Logical Structure of Noun Agreement (2)

L322

Contents:     Agreement | Indefinite Quantifiers | Non-quantified Quantifiers | Generic Quantifiers | Phonological Form | Emphasis | Feature Matrix | Irregular Affixation | Latinate and Greek Affixes | Bibliography

• 3.3     Agreement

First note that the quantifier c-commands BOOK. Short C-command of this sort is called government. Government differs from c-command in that a node can be governed by only one governor, where as a node may be c-commanded by more than one node. If A governs B, then A is called a governor. A governor must also be a head. B is called a governee, but this term is rarely used. The governee is a complement of the governor (head). The closest c-commanding node is the governing node. We may say that government blocks government of an internal node by an outside c-commanding node. This is called a barrier. In the above structure, ONE is an operator whose argument is NP BOOK. ONE functions as the head of the phrase and NP BOOK as its complement. ONE is the governor, and BOOK is the governee.

In Figure (30) note that ONE is a governor of BOOK in that ONE c-commands BOOK, ONE is a head, and there is no node that governs BOOK, such that ONE governs it--i.e., there is no intervening governor. In a sentence such as

(33)     John read one book.

Read governs the NP one book, but it does not govern the NP book since one governs book.

The condition on no intervening governor plays a significant role. In structure (35) below note that Qu (one) governs both the phrasal complement NP, and the head of the NP, N. However, Qu (one) cannot govern any complement of the head N, since the head N always governs its complement or complements; e.g.:

(34)     John read one book of verses.

(35)

Qu (one) governs NP, N; N (book) governs PP, P; P governs QuP, Qu; and Qu governs NP, N (verse).

Next, let us establish link between the governor and the governed predicate; here, a link is established between ONE and BOOK:

(36)

Next, we propose that features may be copied and transferred through the link. The plus feature of [+Pl] is copied and transferred to the empty Plural slot in the feature matrix of BOOK:

(37)

Now, BOOK is marked with a value for plural. The noun will not crash with respect to this feature.

Note that both forms are marked as [+Ct]. In this respect they agree. They agree now in both features. Suppose "*one water" is generated, where water is a non-count noun:

(38)

The features of Count do not match; one is plus, the other minus. Therefore, these features clash. When there is a clash, the construction is rendered ungrammatical. The goal of linking is to ensure that all duplicate features match.

• 3.4     Indefinite quantifiers

Next is the problem of the so-called indefinite quantifiers: some, few, many, much, more, less, a few, little, fewer, and so forth. This lies is opposed to the so-called definite numerals: one, two, five, one half, two thirds, 11/35ths, -8, -1.5, -234.82815, p (the circumference of a circle divided by its radius), the square root of minus one, irreal numbers, and so forth. These numerals are [+Count] ([+Ct]). Some count nouns can be modified by the indefinite quantifiers:

(39a)     Four books.

(39b)     Some books.

We cannot use the features definite or specific since these are already conscripted for other uses. Let us use the feature "fixed value" (FV) to differentiate the definite set of numeric quantifiers from the indefinite set.

Fix value has one interesting property. If a quantifier is [-Qf] (quantified), the feature FV is always negative. That is, if something is not quantified, it cannot have a fixed value. Hence the feature is NIL if [NULL]; otherwise it is marked.

The indefinite quantifier some as in some books, for example, contains at least the following features

(40a)

SOME	lexical form
some	orthographic form
/s^m/	phonological form
NIL	Count
NIL	Plural
NIL	FV
Qu	category
___NP	subcategorization

The NIL features for Count and Plural are discussed below.

Definite quantifiers are marked with the feature [+FV] as five in five books:

(40b)

FIVE	lexical form
five	orthographic form
/fajv/	phonological form
+	Count
+	Plural
+	FV
Qu	category
___NP	subcategorization

Certain indefinite quantifiers may modify non-count nouns:

(41a)    some water

(41b)     *five waters (in the normal sense of water)

The quantifier some can modify either mass nouns or count nouns:

(42a)     some books, some fingers, some houses, some students.

