There is, however, a third and more general way of describing languages. As native speakers of English, we know intuitively when a string of words is a possible sentence in the language, and when it is not, even though it may be a sentence we have never seen or heard before. Perhaps, then, it is a sensible strategy to try and specify a finite, and if possible small, number of abstract criteria that any sentence in English has to fulfill; criteria which we, as English speakers, draw on when making judgements about grammaticality.
This raises some interesting questions about the cognitive basis of linguistic knowledge. How is it that we are able to make such judgements? What does it mean to `know a language' or to have `learned a language'? Clearly, to learn a language is not simply to learn lists of sentences. A small child does not just memorize and imitate her parent's speech; indeed, children's language has its own unique features, and we can plot quite distinct stages of its development over time. Often, very small children correctly use irregular verb forms like `came' and `went' when they first begin to form simple sentences, but later mysteriously lapse into forms like `comed' and `goed'. Or they may form plurals like `mouses' and `foots' even though they have heard their parents use the words `mice' and `feet', and despite their parents' exasperated attempts to correct them. The psycholinguist Courtney Cazden (1972, p. 92) gives the following example of a conversation between an adult and child:
Child: My teacher holded the baby rabbits and we patted them.
Adult: Did you say your teacher held the baby rabbits?
Child: Yes.
Adult: What did you say she did?
Child: She holded the baby rabbits and we patted them.
Adult: Did you say she held them tightly?
Child: No, she holded them loosely.
From this kind of evidence, it would seem that children gradually acquire some very general principles governing the forms of words in their language. They learn, for example, that the past tense of a verb can be formed by adding the sound `-ed'. Then they overgeneralize the rule, and produce incorrect forms like `holded'. Or they acquire the rule that plurals can be formed by adding the sound `-s' to a noun, and again they overgeneralize. Only later do they learn specific exceptions to the rules. In chapter 8 we describe a program that attempts to model the development of children in forming the past tense of English verbs.
The same mechanism also applies to the learning of formal rules for the construction of sentences. How, for instance, do we learn to form questions? As children we might have heard sentences like
The doll which is in the toy box is wearing a pink dress.
and know that to question statements like that, adults begin their sentence with ``Is ...?'' So we might hypothesize that to form a question, we move the first occurrence of `is' to the front:
Is the doll which in the toy box is wearing a pink dress?
But this is clearly wrong. It is not so much to do with the positions of words in sentences as with their grammatical function. We very quickly learn that the main verb in what grammarians call the main clause should be moved to the front, not the verb in the subordinate relative clause:
Is the doll which is in the toy box wearing a pink dress?
A theory of a natural language, then, is a theory about the underlying rules of word-structure and sentence-structure that its native speakers have acquired during infancy. These rules have been abstracted from actual utterances, and they can be used to produce and understand new sentences. This does not mean to say that a child can recite the rules that govern English language, but rather that people, children and adults, produce and understand language as if driven by rules. Whether the rules of language structure do exist in the mind, but are hidden from conscious inspection, or whether describing people's language as `rule governed' is just a convenient way of saying that it `shows regularity', in the same way that the orbit of a planet shows regularity, is a deep issue of philosophy and psychology.
Nevertheless, describing language in terms of underlying rules of structure makes sense: a string of words is a sentence in a language not according to whether it appears in some hypothetical database (and in any case, who would decide, and by what criteria, which strings should be in the list and which not?), nor whether it matches some pattern in a set of sentence patterns, but according to whether it meets certain conditions for sentence-hood, such conditions being implicitly known to speakers of the language and constituting, when formally expressed, the grammar of the language. This third method for describing languages has on its side not merely economy, productivity, and efficiency but also cognitive plausibility.
The conditions for sentence-hood can, as we shall see, be expressed quite simply and elegantly as sets of rules. Before we characterize these rules we shall explain the term `grammar'. We may provisionally think of the grammar of a language as made up of three parts. (Do not worry if you find this difficult to follow now. It will become clearer, and the terms more familiar, as we work through the chapter.) First, there is a finite set of terminal symbols: the actual words in the language, and the ultimate constituents of sentences. Second, there is a finite set of non-terminal symbols, of which we can distinguish three types:
See table 5.1 for an illustration.
