程序代写代做代考 information theory data structure algorithm Speech and Language Processing. Daniel Jurafsky & James H. Martin. Copyright c© 2018. All

Speech and Language Processing. Daniel Jurafsky & James H. Martin. Copyright c© 2018. All
rights reserved. Draft of September 23, 2018.

CHAPTER

10 Formal Grammars of English
The study of grammar has an ancient pedigree; Panini’s grammar of Sanskrit was
written over two thousand years ago and is still referenced today in teaching San-
skrit. Despite this history, knowledge of grammar remains spotty at best. In this
chapter, we make a preliminary stab at addressing some of these gaps in our knowl-
edge of grammar and syntax, as well as introducing some of the formal mechanisms
that are available for capturing this knowledge in a computationally useful manner.

The word syntax comes from the Greek sýntaxis, meaning “setting out togethersyntax
or arrangement”, and refers to the way words are arranged together. We have seen
various syntactic notions in previous chapters. The regular languages introduced
in Chapter 2 offered a simple way to represent the ordering of strings of words, and
Chapter 3 showed how to compute probabilities for these word sequences. Chapter 8
showed that part-of-speech categories could act as a kind of equivalence class for
words. In this chapter and next few we introduce a variety of syntactic phenomena
and models for syntax and grammar that go well beyond these simpler approaches.

The bulk of this chapter is devoted to the topic of context-free grammars. Context-
free grammars are the backbone of many formal models of the syntax of natural
language (and, for that matter, of computer languages). As such, they are integral to
many computational applications, including grammar checking, semantic interpreta-
tion, dialogue understanding, and machine translation. They are powerful enough to
express sophisticated relations among the words in a sentence, yet computationally
tractable enough that efficient algorithms exist for parsing sentences with them (as
we show in Chapter 11). In Chapter 12, we show that adding probability to context-
free grammars gives us a powerful model of disambiguation. And in Chapter 15 we
show how they provide a systematic framework for semantic interpretation.

In addition to an introduction to this grammar formalism, this chapter also pro-
vides a brief overview of the grammar of English. To illustrate our grammars, we
have chosen a domain that has relatively simple sentences, the Air Traffic Informa-
tion System (ATIS) domain (Hemphill et al., 1990). ATIS systems were an early
example of spoken language systems for helping book airline reservations. Users
try to book flights by conversing with the system, specifying constraints like I’d like
to fly from Atlanta to Denver.

10.1 Constituency

The fundamental notion underlying the idea of constituency is that of abstraction —
groups of words behaving as a single units, or constituents. A significant part of
developing a grammar involves discovering the inventory of constituents present in
the language.

How do words group together in English? Consider the noun phrase, a sequencenoun phrase
of words surrounding at least one noun. Here are some examples of noun phrases

2 CHAPTER 10 • FORMAL GRAMMARS OF ENGLISH

(thanks to Damon Runyon):

Harry the Horse a high-class spot such as Mindy’s
the Broadway coppers the reason he comes into the Hot Box
they three parties from Brooklyn

What evidence do we have that these words group together (or “form constituents”)?
One piece of evidence is that they can all appear in similar syntactic environments,
for example, before a verb.

three parties from Brooklyn arrive. . .
a high-class spot such as Mindy’s attracts. . .
the Broadway coppers love. . .
they sit

But while the whole noun phrase can occur before a verb, this is not true of each
of the individual words that make up a noun phrase. The following are not grammat-
ical sentences of English (recall that we use an asterisk (*) to mark fragments that
are not grammatical English sentences):

*from arrive. . . *as attracts. . .
*the is. . . *spot sat. . .

Thus, to correctly describe facts about the ordering of these words in English, we
must be able to say things like “Noun Phrases can occur before verbs”.

Other kinds of evidence for constituency come from what are called preposed orpreposed
postposed constructions. For example, the prepositional phrase on September sev-postposed
enteenth can be placed in a number of different locations in the following examples,
including at the beginning (preposed) or at the end (postposed):

On September seventeenth, I’d like to fly from Atlanta to Denver
I’d like to fly on September seventeenth from Atlanta to Denver
I’d like to fly from Atlanta to Denver on September seventeenth

But again, while the entire phrase can be placed differently, the individual words
making up the phrase cannot be

*On September, I’d like to fly seventeenth from Atlanta to Denver
*On I’d like to fly September seventeenth from Atlanta to Denver
*I’d like to fly on September from Atlanta to Denver seventeenth

See Radford (1988) for further examples of groups of words behaving as a single
constituent.

10.2 Context-Free Grammars

The most widely used formal system for modeling constituent structure in English
and other natural languages is the Context-Free Grammar, or CFG. Context-CFG
free grammars are also called Phrase-Structure Grammars, and the formalism
is equivalent to Backus-Naur Form, or BNF. The idea of basing a grammar on
constituent structure dates back to the psychologist Wilhelm Wundt (1900) but was
not formalized until Chomsky (1956) and, independently, Backus (1959).

A context-free grammar consists of a set of rules or productions, each of whichrules

10.2 • CONTEXT-FREE GRAMMARS 3

expresses the ways that symbols of the language can be grouped and ordered to-
gether, and a lexicon of words and symbols. For example, the following productionslexicon
express that an NP (or noun phrase) can be composed of either a ProperNoun orNP
a determiner (Det) followed by a Nominal; a Nominal in turn can consist of one or
more Nouns.

NP → Det Nominal
NP → ProperNoun

Nominal → Noun | Nominal Noun

Context-free rules can be hierarchically embedded, so we can combine the pre-
vious rules with others, like the following, that express facts about the lexicon:

Det → a
Det → the

Noun → flight

The symbols that are used in a CFG are divided into two classes. The symbols
that correspond to words in the language (“the”, “nightclub”) are called terminalterminal
symbols; the lexicon is the set of rules that introduce these terminal symbols. The
symbols that express abstractions over these terminals are called non-terminals. Innon-terminal
each context-free rule, the item to the right of the arrow (→) is an ordered list of one
or more terminals and non-terminals; to the left of the arrow is a single non-terminal
symbol expressing some cluster or generalization. Notice that in the lexicon, the
non-terminal associated with each word is its lexical category, or part-of-speech,
which we defined in Chapter 8.

A CFG can be thought of in two ways: as a device for generating sentences
and as a device for assigning a structure to a given sentence. Viewing a CFG as a
generator, we can read the→ arrow as “rewrite the symbol on the left with the string
of symbols on the right”.

So starting from the symbol: NP
we can use our first rule to rewrite NP as: Det Nominal
and then rewrite Nominal as: Det Noun
and finally rewrite these parts-of-speech as: a flight

We say the string a flight can be derived from the non-terminal NP. Thus, a CFG
can be used to generate a set of strings. This sequence of rule expansions is called a
derivation of the string of words. It is common to represent a derivation by a parsederivation
tree (commonly shown inverted with the root at the top). Figure 10.1 shows the treeparse tree
representation of this derivation.

In the parse tree shown in Fig. 10.1, we can say that the node NP dominatesdominates
all the nodes in the tree (Det, Nom, Noun, a, flight). We can say further that it
immediately dominates the nodes Det and Nom.

The formal language defined by a CFG is the set of strings that are derivable
from the designated start symbol. Each grammar must have one designated startstart symbol
symbol, which is often called S. Since context-free grammars are often used to define
sentences, S is usually interpreted as the “sentence” node, and the set of strings that
are derivable from S is the set of sentences in some simplified version of English.

Let’s add a few additional rules to our inventory. The following rule expresses
the fact that a sentence can consist of a noun phrase followed by a verb phrase:verb phrase

S → NP VP I prefer a morning flight

4 CHAPTER 10 • FORMAL GRAMMARS OF ENGLISH

Nom

Noun

flight

Det

Figure 10.1 A parse tree for “a flight”.

A verb phrase in English consists of a verb followed by assorted other things;
for example, one kind of verb phrase consists of a verb followed by a noun phrase:

VP → Verb NP prefer a morning flight

Or the verb may be followed by a noun phrase and a prepositional phrase:

VP → Verb NP PP leave Boston in the morning

Or the verb phrase may have a verb followed by a prepositional phrase alone:

VP → Verb PP leaving on Thursday

A prepositional phrase generally has a preposition followed by a noun phrase.
For example, a common type of prepositional phrase in the ATIS corpus is used to
indicate location or direction:

PP → Preposition NP from Los Angeles

The NP inside a PP need not be a location; PPs are often used with times and
dates, and with other nouns as well; they can be arbitrarily complex. Here are ten
examples from the ATIS corpus:

to Seattle on these flights
in Minneapolis about the ground transportation in Chicago
on Wednesday of the round trip flight on United Airlines
in the evening of the AP fifty seven flight
on the ninth of July with a stopover in Nashville

Figure 10.2 gives a sample lexicon, and Fig. 10.3 summarizes the grammar rules
we’ve seen so far, which we’ll call L0. Note that we can use the or-symbol | to
indicate that a non-terminal has alternate possible expansions.