(42b)     some rice, some water, some snow, some air, some smoke.

Note that when it is modifying count nouns, the count noun is always plural; when it is modifying mass nouns, the mass noun is always singular:

(43)     *some book; *some rices (in the intended meaning).

This is true for all the non-fixed quantifiers that can modify either mass or count nouns (lots of, a lot of). This leads to a generalization: if a quantifier may modify both count and mass nouns, the count noun is always plural and the mass nouns is always singular.

Rather than have two quantifiers, e.g. some-1 and some-2, suppose some is not marked for either +Ct or -Ct, but is NIL, which means that it is underspecified, and that it must agree with the noun for this feature:

(44)       SOME [NIL Ct] BOOK [+Ct] --> SOME [+Ct] BOOK [+Ct].

Because of the above generalization, we can predict that the NIL feature of number in this class of quantifiers is [+Pl] if [+Ct], and [-Pl] if [-Ct]. Once number has been determined for the quantifier, then the nouns will copy the feature (agreement):

(45)      SOME [NIL Ct, NIL Pl] BOOK [+Ct, NIL Pl]

         SOME [+Ct, NIL Pl] BOOK [+CT, NIL Pl]

         SOME [+Ct, + Pl] BOOK [+CT, NIL Pl]

         SOME [+Ct, + Pl] BOOK [+CT, +Pl]. (= some books)

(46)     SOME [NIL Ct, NIL Pl] RICE [-Ct, NIL Pl]

         SOME [- Ct, NIL Pl] RICE [-Ct, NIL Pl]

         SOME [- Ct, -Pl] RICE [-Ct, NIL Pl]

         SOME [- Ct, -Pl] RICE [-Ct, -Pl]. (= some rice).

The lexical entry for some is given above in (40a).

Several and similar quantifiers differs from some in that it is inherently [+Ct]:

(47a)     several books

(47b)     *several rice.

We can now use the generalization that indefinite quantifiers which are marked at some point for the feature [+Ct] are [+Pl]. The lexical entry for several is now the following:

(48)

SEVERAL	lexical form
several	orthographic form
/sEvrl//	phonological form
+	Count
NIL	Plural
--	FV
Qu	category
___NP	subcategorization

The quantifier much is similar to the quantifier little except that is can only occur in questions and negative constructions:

(48a)     *much water

(48b)     not much water

(48c)     how much water?

(48c)     *much books

This interesting property lies beyond the scope of our topic here. Many does not have this restriction:

(49a)     *many waters (in the normal sense of water)

(49b)     many books.

(49c)      not many books.

(49d)      how many books?

much as -Ct, and many as +Ct (40a):

(50a)

MUCH	lexical form
much	orthographic form
/m/	phonological form
--	Count
NIL	Plural
+	Quantified
-	FV
Qu	category
___NP	subcategorization

(50b)

MANY	lexical form
many	orthographic form
/mEni/	phonological form
+	Count
NIL	Plural
+	Quantified
-	FV
Qu	category
___NP	subcategorization

One final point here. Some, as well as more, less are marked ±Ct, which means they can modify either count or mass noun. We have also marked them ±Pl. This is an oversimplification. When this class of quantifiers modifies count nouns, the noun is always plural; when it modifies mass nouns, the noun is always singular:

(51a)    more books are

(51b)    more water is

(51c)    *more book is

(51d)    *more waters are (in the normal sense of the term.)

• 3.5      Non-quantified quantifiers

Under certain conditions mass and plural count nouns occur unmodified by an overt quantifier. We will consider the quantifier feature here as "unquantified":

(52a)     Mary went to the store to buy potatoes for dinner.

(52b)    Tomorrow John will buy the necessary parts for his car.

There is one or more constraints on this construction. Although all the conditions are not known, it apparently cannot occur in the subject position of an active voice verb:

(53a)    *Students went to the store to buy a few books.