Non-terminal symbols Terminal symbols Distinguished Syntactic Lexical
symbol categories categories
S Noun phrase Noun dog, chair, computer
(i.e., `sentence')
Prepositional Preposition in, through, by
phrase
Adverbial Adverb very, directly, well
phrase
... etc. ... etc. ... etc. ...
Third, a grammar will have a finite set of rules, frequently expressed as phrase-structure rules (sometimes called `rewrite rules'), which specify all and only the permissible combinations of words in the language. The terminal symbols we shall call the dictionary, or lexicon, of the language; we shall call the set of non-terminal symbols together with the set of rules governing their combination, its syntax. (In the course of your further reading, you may find that many linguists prefer to use the word `syntax' to refer to the study of the rules, rather than to the rules themselves.
In much the same way, the small number of pieces on a chess board (its `dictionary'), together with labels for the types of pieces (`pawns', `knights', `rooks', ...) and the rules for moving and capturing (its `syntax') account for the quasi-infinite number of possible chess games.
We shall say that the grammar of a language generates all and only well-formed strings in the language. That is, it will generate all the possible sentences and no nonsentences. By `generate' we mean not only that the grammar is able to show the derivation of sentences from the rules for well-formedness but also that, as a consequence, it can `assign a structural description to' those sentences. In other words, it will label the terminal symbols (the words) with lexical category names and show how these can be combined into larger units (syntactic categories) and how these can be ultimately combined together to form a sentence. The term `generate' is in fact neutral as between the production and interpretation of sentences. Later in the chapter we will write a mini-grammar that generates a small subset of English, and leave it as an exercise to you to show how it assigns structural descriptions to sentences.
How might we go about discovering the rules governing the well-formedness of sentences in English? Try to follow the arguments below carefully, and you will get a sense of the method we are using, so that you will be able, as an exercise at the end of the chapter, to extend the grammar yourself. I presume we all intuitively feel that the sentences in (3) below share certain structural features, which are different from those shared by the sentences in (4) below. What is it that distinguishes the two groups of sentences?
3. a. My pet wallaby bit the postman.
b. My mother got your letter.
c. My girlfriend caught a bus.
4. a. My pet wallaby disappeared.
b. My mother died.
c. My girlfriend fainted.
One thing we might say is that the general form of the sentences in (3) is
SUBJECT + SOMETHING-ED + OBJECT
and of (4) is
SUBJECT + SOMETHING-ED
That is, sentences in (3) have a final `direct object'. Since the subject in both groups of sentences can be the same, the difference between the two groups must lie in the rest of the sentence. The verb (the `something' in the above patterns) in each of the sentences in (3) has different properties from that in the sentences in (4). Notice the strangeness of the sentences we get if, for example, we switch the verbs in (3) and (4) around (an asterisk conventionally indicates that the sentence is ungrammatical):
3'. a. *My pet wallaby disappeared the postman.
b. *My mother died your letter.
c. *My girlfriend fainted a bus.
4'. a. *My pet wallaby bit.
b. *My mother got.
c. *My girlfriend caught.
We can now say, then, that there is a lexical category called a `verb', and that, of those words classified in the dictionary as verbs, some require an object while others do not. Verbs requiring an object are called `transitive' verbs, and verbs not requring an object are `intransitive' verbs.
Can we be more specific about the form of the subject and object? Let us go back to one of the Eliza-type patterns and look at some more examples of possible and impossible sentences in the English language. We began with the pattern
[my ??words drinks ??more_words]
and decided that input sentence (5) below produced a grammatical response, shown below as (5'), but that sentence (6) below did not:
5. My aunt Mabel drinks pina colada.
5'. Tell your aunt Mabel to stop drinking pina colada.
6. My collection of drinks is legendary.
6'. *Tell your collection of to stop drinking is legendary.