We can use this grammar to generate sentences of this “ATIS-language”. We
start with S, expand it to NP VP, then choose a random expansion of NP (let’s say, to
I), and a random expansion of VP (let’s say, to Verb NP), and so on until we generate
the string I prefer a morning flight. Figure 10.4 shows a parse tree that represents a
complete derivation of I prefer a morning flight.

It is sometimes convenient to represent a parse tree in a more compact format
called bracketed notation; here is the bracketed representation of the parse tree ofbracketednotation
Fig. 10.4:

(10.1) [S [NP [Pro I]] [VP [V prefer] [NP [Det a] [Nom [N morning] [Nom [N flight]]]]]]

10.2 • CONTEXT-FREE GRAMMARS 5

Conjunction→ and | or | but
Figure 10.2 The lexicon for L0.

Grammar Rules Examples
S → NP VP I + want a morning flight

NP → Pronoun I
| Proper-Noun Los Angeles
| Det Nominal a + flight

Nominal → Nominal Noun morning + flight
| Noun flights

VP → Verb do
| Verb NP want + a flight
| Verb NP PP leave + Boston + in the morning
| Verb PP leaving + on Thursday

PP → Preposition NP from + Los Angeles
Figure 10.3 The grammar for L0, with example phrases for each rule.

A CFG like that of L0 defines a formal language. We saw in Chapter 2 that a for-
mal language is a set of strings. Sentences (strings of words) that can be derived by a
grammar are in the formal language defined by that grammar, and are called gram-
matical sentences. Sentences that cannot be derived by a given formal grammar aregrammatical
not in the language defined by that grammar and are referred to as ungrammatical.ungrammatical
This hard line between “in” and “out” characterizes all formal languages but is only
a very simplified model of how natural languages really work. This is because de-
termining whether a given sentence is part of a given natural language (say, English)
often depends on the context. In linguistics, the use of formal languages to model
natural languages is called generative grammar since the language is defined bygenerativegrammar
the set of possible sentences “generated” by the grammar.

10.2.1 Formal Definition of Context-Free Grammar

We conclude this section with a quick, formal description of a context-free gram-
mar and the language it generates. A context-free grammar G is defined by four
parameters: N, Σ, R, S (technically this is a “4-tuple”).

6 CHAPTER 10 • FORMAL GRAMMARS OF ENGLISH

Nom

Noun

flight

Nom

Noun

morning

Det

Verb

prefer

Pro

Figure 10.4 The parse tree for “I prefer a morning flight” according to grammar L0.

N a set of non-terminal symbols (or variables)
Σ a set of terminal symbols (disjoint from N)
R a set of rules or productions, each of the form A→ β ,

where A is a non-terminal,
β is a string of symbols from the infinite set of strings (Σ∪N)∗

S a designated start symbol and a member of N

For the remainder of the book we adhere to the following conventions when dis-
cussing the formal properties of context-free grammars (as opposed to explaining
particular facts about English or other languages).

Capital letters like A, B, and S Non-terminals
S The start symbol
Lower-case Greek letters like α , β , and γ Strings drawn from (Σ∪N)∗
Lower-case Roman letters like u, v, and w Strings of terminals

A language is defined through the concept of derivation. One string derives an-
other one if it can be rewritten as the second one by some series of rule applications.
More formally, following Hopcroft and Ullman (1979),

if A→ β is a production of R and α and γ are any strings in the set
(Σ∪N)∗, then we say that αAγ directly derives αβγ , or αAγ ⇒ αβγ .directly derives

Derivation is then a generalization of direct derivation:

Let α1, α2, . . . , αm be strings in (Σ∪N)∗,m≥ 1, such that

α1⇒ α2,α2⇒ α3, . . . ,αm−1⇒ αm

We say that α1 derives αm, or α1
∗⇒ αm.derives

We can then formally define the language LG generated by a grammar G as the
set of strings composed of terminal symbols that can be derived from the designated

10.3 • SOME GRAMMAR RULES FOR ENGLISH 7

start symbol S.
LG = {w|w is in Σ∗ and S

∗⇒ w}

The problem of mapping from a string of words to its parse tree is called syn-
tactic parsing; we define algorithms for parsing in Chapter 11.syntacticparsing

10.3 Some Grammar Rules for English

In this section, we introduce a few more aspects of the phrase structure of English;
for consistency we will continue to focus on sentences from the ATIS domain. Be-
cause of space limitations, our discussion is necessarily limited to highlights. Read-
ers are strongly advised to consult a good reference grammar of English, such as
Huddleston and Pullum (2002).

10.3.1 Sentence-Level Constructions
In the small grammar L0, we provided only one sentence-level construction for
declarative sentences like I prefer a morning flight. Among the large number of
constructions for English sentences, four are particularly common and important:
declaratives, imperatives, yes-no questions, and wh-questions.

Sentences with declarative structure have a subject noun phrase followed bydeclarative
a verb phrase, like “I prefer a morning flight”. Sentences with this structure have
a great number of different uses that we follow up on in Chapter 24. Here are a
number of examples from the ATIS domain:

I want a flight from Ontario to Chicago
The flight should be eleven a.m. tomorrow
The return flight should leave at around seven p.m.

Sentences with imperative structure often begin with a verb phrase and haveimperative
no subject. They are called imperative because they are almost always used for
commands and suggestions; in the ATIS domain they are commands to the system.

Show the lowest fare
Give me Sunday’s flights arriving in Las Vegas from New York City
List all flights between five and seven p.m.

We can model this sentence structure with another rule for the expansion of S:

S → VP

Sentences with yes-no question structure are often (though not always) used toyes-no question
ask questions; they begin with an auxiliary verb, followed by a subject NP, followed
by a VP. Here are some examples. Note that the third example is not a question at
all but a request; Chapter 24 discusses the uses of these question forms to perform
different pragmatic functions such as asking, requesting, or suggesting.

Do any of these flights have stops?
Does American’s flight eighteen twenty five serve dinner?
Can you give me the same information for United?

Here’s the rule:

S → Aux NP VP

8 CHAPTER 10 • FORMAL GRAMMARS OF ENGLISH

The most complex sentence-level structures we examine here are the various wh-
structures. These are so named because one of their constituents is a wh-phrase, thatwh-phrase
is, one that includes a wh-word (who, whose, when, where, what, which, how, why).wh-word
These may be broadly grouped into two classes of sentence-level structures. The
wh-subject-question structure is identical to the declarative structure, except that
the first noun phrase contains some wh-word.

What airlines fly from Burbank to Denver?
Which flights depart Burbank after noon and arrive in Denver by six p.m?
Whose flights serve breakfast?

Here is a rule. Exercise 10.7 discusses rules for the constituents that make up the
Wh-NP.

S → Wh-NP VP

In the wh-non-subject-question structure, the wh-phrase is not the subject of thewh-non-subject-question
sentence, and so the sentence includes another subject. In these types of sentences
the auxiliary appears before the subject NP, just as in the yes-no question structures.
Here is an example followed by a sample rule:

What flights do you have from Burbank to Tacoma Washington?

S → Wh-NP Aux NP VP

Constructions like the wh-non-subject-question contain what are called long-
distance dependencies because the Wh-NP what flights is far away from the predi-long-distancedependencies
cate that it is semantically related to, the main verb have in the VP. In some models
of parsing and understanding compatible with the grammar rule above, long-distance
dependencies like the relation between flights and have are thought of as a semantic
relation. In such models, the job of figuring out that flights is the argument of have
is done during semantic interpretation. In other models of parsing, the relationship
between flights and have is considered to be a syntactic relation, and the grammar is
modified to insert a small marker called a trace or empty category after the verb.
We return to such empty-category models when we introduce the Penn Treebank on
page 15.

10.3.2 Clauses and Sentences
Before we move on, we should clarify the status of the S rules in the grammars we
just described. S rules are intended to account for entire sentences that stand alone
as fundamental units of discourse. However, S can also occur on the right-hand side
of grammar rules and hence can be embedded within larger sentences. Clearly then,
there’s more to being an S than just standing alone as a unit of discourse.

What differentiates sentence constructions (i.e., the S rules) from the rest of the
grammar is the notion that they are in some sense complete. In this way they corre-
spond to the notion of a clause, which traditional grammars often describe as form-clause
ing a complete thought. One way of making this notion of “complete thought” more
precise is to say an S is a node of the parse tree below which the main verb of the S
has all of its arguments. We define verbal arguments later, but for now let’s just see
an illustration from the tree for I prefer a morning flight in Fig. 10.4 on page 6. The
verb prefer has two arguments: the subject I and the object a morning flight. One of
the arguments appears below the VP node, but the other one, the subject NP, appears
only below the S node.