(53b)     Potatoes were bought for dinner (<- X bought potatoes for dinner),

        (where X is an unknown agent).

This quantifier contrast with quantified quantifiers (one, some, more) by failing to mark a quantity.

Since we do not consider the feature of plurality inherent in count nouns, but subject to agreement with that in the quantifier, we differentiate quantified quantifiers from unquantified quantifiers by the feature "Qf" (for [±Quantified]. Quantifiers marked [-Qf] are phonetically null. The null quantifier is like other indefinite quantifiers in that is may modify a count noun, which must be plural, and a mass noun, which must be singular:

(54) books, *book, rice, *rices. (As in "John likes ____).

(55)

[NULL]	lexical form
--	orthographic form
//	phonological form
NIL	Count
NIL	Plural
--	FV
--	Qf
Qu	category
___NP	subcategorization

This class should not be confused with generic quantifiers which are also null.

• 3.6      Generic quantifiers

Finally we need to differentiate between the unquantified quantifiers mentioned above and generic unquantified quantifiers. Null generic unquantified quantifiers may occur in the subject position of active clauses as well as in the direct object position:

(48a)     Monkeys like bananas for dinner.

(48b)     Some monkeys like bananas for dinner.

(39) seems to imply that all or nearly all monkeys like at least one banana for dinner. They seem to mark an indefinite but unspecified quantity. These quantifiers are plural (47) if they mark count nouns and singular if they mark mass nouns:

(49)     Water is necessary for life.

Water is a mass noun and is singular (*Water are ...).

A second type of a generic quantifier is singular, but has nearly the same meaning as the above quantifier, and it is modified by the definite determiner, or it may be indefinite:

(50a)     The monkey likes bananas.

(50b)     A monkey likes bananas.

The feature [+Generic] is proposed here to refer to these two types of generic quantifiers and [-Generic] to the the remainder. [-Generic] is considered to be the default or unmarked feature.

The null quantifier in (48) is [+Generic, +Count, +Plural], that in (49) is [+Generic, -Count, -Plural]. The null quantifier in (50) is [+Generic, +Count, -Plural]. The evidence that it is [+Count] is that it cannot modify mass nouns:

(51a)     *The water is necessary for life.

(51b)     *A water is necessary for life.

Thus the null quantifier in (48) is:

(52a)

	lexical form
[NULL]	orthographic form
//	phonological form
NIL	Count
NIL	Plural
NIL	FV
--	Qf
+	Generic
Qu	category
___NP	subcategorization

The null quantifier in (49) is:

(52b)

	lexical form
[NULL]	orthographic form
//	phonological form
NIL	Count
NIL	Plural
NIL	FV
--	Qf
+	Generic
-	definiteness
Qu	category
___NP	subcategorization

And the indefinite general (non-generic) quantifier is:

(52d)

	lexical form
[NULL]	orthographic form
//	phonological form
NIL	Count
NIL	Plural
NIL	FV
--	Qf
-	Generic
Qu	category
___NP	subcategorization

The lexical entry for five (40b) and similar definite quantifiers is the following; definiteness is not marked and is thus empty:

(52e)

FIVE	lexical form
five	orthographic form
/fajv/	phonological form
+	Count
+	Plural
+	FV
+	Qf
Qu	category
___NP	subcategorization

• 3.7     Feature Matrix of Quantifiers.

