Logical Structure of Noun Agreement

Contents: Proposition Structure | Noun Phrases | Count Nouns | Lexicon - Agreement | Inherent Features | Agreement | Phonological Form | Irregular Affixation | Latinate and Greet Affixes | Bibliography

1. Introduction

The theory of grammar adopted here is that grammar is based on a logical form based on proposition structure. A proposition is that part of a sentence less its modal modifiers--roughly, the node S. A proposition contains a predicate and its arguments. Predicates take two forms: lexical predicates and operators which are the foundation of a grammar (Propositions). An argument can be an object (noun) or it can be an incomplete proposition. If a predicate is an eventuality (event and states), it takes may take a still undetermined number of arguments. If a predicate is an object, it often takes no arguments; if it represents a relationship, it may take one or more arguments. Let us illustrate with a simple verb:

(1)     John saw Mary.

The verb see requires two arguments: John and Mary--the seer and the seen. The names for these arguments, experiencer and theme, respectively, are discussed in theta roles. Let us represent the logical form of the verb and its arguments in sentence (1) as:

(2)     SEE <experiencer: JOHN> <theme: MARY>.

Forms in upper case represent lexical items. Basic morphemes are written in {CAPS} enclosed in braces. Lexical items may contain two or more morphemes: REWRITE = {RE+WRITE}, REAPPLICATION = {RE+AD+PLIC+AT+ION}. We assume without argument here that they are linked to conceptual structures in semantics. Names are also represented in upper case, though they are, strictly speaking, not lexical items; they are referential and somewhat similar to lexical items, and their function is similar. The use of upper case here is employed for convenience. Note that

(3)     The cat saw a dog.

would have the following logical form ignoring the determiners for the moment:

(4)     SEE <experiencer: CAT> <theme: DOG>.

The representation of noun phrases follows in the next section. In both (2) and (4) SEE is a lexical item whose phonological properties have not been spelled out. That is, SEE has no phonetic form yet. The phonological form of SEE can be determined until certain processes have been applied. This also holds for CAT, DOG, MARY, and JOHN. The processes that apply to nouns are discussed below.

A lexical incomplete proposition such as, (4) can be modified in one of two ways: either by an operator or by a lexical predicate. One example of an operator is TENSE (see verbal operator: tense). An example of a lexical predicate modifier is an adverb:

(5 )      a.     John suddenly saw Mary.

           b.     SUDDENLY < SEE <experiencer: JOHN> <theme>: MARY>>.

(5b) shows that (4) is an argument of SUDDENLY. (5b) may be represented in the following tree structure:

An eventuality (Bach: 1981) contains all events and states. SEE is an event modified by the lexical modifier SUDDENLY. SEE takes two arguments: a theme and an experiencer. An eventuality that is properly modified by the required operators is called an incomplete proposition. See propositions.

In sum, the lexical predicate (a lexical item) and its arguments can be modified by a lexical predicate (an adverb or adverbial in the syntax) or by an operator such as TENSE.

2.     The Noun Phrase -- Part I.

The noun forms the head of a noun phrase. In the logical structure of sentences, the first division is between eventualities and objects. The term eventuality is used to refer to a state or an event. The term object is used to refer to any kind of an object, concrete or abstract, real or imaginary. Let us start with the noun cat.

Conceptually, cat is an object (a thing in Jackendoff's terminology). The lexical item for cat we will write as "CAT." The theme argument of see is an object in (3) . The experiencer argument must be an object. Here, CAT refers to any object that we recognize as a member of the domestic feline species for which we have a common lexical item. There are other meanings for cat, which we will not represent at this time. For example, in colloquial English, a cat may refer to a spiteful woman or to a play or devotee of jazz. Their different meanings will have to be handled in the lexical entry for CAT. We will put this problem aside for now.

Nouns must be marked for the features of Number, Count, Gender, Person, Case, and probably a few other features. We will concentrate on this five ultimately, but let us consider Number and Count here.