10.3 • SOME GRAMMAR RULES FOR ENGLISH 9

10.3.3 The Noun Phrase
Our L0 grammar introduced three of the most frequent types of noun phrases that
occur in English: pronouns, proper nouns and the NP→Det Nominal construction.
The central focus of this section is on the last type since that is where the bulk of
the syntactic complexity resides. These noun phrases consist of a head, the central
noun in the noun phrase, along with various modifiers that can occur before or after
the head noun. Let’s take a close look at the various parts.

The Determiner

Noun phrases can begin with simple lexical determiners, as in the following exam-
ples:

a stop the flights this flight
those flights any flights some flights

The role of the determiner in English noun phrases can also be filled by more
complex expressions, as follows:

United’s flight
United’s pilot’s union
Denver’s mayor’s mother’s canceled flight

In these examples, the role of the determiner is filled by a possessive expression
consisting of a noun phrase followed by an ’s as a possessive marker, as in the
following rule.

Det → NP ′s

The fact that this rule is recursive (since an NP can start with a Det) helps us
model the last two examples above, in which a sequence of possessive expressions
serves as a determiner.

Under some circumstances determiners are optional in English. For example,
determiners may be omitted if the noun they modify is plural:

(10.2) Show me flights from San Francisco to Denver on weekdays

As we saw in Chapter 8, mass nouns also don’t require determination. Recall that
mass nouns often (not always) involve something that is treated like a substance
(including e.g., water and snow), don’t take the indefinite article “a”, and don’t tend
to pluralize. Many abstract nouns are mass nouns (music, homework). Mass nouns
in the ATIS domain include breakfast, lunch, and dinner:

(10.3) Does this flight serve dinner?

The Nominal

The nominal construction follows the determiner and contains any pre- and post-
head noun modifiers. As indicated in grammar L0, in its simplest form a nominal
can consist of a single noun.

Nominal → Noun

As we’ll see, this rule also provides the basis for the bottom of various recursive
rules used to capture more complex nominal constructions.

10 CHAPTER 10 • FORMAL GRAMMARS OF ENGLISH

Before the Head Noun

A number of different kinds of word classes can appear before the head noun (theCardinalnumbers
“postdeterminers”) in a nominal. These include cardinal numbers, ordinal num-
bers, quantifiers, and adjectives. Examples of cardinal numbers:ordinalnumbers

quantifiers
two friends one stop

Ordinal numbers include first, second, third, and so on, but also words like next,
last, past, other, and another:

the first one the next day the second leg
the last flight the other American flight

Some quantifiers (many, (a) few, several) occur only with plural count nouns:

many fares

Adjectives occur after quantifiers but before nouns.

a first-class fare a non-stop flight
the longest layover the earliest lunch flight

Adjectives can also be grouped into a phrase called an adjective phrase or AP.adjectivephrase
APs can have an adverb before the adjective (see Chapter 8 for definitions of adjec-
tives and adverbs):

the least expensive fare

After the Head Noun

A head noun can be followed by postmodifiers. Three kinds of nominal postmodi-
fiers are common in English:

prepositional phrases all flights from Cleveland
non-finite clauses any flights arriving after eleven a.m.
relative clauses a flight that serves breakfast

common in the ATIS corpus since they are used to mark the origin and destina-
tion of flights.

Here are some examples of prepositional phrase postmodifiers, with brackets
inserted to show the boundaries of each PP; note that two or more PPs can be strung
together within a single NP:

all flights [from Cleveland] [to Newark]
arrival [in San Jose] [before seven p.m.]
a reservation [on flight six oh six] [from Tampa] [to Montreal]

Here’s a new nominal rule to account for postnominal PPs:

Nominal → Nominal PP

The three most common kinds of non-finite postmodifiers are the gerundive (-non-finite
ing), -ed, and infinitive forms.

Gerundive postmodifiers are so called because they consist of a verb phrase thatgerundive
begins with the gerundive (-ing) form of the verb. Here are some examples:

any of those [leaving on Thursday]
any flights [arriving after eleven a.m.]
flights [arriving within thirty minutes of each other]

10.3 • SOME GRAMMAR RULES FOR ENGLISH 11

We can define the Nominals with gerundive modifiers as follows, making use of
a new non-terminal GerundVP:

Nominal → Nominal GerundVP

We can make rules for GerundVP constituents by duplicating all of our VP pro-
ductions, substituting GerundV for V.

GerundVP → GerundV NP
| GerundV PP | GerundV | GerundV NP PP

GerundV can then be defined as

GerundV → being | arriving | leaving | . . .

The phrases in italics below are examples of the two other common kinds of
non-finite clauses, infinitives and -ed forms:

the last flight to arrive in Boston
I need to have dinner served
Which is the aircraft used by this flight?

A postnominal relative clause (more correctly a restrictive relative clause), is
a clause that often begins with a relative pronoun (that and who are the most com-relativepronoun
mon). The relative pronoun functions as the subject of the embedded verb in the
following examples:

a flight that serves breakfast
flights that leave in the morning
the one that leaves at ten thirty five

We might add rules like the following to deal with these:

Nominal → Nominal RelClause
RelClause → (who | that) VP

The relative pronoun may also function as the object of the embedded verb, as
in the following example; we leave for the reader the exercise of writing grammar
rules for more complex relative clauses of this kind.

the earliest American Airlines flight that I can get

Various postnominal modifiers can be combined, as the following examples
show:

a flight [from Phoenix to Detroit] [leaving Monday evening]
evening flights [from Nashville to Houston] [that serve dinner]
a friend [living in Denver] [that would like to visit me here in Washington DC]

Before the Noun Phrase

Word classes that modify and appear before NPs are called predeterminers. Manypredeterminers
of these have to do with number or amount; a common predeterminer is all:

all the flights all flights all non-stop flights

The example noun phrase given in Fig. 10.5 illustrates some of the complexity
that arises when these rules are combined.

12 CHAPTER 10 • FORMAL GRAMMARS OF ENGLISH

Nom

GerundiveVP

leaving before 10

Nom

to Tampa

Nom

from Denver

Nom

Noun

flights

Nom

Noun

morning

Det

the

PreDet

all

Figure 10.5 A parse tree for “all the morning flights from Denver to Tampa leaving before 10”.

10.3.4 The Verb Phrase
The verb phrase consists of the verb and a number of other constituents. In the
simple rules we have built so far, these other constituents include NPs and PPs and
combinations of the two:

VP → Verb disappear
VP → Verb NP prefer a morning flight
VP → Verb NP PP leave Boston in the morning
VP → Verb PP leaving on Thursday

Verb phrases can be significantly more complicated than this. Many other kinds
of constituents, such as an entire embedded sentence, can follow the verb. These are
called sentential complements:sententialcomplements

You [VP [V said [S you had a two hundred sixty six dollar fare]]
[VP [V Tell] [NP me] [S how to get from the airport in Philadelphia to down-
town]]
I [VP [V think [S I would like to take the nine thirty flight]]

Here’s a rule for these:

VP → Verb S

Similarly, another potential constituent of the VP is another VP. This is often the
case for verbs like want, would like, try, intend, need:

I want [VP to fly from Milwaukee to Orlando]
Hi, I want [VP to arrange three flights]

10.3 • SOME GRAMMAR RULES FOR ENGLISH 13

Frame Verb Example
/0 eat, sleep I ate
NP prefer, find, leave Find [NP the flight from Pittsburgh to Boston]
NP NP show, give Show [NP me] [NP airlines with flights from Pittsburgh]
PPfrom PPto fly, travel I would like to fly [PP from Boston] [PP to Philadelphia]
NP PPwith help, load Can you help [NP me] [PP with a flight]
VPto prefer, want, need I would prefer [VPto to go by United airlines]
VPbrst can, would, might I can [VPbrst go from Boston]
S mean Does this mean [S AA has a hub in Boston]

Figure 10.6 Subcategorization frames for a set of example verbs.

While a verb phrase can have many possible kinds of constituents, not every
verb is compatible with every verb phrase. For example, the verb want can be used
either with an NP complement (I want a flight . . . ) or with an infinitive VP comple-
ment (I want to fly to . . . ). By contrast, a verb like find cannot take this sort of VP
complement (* I found to fly to Dallas).

This idea that verbs are compatible with different kinds of complements is a very
old one; traditional grammar distinguishes between transitive verbs like find, whichtransitive
take a direct object NP (I found a flight), and intransitive verbs like disappear,intransitive
which do not (*I disappeared a flight).