'º' means that the feature does not occur. NIL means that it must be filled:

(53)

Quantifier	Count	Plural	Fixed Value	Quantified
[-Qf]	NIL	NIL	ø	--
one	+	--	+	+
two - infinity	+	+	+	+
couple	+	+	+	+
some	NIL	NIL	--	+
several	+	+	--	+
few	+	+	--	+
a few	+	+	--	+
many	+	+	--	+
much	--	--	--	+
a lot	NIL	NIL	--	+
lots of	--	--	--	+
little	--	--	--	+

• 3.8     Determining the Phonological Form of the Lexical Item

Once all the features are in place, we may determine the phonological form of the lexical item. Here, the phonological and the orthographic forms of each lexical item are inserted. The singular of BOOK is spelled out as book in the orthography, and ONE is spelled out as 'a ' if is not marked as emphatic; if it is emphatic is spelled out as 'one '. We will return to this below:

Now let us consider five books. The logical form is:

FIVE contains the feature [+Pl], differentiating it from ONE. The first pass to the lexicon fills in the categorial and other features:

The link is established between the governor and the governee, and the plus feature of the governor is copied onto the governee:

(41)

There is no problem in spelling out FIVE. The lexical entry for FIVE gives five (/fajv/). The spelling out of the plural form of BOOK is more interesting. This we shall do in the following subsection.

• 3.5     Emphasis in the Quantifier

As noted above the difference between 'a' and 'one' is basically one of emphasis:

(42a)     John bought a book.

(42b)     John bought one book.

Note that it is only one book that John bought in (42a), the same number as in (42b). In (42b) the speaker is emphasizing the number. Emphasis is both a feature of many parts of speech and an operator. We won't cover the operator aspect of quantifiers at this time. Note also:

(43a)     John bought the book that Mary had read.

(43b)     John bought the one book that Mary had read.

Here again, it is only one book that John has bought in both sentences. The speaker is emphasis that Mary had read one book.

'a' is a reduced form of one when it is not emphatic. This form is used when no determiner is used. If a determiner is used, the unemphatic form is null. The lexical form for 'a', 'one', and [NULL] here we write as ONE. It is spelled out as one if emphatic. If it is not emphatic it is spelled out as 'a' if no determiner, as [NULL] if there is a determiner:

(44)        ONE --> one / _____ , [+Emph]

          ONE --> a / [D -Def ] _____ , [-Emph, -Voc]

ONE --> an / [D -Def ] _____. [-Emph, +Voc]

          ONE --> [NULL] / [D [+Def] _____ , [-Emph].

On html files, we use the convention of an underscore plus a comma plus a feature to indicate that the feature is part of the form that occurs in the underscore position. There are other ways to write this, but this is the easiest.

• 3.6     The Spelling Out of Plural Nouns

Let us start with irregular nouns of the following type:

(45)     a.      foot, feet

        b.      tooth, teeth

        c.      goose, geese

Foot and feet are usually considered different words, but intuitively, nearly everyone feels that they are related. They are: they are both linked to the same lexical entry: that of FOOT. These two words differ only in the feature of Plural. Recall that the feature of Plural is empty in most nouns in English. This is the only feature that is empty. Once this feature is filled, two words occur: one marked [+Pl] and the other [-Pl]. The initial form is an underspecified feature matrix. From this form are derived the singular and plural words. All three forms constitute the lexical entry of FOOT. Note the main property of [Object] is that has no arguments (dog, house, pencil) :

46

FOOT	lexical entry
+	Count
NIL	Plural
N	category
[Thing]	type
	subcategorization
[-Pers]	Personal
Object	Conc. Feature

47

+	Plural		-	Plural
foot	orth. form		feet	orth. form
/fËt/	phon. form		/fit/	phon. form

The lower set of features cannot be applied until agreement has been applied. We cannot spell out FOOT until we know it is [+Plural] or [-Plural]. If it is [+Plural], then it is spelled out as foot; if it is [-Plural], it is spelled out as feet.

The orthographic and phonological forms have been moved to the word matrices, since these forms can't be spelled out until the missing features have been inserted. In the original matrix we replace the orthographic form with the morpheme that underlies the word. The plural of the noun in this class are irregular in that there is no way to predict the differences in the forms differentiating the singular from the plural.