• 2.1      Count

Some nouns can be counted and some can not:

(7 )     a.      one dog

           b.     one tooth

           c.     one house

          d.      one country

          e.      one unicorn.

(8)     a.     rice

         b.     snow

         c.     water

         d.     beef

         e.     mud

The nouns in (8 ), often called mass nouns, cannot be counted:

(9)     a.      *one rice

          b.      *one snow

          c.      * two waters

          d.     *five beefs

          e.     *128 muds

Occasionally, there are count nouns that have the same form as mass nouns. They should not be confused:

(10)       John had a beef with his boss.

Here, beef refers to a disagreement, not the edible meet of cows.

•  2.2      Number

Most nouns are inflected for number. The default (the predictable or expected form) for singular nouns is unmarked. The singular form of a noun is a single morpheme marking both the lexical meaning and the grammatical category [-Plural] if there is no overt ending: dog, snow, house, rice, snow, water, beef, mud. If the word contains more than one morpheme, the singular feataure [-Plural] is incorporated into the morpheme of the word that determines that the word is a noun: uni+corn, pre+sup+pos+it+ion, sing+er. For example, in sing+er sing is a verb stem; the suffix '-er' makes it a noun stem. It is the nominal morpheme that is makred for number, not the verbal morpheme.

The default for the plural is the suffix `-s/-es'. The form `-es' is largely predictable: it follows nouns which end in `s', `z', `ch', `sh', `x'. If the noun ends in a consonant plus `y', `y' is replaced with `i' and the plural form is `es':

(11)     loss, loss+es;, church, church+es; dish, dish+es; fox, fox+es; spy, spi+es.

There are various kinds of irregular plurals of nouns. In the first class, the plural form is a single morpheme that is related to the singular morpheme by the change of a vowel:

(12)     tooth, teeth; foot, feet; goose, geese; louse, lice; mouse, mice.

That is, tooth and teeth are each a distinct morpheme, but they are related by being connected to the same lexical entry for tooth:: TOOTH.

Some nouns share the same form for the singular and the plural:

(13)     deer, sheep, elk, antelope.

We consider each form to represent two morphemes: one singular and the other plural. That is, the form deer is either a singular morpheme or it is a plural morpheme. The two morphemes share the same phonological shape, but they differ in terms of the grammatical features they each contain. In a number of nouns borrowed from Latin or Greek where the singular is marked by an affix, and the plural by another affix:

(14)     a.     radi+us, radi+i

            b.     agend+um, agend+a

            c.     dat+um, dat+a

            d.     octop+us, octop+i

            e.     octopu+s, octopod+i

            f.      thes+is, thes+es

            g.     pleur+a, pleur+ae

            h.     criter+ion, criteri+a

(14e) is a rare and rather unknown Greek variant of (14d). The word is a compound formed with "oct-" `8' plus "pod-" `foot.' The Neo-Latin variant treats the stem 'octop' as a single morpheme in place of the compound stem in the Greek variant (14e). A stem is the basic morpheme upon which a word is built.

However, a better analysis for this class of nouns (14) is to assume that the endings 'us', 'um', 'is', 'a', and 'ion' are stem extender morphemes.:

radi+us = noun stem = noun root + stem extender

radi+i = noun (word) = noun root/stem [no extender].

These suffixes are required when the stem is marked as [+Pl]. In this way, [-Pl] is never phonetically marked in Standard English.

• 2.3     Nominal Features

Long prominent in phonology, features have played a less significant role in syntax, though in this decade they have become more significant. Nouns must be marked for the inherent feature [Ct] ([Count]). To illustrate, dog and water are marked as follows:

  
Lexical Enry for dog

dog
orthographic form
 

      
+

      
Count

All nouns must be marked for the feature [+Coun].