Where traditional grammars subcategorize verbs into these two categories (tran-subcategorize
sitive and intransitive), modern grammars distinguish as many as 100 subcategories.
We say that a verb like find subcategorizes for an NP, and a verb like want sub-Subcategorizesfor
categorizes for either an NP or a non-finite VP. We also call these constituents the
complements of the verb (hence our use of the term sentential complement above).complements
So we say that want can take a VP complement. These possible sets of complements
are called the subcategorization frame for the verb. Another way of talking aboutSubcategorizationframe
the relation between the verb and these other constituents is to think of the verb as
a logical predicate and the constituents as logical arguments of the predicate. So we
can think of such predicate-argument relations as FIND(I, A FLIGHT) or WANT(I, TO
FLY). We talk more about this view of verbs and arguments in Chapter 14 when we
talk about predicate calculus representations of verb semantics. Subcategorization
frames for a set of example verbs are given in Fig. 10.6.

We can capture the association between verbs and their complements by making
separate subtypes of the class Verb (e.g., Verb-with-NP-complement, Verb-with-Inf-
VP-complement, Verb-with-S-complement, and so on):

Verb-with-Inf-VP-complement → want | try | need | . . .

Each VP rule could then be modified to require the appropriate verb subtype:

VP → Verb-with-no-complement disappear
VP → Verb-with-NP-comp NP prefer a morning flight
VP → Verb-with-S-comp S said there were two flights

A problem with this approach is the significant increase in the number of rules
and the associated loss of generality.

14 CHAPTER 10 • FORMAL GRAMMARS OF ENGLISH

10.3.5 Coordination
The major phrase types discussed here can be conjoined with conjunctions like and,conjunctions
or, and but to form larger constructions of the same type. For example, a coordinatecoordinate
noun phrase can consist of two other noun phrases separated by a conjunction:

Please repeat [NP [NP the flights] and [NP the costs]]
I need to know [NP [NP the aircraft] and [NP the flight number]]

Here’s a rule that allows these structures:

NP → NP and NP

Note that the ability to form coordinate phrases through conjunctions is often
used as a test for constituency. Consider the following examples, which differ from
the ones given above in that they lack the second determiner.

Please repeat the [Nom [Nom flights] and [Nom costs]]
I need to know the [Nom [Nom aircraft] and [Nom flight number]]

The fact that these phrases can be conjoined is evidence for the presence of the
underlying Nominal constituent we have been making use of. Here’s a new rule for
this:

Nominal → Nominal and Nominal

The following examples illustrate conjunctions involving VPs and Ss.

What flights do you have [VP [VP leaving Denver] and [VP arriving in
San Francisco]]
[S [S I’m interested in a flight from Dallas to Washington] and [S I’m
also interested in going to Baltimore]]

The rules for VP and S conjunctions mirror the NP one given above.

VP → VP and VP
S → S and S

Since all the major phrase types can be conjoined in this fashion, it is also pos-
sible to represent this conjunction fact more generally; a number of grammar for-
malisms such as GPSG ((Gazdar et al., 1985)) do this using metarules such as themetarules
following:

X → X and X

This metarule simply states that any non-terminal can be conjoined with the same
non-terminal to yield a constituent of the same type. Of course, the variable X
must be designated as a variable that stands for any non-terminal rather than a non-
terminal itself.

10.4 Treebanks

Sufficiently robust grammars consisting of context-free grammar rules can be used
to assign a parse tree to any sentence. This means that it is possible to build a
corpus where every sentence in the collection is paired with a corresponding parse

10.4 • TREEBANKS 15

tree. Such a syntactically annotated corpus is called a treebank. Treebanks playtreebank
an important role in parsing, as we discuss in Chapter 11, as well as in linguistic
investigations of syntactic phenomena.

A wide variety of treebanks have been created, generally through the use of
parsers (of the sort described in the next few chapters) to automatically parse each
sentence, followed by the use of humans (linguists) to hand-correct the parses. The
Penn Treebank project (whose POS tagset we introduced in Chapter 8) has pro-Penn Treebank
duced treebanks from the Brown, Switchboard, ATIS, and Wall Street Journal cor-
pora of English, as well as treebanks in Arabic and Chinese. A number of treebanks
use the dependency representation we will introduce in Chapter 13, including many
that are part of the Universal Dependencies project (Nivre et al., 2016).

10.4.1 Example: The Penn Treebank Project
Figure 10.7 shows sentences from the Brown and ATIS portions of the Penn Tree-
bank.1 Note the formatting differences for the part-of-speech tags; such small dif-
ferences are common and must be dealt with in processing treebanks. The Penn
Treebank part-of-speech tagset was defined in Chapter 8. The use of LISP-style
parenthesized notation for trees is extremely common and resembles the bracketed
notation we saw earlier in (10.1). For those who are not familiar with it we show a
standard node-and-line tree representation in Fig. 10.8.

((S

(NP-SBJ (DT That)

(JJ cold) (, ,)

(JJ empty) (NN sky) )

(VP (VBD was)

(ADJP-PRD (JJ full)

(PP (IN of)

(NP (NN fire)

(CC and)

(NN light) ))))

(. .) ))

((S

(NP-SBJ The/DT flight/NN )

(VP should/MD

(VP arrive/VB

(PP-TMP at/IN

(NP eleven/CD a.m/RB ))

(NP-TMP tomorrow/NN )))))

(a) (b)

Figure 10.7 Parsed sentences from the LDC Treebank3 version of the Brown (a) and ATIS
(b) corpora.

Figure 10.9 shows a tree from the Wall Street Journal. This tree shows an-
other feature of the Penn Treebanks: the use of traces (-NONE- nodes) to marktraces
long-distance dependencies or syntactic movement. For example, quotations oftensyntacticmovement
follow a quotative verb like say. But in this example, the quotation “We would have
to wait until we have collected on those assets” precedes the words he said. An
empty S containing only the node -NONE- marks the position after said where the
quotation sentence often occurs. This empty node is marked (in Treebanks II and
III) with the index 2, as is the quotation S at the beginning of the sentence. Such
co-indexing may make it easier for some parsers to recover the fact that this fronted
or topicalized quotation is the complement of the verb said. A similar -NONE- node

1 The Penn Treebank project released treebanks in multiple languages and in various stages; for ex-
ample, there were Treebank I (Marcus et al., 1993), Treebank II (Marcus et al., 1994), and Treebank III
releases of English treebanks. We use Treebank III for our examples.

16 CHAPTER 10 • FORMAL GRAMMARS OF ENGLISH

ADJP-PRD

light

and

fire

full

VBD

was

NP-SBJ

sky

empty

cold

That

Figure 10.8 The tree corresponding to the Brown corpus sentence in the previous figure.

marks the fact that there is no syntactic subject right before the verb to wait; instead,
the subject is the earlier NP We. Again, they are both co-indexed with the index 1.

( (S (‘‘ ‘‘)

(S-TPC-2

(NP-SBJ-1 (PRP We) )

(VP (MD would)

(VP (VB have)

(NP-SBJ (-NONE- *-1) )

(VP (TO to)

(VP (VB wait)

(SBAR-TMP (IN until)

(NP-SBJ (PRP we) )

(VP (VBP have)

(VP (VBN collected)

(PP-CLR (IN on)

(NP (DT those)(NNS assets)))))))))))))

(, ,) (’’ ’’)

(NP-SBJ (PRP he) )

(VP (VBD said)

(S (-NONE- *T*-2) ))

(. .) ))

Figure 10.9 A sentence from the Wall Street Journal portion of the LDC Penn Treebank.
Note the use of the empty -NONE- nodes.

The Penn Treebank II and Treebank III releases added further information to
make it easier to recover the relationships between predicates and arguments. Cer-

10.4 • TREEBANKS 17

Figure 10.10 A sample of the CFG grammar rules and lexical entries that would be ex-
tracted from the three treebank sentences in Fig. 10.7 and Fig. 10.9.

tain phrases were marked with tags indicating the grammatical function of the phrase
(as surface subject, logical topic, cleft, non-VP predicates) its presence in particular
text categories (headlines, titles), and its semantic function (temporal phrases, lo-
cations) (Marcus et al. 1994, Bies et al. 1995). Figure 10.9 shows examples of the
-SBJ (surface subject) and -TMP (temporal phrase) tags. Figure 10.8 shows in addi-
tion the -PRD tag, which is used for predicates that are not VPs (the one in Fig. 10.8
is an ADJP). We’ll return to the topic of grammatical function when we consider
dependency grammars and parsing in Chapter 13.