We may think of the first pass to the lexicon as establishing a link between the lexical item in the syntax and the lexical entry. Once the proper features are filled in, the orthographic and phonological forms are filled in. This is equivalent to the second lexical pass. The lexicon resides in an area separate from the syntax and phonology, but linked to it.

For the small class of nouns whose singular and plural form are identical:

(48)      sheep, deer, elk, antelope, and so forth,

we may simplify the lexical entry to:

(49)

Lexical Entry for SHEEP

SHEEP	lexical item
+	Count
NIL	Plural
N	category
	subcategorization
[Object]	Conc. type

(50)

+/-	Plural
sheep	orthographic form
/¢ip/	phonological form

The symbol "+/-" is a convenient way to represent two words, one plural one singular, when they have the same forms.

The normal plural of nouns involves a bit more. The normal plural is formed with the suffix {S} which has the basic allomorph /z/. Let us start with book. Its plural is books. Here, the ending `-s' is a separate morpheme.Before the phonological shape of the lexical item can be assigned, the default rule applies splitting N into N plus Num. Note that `N' and `Num' are arbitrary names which we list for convenience of the reader:

This process occurs in the lexicon. It occurs after the irregular rules mentioned above have taken place. Default rules are always applied last when a set of rules applying to a particular form apply. The following is the rule of Plural Affix Formation: (PAF)

(52a)     Plural Affix Formation

(52b)     [N, +Pl] --> [N] + [+Pl].    

(The '+' sign indicates morpheme boundary. The copied category is a stem (N), the other form an affix (here, [+Pl] is a suffix that follows the stem.

(52c)     [Default Rule] (Unmarked rule in Grammar)

PAF does not apply to such words as geese and sheep, because [+Pl] has been spelled out as a particular lexical item (word). "N" is defined here to mean all the features that define the category commonly called a noun. The feature [+Pl] is selected since it is specifically copied and assigned to the newly created suffix ([Suf]). Thus N in both halves of the rule refers to the features of N except [+Pl]. [+Pl] is a feature of N, but the rule applies specifically to it.

[Suf, +Pl] is linked to the morpheme {S} which occurs in the grammatical morphemes component of the lexicon. {S} is a morpheme which contains several allomorphs. The first allomorph is /^z/, the default. The phonological rules of English will derive the three variants of /^z/: [z], [^z], and [s]. We presume that the result of plural affixation (PAF) forms of a word that is learned in the conscious part of the mind. The underlying process occurs in the subconscious mind. That is, book and books, or more formally, [book] and [[book]+[s]], we have instant recall to, but we cannot directly access what goes on in the subconscious mind, where the rules are developed for grammar.

• 3.7     Irregular affixation

In addition to the default ending {S}, there are irregular endings. These must apply before the default rule. The suffix `-en' occurs in up to three nouns in modern English. 3

The examples are:

(53)     a.      ox ox+en

        b.     child childr+en

        c.     brother brethr+en

The form brethren has limited usage: it is used mainly in congregations of certain churches. The form is a hold over from an earlier period when it was the normal plural of brother. Based on brethren we assume the analysis of the plural to be that in (42b). The `-r' at the end of childr- we analyze as a formative morpheme extending the stem. Such stem extensions are extremely rare in modern English nouns. The singular stem is pronounced differently from the plural, they are spelled the same. They form different allomorphs of the morpheme {CHILD}.

The lexical entry for ox must include information about the plural:

54

Lexical Entry for OX (1)

OX	lexical item
ox	orthographic form
/aks/	phonological form
+	Count
NIL	Plural

55

+	Plural
suffix	form type
-en	orthographic form
/^n/	phonological form

It is possible to simplify the plural form to eliminate a small amount of redundancy. Suppose we mark the plural form with the allomorph /^n/. This is linked to the allomorph /^n/ of the morpheme {S} introduced above:

(56)

Lexical Entry for OX

OX	lexical item
ox	orthographic form
/aks/	phonological form
+	Count
NIL	Plural
N	category
[Object]	type
	subcategorization

+	Plural
/^n/	allomorph

The lower box is a property of all nouns mentioned above sharing this ending. The allomorph /^n/ has the following properties listed in the grammatical morpheme component:

57

+	Plural
N+suffix	form type
{S}	morpheme class
/^n/	phonological form

"N+suffix" ensure that the allomorph is adjoined to a noun.

