Logical Structure of Noun Agreement

L322

Contents: Argument Structure | Noun Phrases | Count Nouns | Lexicon--Agreement | Nominal Features | Agreement

1. Introduction

The theory of grammar adopted here is that grammar is linked to the semantic notion of conceptual which includes 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. These are linked to similar forms in grammar which form the basis of syntax. In syntax, a proposition takes the form of a sentence.

In grammar predicates take two forms: lexical predicates and operators which are the foundation of a grammar (see Argument Structure). An argument can be an object (noun) or it can be a phrase. 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 (see 322.theta.roles.htm). 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 features. Lexical entries of lexical items contain lexical features. 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 have no sense (see 322 Sense and Reference); otherwise,they somewhat similar to lexical items, and their function is similar. The use of upper case here is used to represent names 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 cannot 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.

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.

 

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 feature [-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 marked 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.

     (13)     TOOTH+[-Pl] --> tooth; TOOTH+[+Pl] --> teeth.

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.

    (14)     DEER+[-Pl] --> deer; DEER+[+Pl] --> deer.

In a number of nouns borrowed from Latin or Greek where the singular is marked by an affix, and the plural by another affix:

    (15)     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

(15e) is a rare and rather unknown Greek variant of (15d). 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 (15e). A stem is the basic morpheme upon which a word is built.

     (16)     THES+[-Pl] --> thesis; THES+[+Pl] --> theses.

 

The approach in 2.3 is what we call a "minimalist" approach which assumes the Least Effort principle"

Don't do it if you don't have to.

That is splitting a word into a stem plus a suffix occurs only if the derived word has two overt morphemes: day+s. This approach bars null suffixes.

In an alternative approach, employing the principle of Consistency:

If you do X in one context, do it in all contexts (unless the result too involved breaking the Least Effort principle with too many subrules).

Here, the singular of all nouns would split into a stem and a suffix, even where the suffix is null: day+[-Pl] -> day+º; day+[+Pl] -> day+z. Now, if the there is no ending and the word itself is changed, then there is no suffix: man+[-Pl] --> men. A null ending would have no function.

However, this approach takes one extra step as far as it is known. And because there are still non-splitting words like "men", there seems to be little advantage to adopting this approach here.

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:



    
  
  1. Lexical Entry
  for dog



dogorthographic form
 


      
+

      
Count

  1. Lexical Entry for water (1)

water orthographic form

-

Count

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

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:

  1. Lexical Entry for cattle

cattle orthographic form

-

Count

+

Plural

  1. Lexical Entry for police

police orthographic form

-

Count

+

Plural

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:

  1. Lexical Entry for water (2)

water orthographic form

-

Count

-

Plural

  1. lexical entry for rice

rice orthographic form

-

Count

-

Plural

Interesting here is the noun people. It is a count noun that is plural only and is not formed with the suffix '-s':

(17).   Six people were standing at the bus stop.

(18).   *One people was standing near the lamp post.

  1. lexical entry for people

people orthographic form

+

Count

+

Plural

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

    (19)     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:

    (20)     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].

Two more features are needed for the grammatical property of nouns. One is gender, and other is Case. Nouns in English are either gender specific or not. We will use the feature abbreviate: [±GS]. Nouns marked [-GS] include all inanimates and species whose gender is not known. Nouns marked [+GS] includes animate nouns whose gender is known. [+GS] marked nouns are further divided into masculine and feminine. Feminine, the marked category, is [+Fem] while masculine is [-Fem]. Case is also a feature of nouns. It is not inherent, but must be filled. Case is covered in another section 322 Case Theory..

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:

BOOK Lexical Form
 book  orthographic form

+

Count
 

Plural

 --

 GS
 

Case

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

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:

BOOK 
 lexical item

book

orthographic form

/bËk/

phonological form

+

Count
 

Plural

--

 GS
 

 Case

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

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

  1. Lexical Entry for ONE

ONE lexical item

one

orthographic form

/w´n/

phonological form

-

Pl

+

Count

--

GS
 

Case

  1. Lexical Entry for FIVE 1

FIVE lexical item

five

orthographic form

/fajv/

phonological form

+

Pl

+

Count

 --

GS
 

Case

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, vase of flowers, a handful of peanuts, 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 example:

(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:

(29)

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.:

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 a priori 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 certain 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 marred 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:

BOOK 
 lexical item

book

orthographic form

/bËk/

phonological form

 N

 category

+

Count
  

Plural

 --

GS
 

Case

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:

Contents: Argument Structure | Noun Phrases | Count Nouns | Lexicon--Agreement | Nominal Features | Agreement

 

Continued on Logical Structure of Noun Agreement 2

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This page last updated 17 JA 2000