10.4.2 Treebanks as Grammars
The sentences in a treebank implicitly constitute a grammar of the language repre-
sented by the corpus being annotated. For example, from the three parsed sentences
in Fig. 10.7 and Fig. 10.9, we can extract each of the CFG rules in them. For sim-
plicity, let’s strip off the rule suffixes (-SBJ and so on). The resulting grammar is
shown in Fig. 10.10.

The grammar used to parse the Penn Treebank is relatively flat, resulting in very
many and very long rules. For example, among the approximately 4,500 different
rules for expanding VPs are separate rules for PP sequences of any length and every
possible arrangement of verb arguments:

VP → VBD PP
VP → VBD PP PP
VP → VBD PP PP PP
VP → VBD PP PP PP PP
VP → VB ADVP PP
VP → VB PP ADVP
VP → ADVP VB PP

18 CHAPTER 10 • FORMAL GRAMMARS OF ENGLISH

as well as even longer rules, such as

VP → VBP PP PP PP PP PP ADVP PP

which comes from the VP marked in italics:

This mostly happens because we go from football in the fall to lifting in the
winter to football again in the spring.

Some of the many thousands of NP rules include

NP → DT JJ NN
NP → DT JJ NNS
NP → DT JJ NN NN
NP → DT JJ JJ NN
NP → DT JJ CD NNS
NP → RB DT JJ NN NN
NP → RB DT JJ JJ NNS
NP → DT JJ JJ NNP NNS
NP → DT NNP NNP NNP NNP JJ NN
NP → DT JJ NNP CC JJ JJ NN NNS
NP → RB DT JJS NN NN SBAR
NP → DT VBG JJ NNP NNP CC NNP
NP → DT JJ NNS , NNS CC NN NNS NN
NP → DT JJ JJ VBG NN NNP NNP FW NNP
NP → NP JJ , JJ ‘‘ SBAR ’’ NNS

The last two of those rules, for example, come from the following two noun phrases:

[DT The] [JJ state-owned] [JJ industrial] [VBG holding] [NN company] [NNP Instituto]
[NNP Nacional] [FW de] [NNP Industria]
[NP Shearson’s] [JJ easy-to-film], [JJ black-and-white] “[SBAR Where We Stand]”
[NNS commercials]

Viewed as a large grammar in this way, the Penn Treebank III Wall Street Journal
corpus, which contains about 1 million words, also has about 1 million non-lexical
rule tokens, consisting of about 17,500 distinct rule types.

Various facts about the treebank grammars, such as their large numbers of flat
rules, pose problems for probabilistic parsing algorithms. For this reason, it is com-
mon to make various modifications to a grammar extracted from a treebank. We
discuss these further in Chapter 12.

10.4.3 Heads and Head Finding
We suggested informally earlier that syntactic constituents could be associated with
a lexical head; N is the head of an NP, V is the head of a VP. This idea of a head for
each constituent dates back to Bloomfield (1914). It is central to constituent-based
grammar formalisms such as Head-Driven Phrase Structure Grammar (Pollard and
Sag, 1994), as well as the dependency-based approaches to grammar we’ll discuss
in Chapter 13. Heads and head-dependent relations have also come to play a central
role in computational linguistics with their use in probabilistic parsing (Chapter 12)
and in dependency parsing (Chapter 13).

In one simple model of lexical heads, each context-free rule is associated with
a head (Charniak 1997, Collins 1999). The head is the word in the phrase that is
grammatically the most important. Heads are passed up the parse tree; thus, each
non-terminal in a parse tree is annotated with a single word, which is its lexical head.

10.4 • TREEBANKS 19

S(dumped)

VP(dumped)

PP(into)

NP(bin)

NN(bin)

bin

DT(a)

into

NP(sacks)

NNS(sacks)

sacks

VBD(dumped)

dumped

NP(workers)

NNS(workers)

workers

Figure 10.11 A lexicalized tree from Collins (1999).

Figure 10.11 shows an example of such a tree from Collins (1999), in which each
non-terminal is annotated with its head.

For the generation of such a tree, each CFG rule must be augmented to identify
one right-side constituent to be the head daughter. The headword for a node is
then set to the headword of its head daughter. Choosing these head daughters is
simple for textbook examples (NN is the head of NP) but is complicated and indeed
controversial for most phrases. (Should the complementizer to or the verb be the
head of an infinite verb-phrase?) Modern linguistic theories of syntax generally
include a component that defines heads (see, e.g., (Pollard and Sag, 1994)).

An alternative approach to finding a head is used in most practical computational
systems. Instead of specifying head rules in the grammar itself, heads are identified
dynamically in the context of trees for specific sentences. In other words, once
a sentence is parsed, the resulting tree is walked to decorate each node with the
appropriate head. Most current systems rely on a simple set of hand-written rules,
such as a practical one for Penn Treebank grammars given in Collins (1999) but
developed originally by Magerman (1995). For example, the rule for finding the
head of an NP is as follows (Collins, 1999, p. 238):

• If the last word is tagged POS, return last-word.
• Else search from right to left for the first child which is an NN, NNP, NNPS, NX, POS,

or JJR.
• Else search from left to right for the first child which is an NP.
• Else search from right to left for the first child which is a $, ADJP, or PRN.
• Else search from right to left for the first child which is a CD.
• Else search from right to left for the first child which is a JJ, JJS, RB or QP.
• Else return the last word

Selected other rules from this set are shown in Fig. 10.12. For example, for VP
rules of the form VP→ Y1 · · · Yn, the algorithm would start from the left of Y1 · · ·
Yn looking for the first Yi of type TO; if no TOs are found, it would search for the
first Yi of type VBD; if no VBDs are found, it would search for a VBN, and so on.
See Collins (1999) for more details.

20 CHAPTER 10 • FORMAL GRAMMARS OF ENGLISH

Parent Direction Priority List
ADJP Left NNS QP NN $ ADVP JJ VBN VBG ADJP JJR NP JJS DT FW RBR RBS

SBAR RB
ADVP Right RB RBR RBS FW ADVP TO CD JJR JJ IN NP JJS NN
PRN Left
PRT Right RP
QP Left $ IN NNS NN JJ RB DT CD NCD QP JJR JJS
S Left TO IN VP S SBAR ADJP UCP NP
SBAR Left WHNP WHPP WHADVP WHADJP IN DT S SQ SINV SBAR FRAG
VP Left TO VBD VBN MD VBZ VB VBG VBP VP ADJP NN NNS NP
Figure 10.12 Selected head rules from Collins (1999). The set of head rules is often called a head percola-
tion table.

10.5 Grammar Equivalence and Normal Form

A formal language is defined as a (possibly infinite) set of strings of words. This
suggests that we could ask if two grammars are equivalent by asking if they gener-
ate the same set of strings. In fact, it is possible to have two distinct context-free
grammars generate the same language.

We usually distinguish two kinds of grammar equivalence: weak equivalence
and strong equivalence. Two grammars are strongly equivalent if they generate the
same set of strings and if they assign the same phrase structure to each sentence
(allowing merely for renaming of the non-terminal symbols). Two grammars are
weakly equivalent if they generate the same set of strings but do not assign the same
phrase structure to each sentence.

It is sometimes useful to have a normal form for grammars, in which each ofnormal form
the productions takes a particular form. For example, a context-free grammar is in
Chomsky normal form (CNF) (Chomsky, 1963) if it is ε-free and if in additionChomskynormal form
each production is either of the form A→ B C or A→ a. That is, the right-hand side
of each rule either has two non-terminal symbols or one terminal symbol. Chomsky
normal form grammars are binary branching, that is they have binary trees (downbinarybranching
to the prelexical nodes). We make use of this binary branching property in the CKY
parsing algorithm in Chapter 11.

Any context-free grammar can be converted into a weakly equivalent Chomsky
normal form grammar. For example, a rule of the form

A → B C D

can be converted into the following two CNF rules (Exercise 10.8 asks the reader to
formulate the complete algorithm):

A → B X
X → C D

Sometimes using binary branching can actually produce smaller grammars. For
example, the sentences that might be characterized as

VP -> VBD NP PP*

are represented in the Penn Treebank by this series of rules:

VP → VBD NP PP
VP → VBD NP PP PP

10.6 • LEXICALIZED GRAMMARS 21

VP → VBD NP PP PP PP
VP → VBD NP PP PP PP PP
…

but could also be generated by the following two-rule grammar:

VP → VBD NP PP
VP → VP PP

The generation of a symbol A with a potentially infinite sequence of symbols B with
a rule of the form A → A B is known as Chomsky-adjunction.Chomsky-adjunction

10.6 Lexicalized Grammars

The approach to grammar presented thus far emphasizes phrase-structure rules while
minimizing the role of the lexicon. However, as we saw in the discussions of
agreement, subcategorization, and long distance dependencies, this approach leads
to solutions that are cumbersome at best, yielding grammars that are redundant,
hard to manage, and brittle. To overcome these issues, numerous alternative ap-
proaches have been developed that all share the common theme of making bet-
ter use of the lexicon. Among the more computationally relevant approaches are
Lexical-Functional Grammar (LFG) (Bresnan, 1982), Head-Driven Phrase Structure
Grammar (HPSG) (Pollard and Sag, 1994), Tree-Adjoining Grammar (TAG) (Joshi,
1985), and Combinatory Categorial Grammar (CCG). These approaches differ with
respect to how lexicalized they are — the degree to which they rely on the lexicon
as opposed to phrase structure rules to capture facts about the language.