The grammatical feature [Pl] ([Plural]) is not necessarily inherent in nouns, though all nouns must be marked for number. A few nouns are inherently marked for number. Words such as cattle and police are inherently plural. They have no singular form:

(15)     a.     Some cattle are grazing in the neighbor's corn field.

           b.     *Some cattle is grazing in the neighbor's corn field.

           c.     The police are on their way.

           d.     *The police is on their way.

          e.     *The police is on its way.

          f.     *The police are on its way.

Both cattle and police are non-count nouns. They have the following feature matrix:

Mass (non-count) nouns are inherently singular. They have no plural form:

(16)      a       *John drinks waters.

            b.      *Many Asians eat rices.

These nouns have the following feature matrix:

Most mass nouns have a countable counterpart. This counterpart means kinds of, types, species of:

(17)     a.     The rices grown in asia are quite varied.

            b.    The waters that flow into the rivers of B.C. are usually cold and clear.

Here, the rices means species of rice, the waters means the different kinds of water. These forms are considered different lexical items from the mass noun counterpart. They can be counted and they may occur in the singular:

(18)     a.       Only one rice grows in southern China.

            b.      Of the waters that flow into the rivers of B.C., only one (water) is not cold and clear.

We will put this problem of varying lexical items aside for now, noting that nouns of this type are marked [+Ct].

With the exception of the noun classes mentioned above and proper names, nouns do not carry inherent number. Yet they must be marked for number. Agreement is the best evidence for it. Suppose we leave the Number feature box empty in the lexicon as the default for nouns:

Next, we propose that all blank features must be specified as plus or minus. If a blank feature fails to be specified, the noun crashes (i.e., the sentence containing it is rendered ungrammatical). How does the feature become specified? That is the topic of next section.

3.      The logical grammar of count nouns

• 3.1     Introduction

First, we represent the lexical item of book as BOOK. It is spelled out as book in English and assigned the phonological form /bËk/. We represent this in the following feature matrix:

 lexical item

Quantifiers, which include all numerals, are operators which modify count nouns. The logical representation of five books is the following:

1. [QUANT [FIVE]] <BOOK>.

In propositional structure the two basic forms are eventualities and objects. Objects refer to the arguments of eventualities that are not eventualities. They refer to things in the real or imaginary world. In our analysis here, objects are subdivided into [THING], [CONTAINER], [RULER], [RELATION], [PART_OF] and other classes that we will not cover here:

[THING] is define here as the class of objects which do not take an argument; for example:

(21)     tree, house, finger, book, table, dirt, sun, fork, shovel, car, unicorn, faun, and so forth.

[CONTAINER] is defined here as the class of objects which take an argument and imply containment:

(22)     cup of tea, basket of fruit, bowl of cherries, glass of milk, box of chocolates, jar of beans, sack of potatoes, pot of gold, and so forth.

Most container nouns are also [THING]s when they refer to the container as an object and not as a container:

(23)     a.     John broke a cup.

           b.     Mary likes woven baskets.

           c.     The bowl has a crack in it.

           d.     Some of those glasses are chipped.

[RULER]. is defined as an individual or a group of individual who rule or control some political group or a group in general:

(24)      a.       the Queen of England

             b.      the bald King of France

             c.      one of the presidents of the United States

             d.      all late prime ministers of Canada

             e.      the coach of the team

             f.      certain leaders of the boy scouts.

[RELATION] is defined as the relation that holds between members of a family in the broader sense of the term. [RELATION]s take one arguments; only one of them is a complement. For eaxample:

(25)     a.       the mother of Susan.

            b.      the father of John and Mary.

            c.      two sisters of the guy next door.

            d.     one of the brothers-in-law of Harry.

'Of NP' is the complement. The subject of the following sentences is the noun that is identified as the relation:

(26)      a.     Judy is the mother of Susan.

            b.     Bill is the father of John and Mary.

            c.     He found Joan and Kathy to be two sisters of the guy next door.

            d.     I knew Horace as one of the brothers-in-law of Harry.