To get a grammatical response, the subject and the object of the sentence have to be either `noun-phrases' or other expressions which have the same distribution as noun-phrases. That is, they must be able to replace each other in the same position in the sentence. The words `my collection of' do not form a noun-phrase; the words `my aunt Mabel', `the postman', `pina colada', `a bus', and `your letter' do, and as such they all have the same distribution. For example, the sentences in (7) below are all perfectly grammatical sentences -- that is, they are syntactically well-formed -- even if one or two of them have slightly odd meanings:
7. a. The postman bit my mother.
b. My girlfriend burned my pet wallaby.
c. Your letter caught a bus.
d. A bus bit my girlfriend.
So we can say that a possible sentence pattern in English is
NOUN-PHRASE + VERB + NOUN-PHRASE
and you can probably see already that this is a much more formal and specific description of a sentence than our original Eliza-like sentence pattern (we will describe later how a computer program would go about recognizing a noun-phrase or a verb). The sentences in (8) below, like those in (7), are also syntactically well-formed, but differ from those in (7) in having intransitive rather than transitive verbs as main verbs:
8. a. The postman disappeared.
b. A bus died.
c. Your letter fainted.
d. My pet wallaby escaped.
The underlying pattern of these sentences is
NOUN-PHRASE + VERB
So we can see that an initial noun-phrase can be followed by either a transitive verb and another noun-phrase or an intransitive verb. Schematically, we can represent that rule as follows:
In other words, a <TRANSITIVE VERB + NOUN-PHRASE> has the same distribution as an <INTRANSITIVE VERB>, and we can easily demonstrate this fact by listing two sentences which have the same meaning and which differ only in the transitivity of the verb:
![[IMAGE ]](img2.gif){kind=link}
9. a. My pet wallaby kicked the bucket.
b. My pet wallaby died.
In each case, the sentence is made up of a subject and a predicate, and the predicate can have one of two forms, depending on the transitivity of the verb. In fact, predicates can be made up of other things as well, so we shall be more specific and say that, in the above cases, the sentence is made up of an initial noun-phrase and a following verb-phrase. We can write the phrase-structure rules that we have discovered so far in the following conventional form:
S [IMAGE ] NP VP (rule 1)
VP [IMAGE ] Vtrans NP (rule 2)
VP [IMAGE ] Vintrans (rule 3)
The rules are numbered for ease of reference in figure 5.1. The numbering has no other significance.
The non-terminal symbol S stands for `sentence', NP for `noun-phrase', VP for `verb-phrase', Vtrans for `transitive verb', and Vintrans for `intransitive verb'. The arrow `[IMAGE ]' means `can be replaced by' or `may be made up of'. Thus, the first rule can be read as ``A sentence can be replaced by a noun-phrase followed by a verb-phrase.'' Notice, too, that we can establish a one-to-one correspondence between the lexical category symbols `Vtrans' and `Vintrans' and the lexical items `kicked' and `died', respectively. Consequently, we can add to our rewrite rules the following two lexical rules:
Vtrans [IMAGE ] kicked (rule 4)
Vintrans [IMAGE ] died (rule 5)
We can now draw a diagram, called a phrase-marker or parse-tree, to show how these rules capture the syntactic structure of the sentences in (9) (see figure 5.1). In (9a) we can identify a noun-phrase1 (`My pet wallaby'), followed by a transitive verb (`kicked') and a noun-phrase2 (`the bucket'). The verb and the following noun-phrase2 combine to make up a verb-phrase; the noun-phrase1 and the following verb-phrase in turn combine to make a sentence. You will notice that lines connect Vtrans and Vintrans to single words, while a triangle extends from NP over the words making up the noun-phrase; this is because we have not yet analyzed the internal structure of noun-phrases. Conventionally, linguists use such triangles from non-terminals to indicate that they are not concerned with the internal structure of a phrase. If you now compare the form of the parse-trees with the form of the phrase-structure rules, you will see that reading the parse-trees from top to bottom is much like reading the phrase-structure rules from left to right. The difference between the two formalisms is that a parse-tree indicates the structure of a single string of words, while phrase-structure rules specify all, and only, the permissible strings of a language.