The following section provides an introduction to CCG, a heavily lexicalized
approach motivated by both syntactic and semantic considerations, which we will
return to in Chapter 14. Chapter 13 discusses dependency grammars, an approach
that eliminates phrase-structure rules entirely.

10.6.1 Combinatory Categorial Grammar
In this section, we provide an overview of categorial grammar (Ajdukiewicz 1935,categorialgrammar
Bar-Hillel 1953), an early lexicalized grammar model, as well as an important mod-
ern extension, combinatory categorial grammar, or CCG (Steedman 1996,Steed-

combinatory
categorial
grammar

man 1989,Steedman 2000).
The categorial approach consists of three major elements: a set of categories,

a lexicon that associates words with categories, and a set of rules that govern how
categories combine in context.

Categories

Categories are either atomic elements or single-argument functions that return a cat-
egory as a value when provided with a desired category as argument. More formally,
we can define C , a set of categories for a grammar as follows:

• A ⊆ C , where A is a given set of atomic elements
• (X/Y), (X\Y) ∈ C , if X, Y ∈ C
The slash notation shown here is used to define the functions in the grammar.

It specifies the type of the expected argument, the direction it is expected be found,
and the type of the result. Thus, (X/Y) is a function that seeks a constituent of type

22 CHAPTER 10 • FORMAL GRAMMARS OF ENGLISH

Y to its right and returns a value of X; (X\Y) is the same except it seeks its argument
to the left.

The set of atomic categories is typically very small and includes familiar el-
ements such as sentences and noun phrases. Functional categories include verb
phrases and complex noun phrases among others.

The Lexicon

The lexicon in a categorial approach consists of assignments of categories to words.
These assignments can either be to atomic or functional categories, and due to lexical
ambiguity words can be assigned to multiple categories. Consider the following
sample lexical entries.

flight : N
Miami : NP
cancel : (S\NP)/NP

Nouns and proper nouns like flight and Miami are assigned to atomic categories,
reflecting their typical role as arguments to functions. On the other hand, a transitive
verb like cancel is assigned the category (S\NP)/NP: a function that seeks an NP on
its right and returns as its value a function with the type (S\NP). This function can,
in turn, combine with an NP on the left, yielding an S as the result. This captures the
kind of subcategorization information discussed in Section 10.3.4, however here the
information has a rich, computationally useful, internal structure.

Ditransitive verbs like give, which expect two arguments after the verb, would
have the category ((S\NP)/NP)/NP: a function that combines with an NP on its
right to yield yet another function corresponding to the transitive verb (S\NP)/NP
category such as the one given above for cancel.

Rules

The rules of a categorial grammar specify how functions and their arguments com-
bine. The following two rule templates constitute the basis for all categorial gram-
mars.

X/Y Y ⇒ X (10.4)
Y X\Y ⇒ X (10.5)

The first rule applies a function to its argument on the right, while the second
looks to the left for its argument. We’ll refer to the first as forward function appli-
cation, and the second as backward function application. The result of applying
either of these rules is the category specified as the value of the function being ap-
plied.

Given these rules and a simple lexicon, let’s consider an analysis of the sentence
United serves Miami. Assume that serves is a transitive verb with the category
(S\NP)/NP and that United and Miami are both simple NPs. Using both forward
and backward function application, the derivation would proceed as follows:

United serves Miami

NP (S\NP)/NP NP
>

S\NP
< S 10.6 • LEXICALIZED GRAMMARS 23 Categorial grammar derivations are illustrated growing down from the words, rule applications are illustrated with a horizontal line that spans the elements in- volved, with the type of the operation indicated at the right end of the line. In this example, there are two function applications: one forward function application indi- cated by the > that applies the verb serves to the NP on its right, and one backward
function application indicated by the < that applies the result of the first to the NP United on its left. With the addition of another rule, the categorial approach provides a straight- forward way to implement the coordination metarule described earlier on page 14. Recall that English permits the coordination of two constituents of the same type, resulting in a new constituent of the same type. The following rule provides the mechanism to handle such examples. X CONJ X ⇒ X (10.6) This rule states that when two constituents of the same category are separated by a constituent of type CONJ they can be combined into a single larger constituent of the same type. The following derivation illustrates the use of this rule. We flew to Geneva and drove to Chamonix NP (S\NP)/PP PP/NP NP CONJ (S\NP)/PP PP/NP NP > >

PP PP
> >

S\NP S\NP
<Φ>

S\NP
< S Here the two S\NP constituents are combined via the conjunction operator <Φ>
to form a larger constituent of the same type, which can then be combined with the
subject NP via backward function application.

These examples illustrate the lexical nature of the categorial grammar approach.
The grammatical facts about a language are largely encoded in the lexicon, while the
rules of the grammar are boiled down to a set of three rules. Unfortunately, the basic
categorial approach does not give us any more expressive power than we had with
traditional CFG rules; it just moves information from the grammar to the lexicon. To
move beyond these limitations CCG includes operations that operate over functions.

The first pair of operators permit us to compose adjacent functions.

X/Y Y/Z ⇒ X/Z (10.7)
Y\Z X\Y ⇒ X\Z (10.8)

The first rule, called forward composition, can be applied to adjacent con-forwardcomposition
stituents where the first is a function seeking an argument of type Y to its right, and
the second is a function that providesY as a result. This rule allows us to compose
these two functions into a single one with the type of the first constituent and the
argument of the second. Although the notation is a little awkward, the second rule,
backward composition is the same, except that we’re looking to the left instead ofbackwardcomposition
to the right for the relevant arguments. Both kinds of composition are signalled by a
B in CCG diagrams, accompanied by a < or > to indicate the direction.

The next operator is type raising. Type raising elevates simple categories to thetype raising
status of functions. More specifically, type raising takes a category and converts
it to function that seeks as an argument a function that takes the original category

24 CHAPTER 10 • FORMAL GRAMMARS OF ENGLISH

as its argument. The following schema show two versions of type raising: one for
arguments to the right, and one for the left.

X ⇒ T/(T\X) (10.9)
X ⇒ T\(T/X) (10.10)

The category T in these rules can correspond to any of the atomic or functional
categories already present in the grammar.

A particularly useful example of type raising transforms a simple NP argument
in subject position to a function that can compose with a following VP. To see how
this works, let’s revisit our earlier example of United serves Miami. Instead of clas-
sifying United as an NP which can serve as an argument to the function attached to
serve, we can use type raising to reinvent it as a function in its own right as follows.

NP ⇒ S/(S\NP)

Combining this type-raised constituent with the forward composition rule (10.7)
permits the following alternative to our previous derivation.

United serves Miami

NP (S\NP)/NP NP
>T

S/(S\NP)
>B

S/NP
>

S
By type raising United to S/(S\NP), we can compose it with the transitive verb
serves to yield the (S/NP) function needed to complete the derivation.

There are several interesting things to note about this derivation. First, is it
provides a left-to-right, word-by-word derivation that more closely mirrors the way
humans process language. This makes CCG a particularly apt framework for psy-
cholinguistic studies. Second, this derivation involves the use of an intermediate
unit of analysis, United serves, that does not correspond to a traditional constituent
in English. This ability to make use of such non-constituent elements provides CCG
with the ability to handle the coordination of phrases that are not proper constituents,
as in the following example.

(10.11) We flew IcelandAir to Geneva and SwissAir to London.

Here, the segments that are being coordinated are IcelandAir to Geneva and
SwissAir to London, phrases that would not normally be considered constituents, as
can be seen in the following standard derivation for the verb phrase flew IcelandAir
to Geneva.

flew IcelandAir to Geneva

(VP/PP)/NP NP PP/NP NP
> >

VP/PP PP
>

VP
In this derivation, there is no single constituent that corresponds to IcelandAir

to Geneva, and hence no opportunity to make use of the <Φ> operator. Note that
complex CCG categories can can get a little cumbersome, so we’ll use VP as a
shorthand for (S\NP) in this and the following derivations.

The following alternative derivation provides the required element through the
use of both backward type raising (10.10) and backward function composition (10.8).

