Imposed by Determiners on the NP foot node

Det	defin	quan	card	gen	wh	decreas	const	agr	compl	e.g.
	-	-	-	-	-	-	-	3pl	-	dogs
all	+	-	-	UN	-	UN	UN	3pl	-	these dogs
	UN	UN	+	UN	UN	UN	UN	3pl	UN	five dogs
	-	-	-	-	-	-	-	3pl	-	dogs
both	+	-	-	UN	-	UN	UN	3pl	-	these dogs
	-	-	-	-	-	-	-	3sg	-	dog
	-	+	UN	UN	-	+	-	3	UN	few dogs
this/that	-	+	UN	UN	-	-	-	3pl	+	many dogs
	UN	UN	+	UN	UN	UN	UN	3sg	UN	five dogs
	-	-	-	-	-	-	-	3pl	-	dogs
these/those	-	+	UN	UN	-	+	-	3pl	UN	few dogs
	UN	UN	+	UN	UN	UN	UN	3pl	UN	five dogs
what/which	-	-	-	-	-	-	-	3	-	dog(s)
whatever	-	+	UN	UN	-	+	-	3	UN	few dogs
whichever	UN	UN	+	UN	UN	UN	UN	3	UN	many dogs
	-	-	-	-	-	-	-	3	-	dog(s)
the	-	+	UN	UN	-	+	-	3	UN	few dogs
	+	-	-	-	-	-	-	UN	-	the me
	-	+	UN	UN	-	-	-	3pl	+	many dogs
	UN	UN	+	UN	UN	UN	UN	3	UN	five dogs
	-	-	-	-	-	-	-	3sg	-	dog
every/each	-	+	UN	UN	-	+	-	3	UN	few dogs
	UN	UN	+	UN	UN	UN	UN	3	UN	five dogs
a/an	-	-	-	-	-	-	-	3sg	-	dog
some1,2	-	-	-	-	-	-	-	3	-	dog(s)
some1	UN	UN	+	UN	UN	UN	UN	3pl	UN	dogs
	-	-	-	-	-	-	-	3sg	-	dog
any	-	+	UN	UN	-	+	-	3	UN	few dogs
	UN	UN	+	UN	UN	UN	UN	3	UN	five dogs
	-	-	-	-	-	-	-	3sg	-	dog
another	-	+	UN	UN	-	+	-	3	UN	few dogs
	UN	UN	+	UN	UN	UN	UN	3	UN	five dogs
few	-	-	-	-	-	-	-	3pl	-	dogs
a few	-	-	-	-	-	-	-	3pl	-	dogs
many	-	-	-	-	-	-	-	3pl	-	dogs
many a/an	-	-	-	-	-	-	-	3sg	-	dog
several	-	-	-	-	-	-	-	3pl	-	dogs
various	-	-	-	-	-	-	-	3pl	-	dogs
sundry	-	-	-	-	-	-	-	3pl	-	dogs
no	-	-	-	-	-	-	-	3	-	dog(s)
neither	-	-	-	-	-	-	-	3sg	-	dog
either	-	-	-	-	-	-	-	3sg	-	dog

 

 

Table 18.3: Selectional Restrictions Imposed by Groups of Determiners/Determiner Constructions

Det	definite	quan	card	gen	wh	decreas	const	agr	compl
	-	-	-	-	-	-	-	3	-
	-	+	UN	UN	-	+	-	3	UN
GENITIVE	-	+	UN	UN	-	-	-	3pl	+
	UN	UN	+	UN	UN	UN	UN	3	UN
	-	+	-	-	-	-	+	3pl	-
	-	-	-	-	-	-	+	3pl	-
CARDINAL	-	-	-	-	-	-	-	3pl18.5	-
PARTITIVE	UN	UN	UN	UN	-	UN	UN	UN	UN