• 3.8     Latinate and Greek affixes

Nouns of this class have a distinctive allomorph marking the singular as well as one marking the plural. We will not cover all the variants here. Consider the following pair of nouns:

(58)     radius, radii.

As most of you know the former is singular, the latter is plural. The base form of the morpheme is {RADI}. The best evidence for this is found in derived adjectives where the suffix `-al' is adjoined directly to `radi-':

(59)     radi+al.

We now adopt RADI as the lexical item underlying radius and radii. In addition to the Plural Affix Formation Rule, we now need the exceptional Singular Affix Formation Rule:

1. Singular Affix Formation (SAF)
2. [N, -Pl] [N] + [Suf, -Pl]
3. [applies in marked cases only]

The Singular Affix Formation rule is not a default rule because of its exceptional nature.

(60)

1. Lexical Entry for RADI

RADI	lexical item
radi-	orthographic form
/rédi/	phonological form (bound allomorph)
+	Count
	Plural
N	category
[Object]	type
	subc.

+	Plural
/aj/	allomorph

-	Plural
/´s/	allomorph
SAF	Exceptional Rule

The exceptional Rule, Singular Affix Formation (SAF), applies only when marked unlike the PAF which applies as a default.

Other nouns that belong to this declension type include:

(61 )     a.       memorandum, memoranda

         b.       plica, plicae (a fold or folded part, esp. of skin)

         c.       phenomenon, phenomena

         d.       plasmodesta, plasmodestata (cytoplasmic strands functioning as living links between cells)

         e.       crisis, crises

4.      Other Inherent Features of the Noun

All nouns with the exception of pronouns are third person. This is an inherent feature of nouns. Formally, we call the feature [Personal]. The feature [+Personal] refers to first and second person pronominals. Nouns are [-Personal]. Most nouns do not make reference to gender, or natural sex. We will call this feature [-Gender]. Nouns marked as [+Gender] refer to natural or arbitrary gender. The default gender is masculine. The marked gender is [+Fem] (Feminine), and the unmarked masculine gender is [-Fem]. Arbitrary gender means that gender is selected for inanimate objects that are not distinguished by sex, such as the use of the pronominal she for boats, cars, and other objects commonly or sometimes used. A noun marked as [-Gender] is not expanded to include [Fem].

The entry for BOOK is now expanded to include person and gender:

(62)

Lexical entry for BOOK (3)

BOOK
book	orthographic form
/bËk/	phonological form
+	Count
-	Personal
-	Gender
NIL	Plural
N	category
[Object]	type
	subc.

5.       Bibliography

Bach, Emmon. (1981). `On time, tense, and aspect: an essay in English Metaphysics.' Peter Cole (ed.), Radical Pragmatics 63-81. New York: Academic Press.

DeArmond, Richard C. (1997). Introduction to Syntax. Under Review. Published on the net:

Contents:     Agreement | Indefinite Quantifiers | Non-quantified Quantifiers | Generic Quantifiers | Phonological Form | Emphasis | Feature Matrix | Irregular Affixation | Latinate and Greet Affixes | Bibliography

Go to Course.outline for L322

2.      Note that we leave the brackets unlabelled. Labelling is something that grammarians do for referential purpose. We believe it has no proper place in the grammar.

3.      There in obsolete plural for cow: kyne. `-ne' is a variant of `en'. However, as far as I know, this plural is not found in North American English.

4.       In a theory that permits only binary branching, NP cannot dominate N alone. In such cases, NP and N are the same node; that is, N is the maximal node (phrase) as well as the minimal node (word).

This page last updated 23 SE 99