10.6 • LEXICALIZED GRAMMARS 25

flew IcelandAir to Geneva

(V P/PP)/NP NP PP/NP NP

(V P/PP)\((V P/PP)/NP) PP
operator, yielding the following derivation for our original example
(10.11).

flew IcelandAir to Geneva and SwissAir to London

(V P/PP)/NP NP PP/NP NP CONJ NP PP/NP NP

(V P/PP)\((V P/PP)/NP) PP (V P/PP)\((V P/PP)/NP) PP

V P\((V P/PP)/NP)
< V P Finally, let’s examine how these advanced operators can be used to handle long- distance dependencies (also referred to as syntactic movement or extraction). As mentioned in Section 10.3.1, long-distance dependencies arise from many English constructions including wh-questions, relative clauses, and topicalization. What these constructions have in common is a constituent that appears somewhere dis- tant from its usual, or expected, location. Consider the following relative clause as an example. the flight that United diverted Here, divert is a transitive verb that expects two NP arguments, a subject NP to its left and a direct object NP to its right; its category is therefore (S\NP)/NP. However, in this example the direct object the flight has been “moved” to the beginning of the clause, while the subject United remains in its normal position. What is needed is a way to incorporate the subject argument, while dealing with the fact that the flight is not in its expected location. The following derivation accomplishes this, again through the combined use of type raising and function composition. the flight that United diverted NP/N N (NP\NP)/(S/NP) NP (S\NP)/NP > >T