[IMAGE ]
Figure 5.1: Parse-trees for sentences (9a) and (9b).
Just as we have been able to analyze a VP into its ultimate constituents, so too we can analyze the structure of an NP. In the following sentences the initial NPs all have the same distribution -- they can all occur in the same syntactic `slot' in the sentence:
10. a. The grey squirrel drank a pink gin.
b. Harvey drank a pink gin.
c. He drank a pink gin.
Yet the three NPs have different forms: `he' is a pronoun; `Harvey' is a name or `proper noun'; and `the grey squirrel' is made up of the definite article `the' (which we shall symbolize by `Det' for `determiner'), the adjective `grey', and the noun `squirrel'. Expressing these facts as phrase-structure rules, we get
NP [IMAGE ] Pronoun
NP [IMAGE ] PropN
NP [IMAGE ] Det Adj Noun
It is quite possible, however, that a noun may be preceded by more than one adjective, as in `long slow cold pink gin'. This would mean that we would have to write an indefinite number of NP rules to capture the fact, which goes against the spirit of our grammar. So instead of writing further rules such as
NP [IMAGE ] Det Adj Adj Noun
NP [IMAGE ] Det Adj Adj Adj Noun
NP [IMAGE ] Det Adj Adj Adj Adj Noun
and so on, we can create a new syntactic category, called `qualified noun', which may be preceded by zero or more adjectives. We shall use the symbol QNoun, and modify our grammar rules thus:
NP [IMAGE ] Pronoun
NP [IMAGE ] PropN
NP [IMAGE ] Det QNoun
QNoun [IMAGE ] Noun
QNoun [IMAGE ] Adj QNoun
The last rule, in which the same symbol, QNoun, appears on both sides of the rewrite arrow, is an instance of a recursive rule -- that is, a rule which allows itself to be reapplied to any depth of embedding. Although not a familiar concept, recursion does sometimes turn up in everyday descriptions, such as the story in which a quick-witted child is granted three wishes and replies, ``I would like a huge ice cream, a holiday by the sea, and three more wishes.'' Repetitive events can be restated as recursions -- for example, you could describe pacing out a square as ``To pace out a square do the following: If you get back to your starting place then finish; otherwise walk forward ten paces, then turn left by 90 degrees, then pace out a square.'' Or another example -- when playing a game of cards, dealing all the cards in your hand can be descibed by the following actions: if there are no more cards in your hand then stop; if it is the first card, then hand the card to the player on your right, turn to the next player on the right, and deal the cards; otherwise hand over the top card to the player you are facing, turn to the next player on the right, and deal the cards in your hand.
We can now add the new rules to the phrase-structure rules we have already discovered:
S [IMAGE ] NP VP
VP [IMAGE ] Vtrans NP
VP [IMAGE ] Vintrans
NP [IMAGE ] Pronoun
NP [IMAGE ] PropN
NP [IMAGE ] Det QNoun
QNoun [IMAGE ] Noun
QNoun [IMAGE ] Adj QNoun
[IMAGE ]
Figure 5.2: Parse-tree for sentence (10b).