[PART_OF] holds between a part of some object and the object itself:

(27)     a.     the top of the table

           b.     the side of the house

           c.     the back of the chair

           d.     the bottom of the pool.

It is extended to include less concrete relations:

(28)     a.     the end of the road.

           b.     the title of the song

           c.     the form of the balloon

          d.      the sound of music.

There are other objects (noun classes) that take one or more than one argument. We won't list them here.

Now, let us look at the logical structure of one book:

As we stated above the empty feature must be filled. Book can only be singular when in construction with ONE:

(30)     *one books.

Obviously, the feature of ONE must be copied into the missing feature for Plural in BOOK. This we show in the section 4.:

• 3.2.     Feature Agreement in the Lexicon

Agreement is a grammatical rule. It occurs in the syntax.. Before we can elaborate on agreement, we must go to the lexicon to get the feature matrix. The feature matrix is part of the lexical item. Initially the lexical item differentiates between inherent and blank features. This distinction is a property of the lexical item. It is the lexical entry for police, cattle, scissors, pants, and so forth, that tells us that these words are plural. We cannot assume in general that mass nouns are necessarily singular in all languages. We have no apriori way of telling that that police is inherently plural. We must obtain this information from the grammar of a given language. It holds for English.

This holds for count nouns, too. For example, pea is a count noun whereas corn is a mass noun. Both are similar food forms:

(31)     a.     John likes corn.

           b.     *John likes a corn.

           c.     John ate a pea.

           d.    *John ate pea for dinner.

We must look first at the lexical item and view the feature matrix. Certain syntactic rules depend on selected features in the feature matrix. However, the phonological and written form cannot be obtained at this point before sertain rules have applied. The phonological and orthographic form depends on the features that have been filled in as we will show below in the following subsection.

Selecting a lexical item whose features will be copied into the syntax may not be as easy as that which we present below. In figure (27) BOOK is not makred for the feature plural. Number is determined by the quantity operator [QUANT] which modifies BOOK. The feature plural in BOOK must be specified as either plus or minus. To do this, the feature [+Plural] is copied from the operator onto the noun it modifies. Let us first start with the logical structure of one book:. By logical structure we mean the minimal structure before copying rules and other rules apply.

First by convention we must assign a category to each of the objects, operators, and node that dominate them. To do this we will include the categorial label in the lexical entry of every form. Another slot is required:

 lexical item

The new slot is category, and here it is N. Therefore, in the above tree structure, N is selected and assigned to [THING].

The node immediately dominating N is standardly labelled as NP. This view has not been challenged as far as I know. The problem is there is no theory for labelling. (See footnotes below.) As we shall see, the logical term object seems to be the key term here. We shall label the node both as NP, in deference to tradition, and retain object as distinct from [THING]:

The category Qu (for Quantifier) is assigned to ONE:

The problem occurs in labelling the top node. The lower object is an argument of ONE. That means that ONE is the head of the construction. Hence, the upper object should be labelled QuP. However, the node is commonly labelled NP, not QuP or some variant thereof. The structure is commonly called a projection of N. Note that NP used this way corresponds with the object in the structure. The object is the projection. We will retain the label object in all object structures as well as the traditional labels. Labelling the node NP follows the more traditional vies of labelling NPs including those taught in L222:

• 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.

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

(34)

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:

(35)

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:

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     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 asone. 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:

(37)

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     The Spelling Out of Plural Nouns

Let us start with irregular nouns of the following type:

(38)     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:

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:

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

we may simplify the lexical entry to:

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 rule of Plural Affix Formation:

1. Plural Affix Formation
2. [N, +Pl] [N] + [Suf, +Pl]
3. [Default Rule],

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.

• 3.5     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:

(42)     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 brethern 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:

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:

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:

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

• 3.7     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:

(43)     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-':

(44)     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.

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:

(46 )     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:

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: Proposition Structure | Noun Phrases | Count Nouns | Lexical Spell Out | Inherent Features | Agreement | Second Pass | 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).