The parse-tree for sentence (10b), for example, can then be represented in the manner shown in figure 5.2. Adding further lexical rules we get
S [IMAGE ] NP VP
VP [IMAGE ] Vtrans NP
VP [IMAGE ] Vintrans
NP [IMAGE ] Pronoun
NP [IMAGE ] PropN
NP [IMAGE ] Det QNoun
QNoun [IMAGE ] Noun
QNoun [IMAGE ] Adj QNoun
N [IMAGE ] man
N [IMAGE ] squirrel
N [IMAGE ] gin
N [IMAGE ] lemonade
Pron [IMAGE ] he
PropN [IMAGE ] Ralph
Adj [IMAGE ] old
Adj [IMAGE ] pink
Adj [IMAGE ] beautiful
Det [IMAGE ] the
Det [IMAGE ] a
Vtrans [IMAGE ] kicked
Vtrans [IMAGE ] drank
Vtrans [IMAGE ] caught
Vintr [IMAGE ] died
Vintr [IMAGE ] evaporated
Let us now consider how we might supplement our grammar so as to enable it to parse (i.e., syntactically analyze) sentences such as the question with which we began this chapter. To avoid filling up pages of the book with parse-trees, we shall simplify our grammar, making the parse-trees slightly `flatter'. In the first place, we shall omit the Pronoun and Qnoun rules for NPs, since we shall not need to to deal with pronouns and adjectives. This gives us
NP [IMAGE ] PropN (rule 1)
NP [IMAGE ] Det Noun (rule 2)
Next, we require a rule for handling prepositional phrases. We pointed out that the phrase
the gallery in the square containing the monument
is ambiguous; it has two interpretations according to whether we understand it to be the gallery or the square that contains the monument. A grammar to generate a large part of English will inevitably need to be ambiguous; that is, for some sentences it will assign two or more structural descriptions. But for the purposes of our Tourist Guide we only want a subset of English, and a single structural description of the phrase. We shall try out two NP rules for parsing prepositional phrases, both of which will generate the sentence fragment, and then determine which of the two rules gives us only the desired reading:
NP [IMAGE ] NP Prep NP (rule 3)
NP [IMAGE ] Det Noun Prep NP (rule 4)
Although the word `containing', in the phrase `the square containing the monument', is strictly speaking a present participle, for the sake of simplifying the grammar, we shall treat it as though it were a preposition. The new rule 3, together with rule 2, gives us the parse-trees in figures 5.3 and 5.4; that is, rule 3 fails to filter out the reading we do not want. Rule 4, on the other hand, gives us uniquely the parse-tree that we want (shown in figure 5.5).
[IMAGE ]
Figure 5.3: Parse-tree 1 for `the gallery in the square containing the monument'
obtained from rule 3.
[IMAGE ]
Figure 5.4: Parse-tree 2 for `the gallery in the square containing the monument'
obtained from rule 3.
[IMAGE ]
Figure 5.5: Single parse-tree for `the gallery in the square containing the
monument' obtained from rule 4.
As rule 3 will sometimes give us the wrong interpretation of the kinds of questions we are asking of the Guide, we shall discard it (though it might well be a useful rule in some other grammar). Since rule 4, on the other hand, gives us just the desired reading, we shall retain this rule and so incorporate rules 1,2, and 4 in the procedure in our program for recognizing noun-phrases.
We shall restrict questions asking directions of the Tourist Guide to the form ``How do I get to X?'' or ``Can you tell me how to get to X?'' so we can specify the simple grammar of the Tourist Guide by the following rules:
S [IMAGE ] How do I get to NP
S [IMAGE ] Can you tell me how to get to NP
NP [IMAGE ] PropN
NP [IMAGE ] Det Noun Prep NP
NP [IMAGE ] Det Noun
Noun [IMAGE ] theatre
Noun [IMAGE ] cinema
Noun [IMAGE ] gallery
Noun [IMAGE ] square
Noun [IMAGE ] monument
Det [IMAGE ] the
Det [IMAGE ] a
Prep [IMAGE ] in
Prep [IMAGE ] containing
PropN [IMAGE ] Trafalgar Square
PropN [IMAGE ] The National Gallery
PropN [IMAGE ] Nelsons Column
PropN [IMAGE ] Hyde Park
PropN [IMAGE ] The Serpentine Lake
PropN [IMAGE ] The Tate Gallery
and so on. The `S' rules, of course, are not proper `S' rules for any serious grammar, insofar as they quote words rather than giving syntactic categories, and rely, to that extent, on Eliza-like pattern matching. This is merely a simplification we have permitted ourselves for the program we are developing. This set of grammar rules will now allow us to assign correct structural descriptions to a wide range of questions asking for directions, which in turn will permit us to obtain the meanings of the sentences.