NP S/(S\NP)
>B

S/NP
>

NP\NP
< NP As we saw with our earlier examples, the first step of this derivation is type raising United to the category S/(S\NP) allowing it to combine with diverted via forward composition. The result of this composition is S/NP which preserves the fact that we are still looking for an NP to fill the missing direct object. The second critical piece is the lexical category assigned to the word that: (NP\NP)/(S/NP). This function seeks a verb phrase missing an argument to its right, and transforms it into an NP seeking a missing element to its left, precisely where we find the flight. 26 CHAPTER 10 • FORMAL GRAMMARS OF ENGLISH CCGBank As with phrase-structure approaches, treebanks play an important role in CCG- based approaches to parsing. CCGBank (Hockenmaier and Steedman, 2007) is the largest and most widely used CCG treebank. It was created by automatically trans- lating phrase-structure trees from the Penn Treebank via a rule-based approach. The method produced successful translations of over 99% of the trees in the Penn Tree- bank resulting in 48,934 sentences paired with CCG derivations. It also provides a lexicon of 44,000 words with over 1200 categories. Chapter 12 will discuss how these resources can be used to train CCG parsers. 10.7 Summary This chapter has introduced a number of fundamental concepts in syntax through the use of context-free grammars. • In many languages, groups of consecutive words act as a group or a con- stituent, which can be modeled by context-free grammars (which are also known as phrase-structure grammars). • A context-free grammar consists of a set of rules or productions, expressed over a set of non-terminal symbols and a set of terminal symbols. Formally, a particular context-free language is the set of strings that can be derived from a particular context-free grammar. • A generative grammar is a traditional name in linguistics for a formal lan- guage that is used to model the grammar of a natural language. • There are many sentence-level grammatical constructions in English; declar- ative, imperative, yes-no question, and wh-question are four common types; these can be modeled with context-free rules. • An English noun phrase can have determiners, numbers, quantifiers, and adjective phrases preceding the head noun, which can be followed by a num- ber of postmodifiers; gerundive VPs, infinitives VPs, and past participial VPs are common possibilities. • Subjects in English agree with the main verb in person and number. • Verbs can be subcategorized by the types of complements they expect. Sim- ple subcategories are transitive and intransitive; most grammars include many more categories than these. • Treebanks of parsed sentences exist for many genres of English and for many languages. Treebanks can be searched with tree-search tools. • Any context-free grammar can be converted to Chomsky normal form, in which the right-hand side of each rule has either two non-terminals or a single terminal. • Lexicalized grammars place more emphasis on the structure of the lexicon, lessening the burden on pure phrase-structure rules. • Combinatorial categorial grammar (CCG) is an important computationally relevant lexicalized approach. BIBLIOGRAPHICAL AND HISTORICAL NOTES 27 Bibliographical and Historical Notes [The origin of the idea of phrasal constituency, cited in Percival (1976)]: den sprachlichen Ausdruck für die willkürliche Gliederung einer Gesammtvorstellung in ihre in logische Beziehung zueinander gesetzten Bestandteile’ [the linguistic expression for the arbitrary division of a total idea into its constituent parts placed in logical relations to one another] W. Wundt According to Percival (1976), the idea of breaking up a sentence into a hierar- chy of constituents appeared in the Völkerpsychologie of the groundbreaking psy- chologist Wilhelm Wundt (Wundt, 1900). Wundt’s idea of constituency was taken up into linguistics by Leonard Bloomfield in his early book An Introduction to the Study of Language (Bloomfield, 1914). By the time of his later book, Language (Bloomfield, 1933), what was then called “immediate-constituent analysis” was a well-established method of syntactic study in the United States. By contrast, tra- ditional European grammar, dating from the Classical period, defined relations be- tween words rather than constituents, and European syntacticians retained this em- phasis on such dependency grammars, the subject of Chapter 13. American Structuralism saw a number of specific definitions of the immediate constituent, couched in terms of their search for a “discovery procedure”: a method- ological algorithm for describing the syntax of a language. In general, these attempt to capture the intuition that “The primary criterion of the immediate constituent is the degree in which combinations behave as simple units” (Bazell, 1966, p. 284). The most well known of the specific definitions is Harris’ idea of distributional similarity to individual units, with the substitutability test. Essentially, the method proceeded by breaking up a construction into constituents by attempting to substitute simple structures for possible constituents—if a substitution of a simple form, say, man, was substitutable in a construction for a more complex set (like intense young man), then the form intense young man was probably a constituent. Harris’s test was the beginning of the intuition that a constituent is a kind of equivalence class. The first formalization of this idea of hierarchical constituency was the phrase- structure grammar defined in Chomsky (1956) and further expanded upon (and argued against) in Chomsky (1957) and Chomsky (1975). From this time on, most generative linguistic theories were based at least in part on context-free grammars or generalizations of them (such as Head-Driven Phrase Structure Grammar (Pollard and Sag, 1994), Lexical-Functional Grammar (Bresnan, 1982), Government and Binding (Chomsky, 1981), and Construction Grammar (Kay and Fillmore, 1999), inter alia); many of these theories used schematic context-free templates known as X-bar schemata, which also relied on the notion of syntactic head.X-barschemata Shortly after Chomsky’s initial work, the context-free grammar was reinvented by Backus (1959) and independently by Naur et al. (1960) in their descriptions of the ALGOL programming language; Backus (1996) noted that he was influenced by the productions of Emil Post and that Naur’s work was independent of his (Backus’) own. (Recall the discussion on page ?? of multiple invention in science.) After this early work, a great number of computational models of natural language processing were based on context-free grammars because of the early development of efficient algorithms to parse these grammars (see Chapter 11). 28 CHAPTER 10 • FORMAL GRAMMARS OF ENGLISH As we have already noted, grammars based on context-free rules are not ubiqui- tous. Various classes of extensions to CFGs are designed specifically to handle long- distance dependencies. We noted earlier that some grammars treat long-distance- dependent items as being related semantically but not syntactically; the surface syn- tax does not represent the long-distance link (Kay and Fillmore 1999, Culicover and Jackendoff 2005). But there are alternatives. One extended formalism is Tree Adjoining Grammar (TAG) (Joshi, 1985). The primary TAG data structure is the tree, rather than the rule. Trees come in two kinds: initial trees and auxiliary trees. Initial trees might, for example, represent simple sentential structures, and auxiliary trees add recursion into a tree. Trees are combined by two operations called substitution and adjunction. The adjunction operation handles long-distance dependencies. See Joshi (1985) for more details. An extension of Tree Adjoining Grammar, called Lexicalized Tree Adjoining Gram- mars is discussed in Chapter 12. Tree Adjoining Grammar is a member of the family of mildly context-sensitive languages. We mentioned on page 15 another way of handling long-distance dependencies, based on the use of empty categories and co-indexing. The Penn Treebank uses this model, which draws (in various Treebank corpora) from the Extended Standard Theory and Minimalism (Radford, 1997). Readers interested in the grammar of English should get one of the three large reference grammars of English: Huddleston and Pullum (2002), Biber et al. (1999), and Quirk et al. (1985). Another useful reference is McCawley (1998). There are many good introductory textbooks on syntax from different perspec- tives. Sag et al. (2003) is an introduction to syntax from a generative perspective,generative focusing on the use of phrase-structure rules, unification, and the type hierarchy in Head-Driven Phrase Structure Grammar. Van Valin, Jr. and La Polla (1997) is an introduction from a functional perspective, focusing on cross-linguistic data and onfunctional the functional motivation for syntactic structures. Exercises 10.1 Draw tree structures for the following ATIS phrases: 1. Dallas 2. from Denver 3. after five p.m. 4. arriving in Washington 5. early flights 6. all redeye flights 7. on Thursday 8. a one-way fare 9. any delays in Denver 10.2 Draw tree structures for the following ATIS sentences: 1. Does American airlines have a flight between five a.m. and six a.m.? 2. I would like to fly on American airlines. 3. Please repeat that. 4. Does American 487 have a first-class section? 5. I need to fly between Philadelphia and Atlanta. 6. What is the fare from Atlanta to Denver? EXERCISES 29 7. Is there an American airlines flight from Philadelphia to Dallas? 10.3 Assume a grammar that has many VP rules for different subcategorizations, as expressed in Section 10.3.4, and differently subcategorized verb rules like Verb-with-NP-complement. How would the rule for postnominal relative clauses (10.4) need to be modified if we wanted to deal properly with examples like the earliest flight that you have? Recall that in such examples the pronoun that is the object of the verb get. Your rules should allow this noun phrase but should correctly rule out the ungrammatical S *I get. 10.4 Does your solution to the previous problem correctly model the NP the earliest flight that I can get? How about the earliest flight that I think my mother wants me to book for her? Hint: this phenomenon is called long-distance dependency. 10.5 Write rules expressing the verbal subcategory of English auxiliaries; for ex- ample, you might have a rule verb-with-bare-stem-VP-complement→ can. 10.6 NPs like Fortune’s office or my uncle’s marks are called possessive or genitivepossessive genitive noun phrases. We can model possessive noun phrases by treating the sub-NP like Fortune’s or my uncle’s as a determiner of the following head noun. Write grammar rules for English possessives. You may treat ’s as if it were a separate word (i.e., as if there were always a space before ’s). 10.7 Page 8 discussed the need for a Wh-NP constituent. The simplest Wh-NP is one of the Wh-pronouns (who, whom, whose, which). The Wh-words what and which can be determiners: which four will you have?, what credit do you have with the Duke? Write rules for the different types of Wh-NPs. 10.8 Write an algorithm for converting an arbitrary context-free grammar into Chom- sky normal form. 30 Chapter 10 • Formal Grammars of English Ajdukiewicz, K. (1935). Die syntaktische Konnexität. Stu- dia Philosophica, 1, 1–27. English translation “Syntactic Connexion” by H. Weber in McCall, S. (Ed.) 1967. Polish Logic, pp. 207–231, Oxford University Press. Backus, J. W. (1959). The syntax and semantics of the pro- posed international algebraic language of the Zurich ACM- GAMM Conference. In Information Processing: Proceed- ings of the International Conference on Information Pro- cessing, Paris, pp. 125–132. UNESCO. Backus, J. W. (1996). Transcript of question and answer ses- sion. In Wexelblat, R. L. (Ed.), History of Programming Languages, p. 162. Academic Press. Bar-Hillel, Y. (1953). A quasi-arithmetical notation for syn- tactic description. Language, 29, 47–58. Reprinted in Y. Bar-Hillel. (1964). Language and Information: Selected Essays on their Theory and Application, Addison-Wesley, 61–74. Bazell, C. E. (1952/1966). The correspondence fallacy in structural linguistics. In Hamp, E. P., Householder, F. W., and Austerlitz, R. (Eds.), Studies by Members of the En- glish Department, Istanbul University (3), reprinted in Readings in Linguistics II (1966), pp. 271–298. University of Chicago Press. Biber, D., Johansson, S., Leech, G., Conrad, S., and Fine- gan, E. (1999). Longman Grammar of Spoken and Written English. Pearson ESL, Harlow. Bies, A., Ferguson, M., Katz, K., and MacIntyre, R. (1995). Bracketing guidelines for Treebank II style Penn Treebank Project.. Bloomfield, L. (1914). An Introduction to the Study of Lan- guage. Henry Holt and Company. Bloomfield, L. (1933). Language. University of Chicago Press. Bresnan, J. (Ed.). (1982). The Mental Representation of Grammatical Relations. MIT Press. Charniak, E. (1997). Statistical parsing with a context-free grammar and word statistics. In AAAI-97, pp. 598–603. AAAI Press. Chomsky, N. (1956). Three models for the description of language. IRE Transactions on Information Theory, 2(3), 113–124. Chomsky, N. (1956/1975). The Logical Structure of Linguis- tic Theory. Plenum. Chomsky, N. (1957). Syntactic Structures. Mouton, The Hague. Chomsky, N. (1963). Formal properties of grammars. In Luce, R. D., Bush, R., and Galanter, E. (Eds.), Handbook of Mathematical Psychology, Vol. 2, pp. 323–418. Wiley. Chomsky, N. (1981). Lectures on Government and Binding. Foris. Collins, M. (1999). Head-Driven Statistical Models for Nat- ural Language Parsing. Ph.D. thesis, University of Penn- sylvania, Philadelphia. Culicover, P. W. and Jackendoff, R. (2005). Simpler Syntax. Oxford University Press. Gazdar, G., Klein, E., Pullum, G. K., and Sag, I. A. (1985). Generalized Phrase Structure Grammar. Blackwell. Harris, Z. S. (1946). From morpheme to utterance. Lan- guage, 22(3), 161–183. Hemphill, C. T., Godfrey, J., and Doddington, G. (1990). The ATIS spoken language systems pilot corpus. In Pro- ceedings DARPA Speech and Natural Language Workshop, Hidden Valley, PA, pp. 96–101. Hockenmaier, J. and Steedman, M. (2007). Ccgbank: a cor- pus of ccg derivations and dependency structures extracted from the penn treebank. Computational Linguistics, 33(3), 355–396. Hopcroft, J. E. and Ullman, J. D. (1979). Introduction to Automata Theory, Languages, and Computation. Addison- Wesley. Huddleston, R. and Pullum, G. K. (2002). The Cambridge Grammar of the English Language. Cambridge University Press. Joshi, A. K. (1985). Tree adjoining grammars: How much context-sensitivity is required to provide reasonable struc- tural descriptions?. In Dowty, D. R., Karttunen, L., and Zwicky, A. (Eds.), Natural Language Parsing, pp. 206– 250. Cambridge University Press. Kay, P. and Fillmore, C. J. (1999). Grammatical construc- tions and linguistic generalizations: The What’s X Doing Y? construction. Language, 75(1), 1–33. Magerman, D. M. (1995). Statistical decision-tree models for parsing. In ACL-95, pp. 276–283. Marcus, M. P., Kim, G., Marcinkiewicz, M. A., MacIntyre, R., Bies, A., Ferguson, M., Katz, K., and Schasberger, B. (1994). The Penn Treebank: Annotating predicate argu- ment structure. In ARPA Human Language Technology Workshop, Plainsboro, NJ, pp. 114–119. Morgan Kauf- mann. Marcus, M. P., Santorini, B., and Marcinkiewicz, M. A. (1993). Building a large annotated corpus of English: The Penn treebank. Computational Linguistics, 19(2), 313– 330. McCawley, J. D. (1998). The Syntactic Phenomena of En- glish. University of Chicago Press. Naur, P., Backus, J. W., Bauer, F. L., Green, J., Katz, C., McCarthy, J., Perlis, A. J., Rutishauser, H., Samelson, K., Vauquois, B., Wegstein, J. H., van Wijnagaarden, A., and Woodger, M. (1960). Report on the algorithmic language ALGOL 60. Communications of the ACM, 3(5), 299–314. Revised in CACM 6:1, 1-17, 1963. Nivre, J., de Marneffe, M.-C., Ginter, F., Goldberg, Y., Hajič, J., Manning, C. D., McDonald, R. T., Petrov, S., Pyysalo, S., Silveira, N., Tsarfaty, R., and Zeman, D. (2016). Uni- versal Dependencies v1: A multilingual treebank collec- tion. In LREC-16. Percival, W. K. (1976). On the historical source of immedi- ate constituent analysis. In McCawley, J. D. (Ed.), Syntax and Semantics Volume 7, Notes from the Linguistic Under- ground, pp. 229–242. Academic Press. Pollard, C. and Sag, I. A. (1994). Head-Driven Phrase Struc- ture Grammar. University of Chicago Press. Quirk, R., Greenbaum, S., Leech, G., and Svartvik, J. (1985). A Comprehensive Grammar of the English Lan- guage. Longman. Radford, A. (1988). Transformational Grammar: A First Course. Cambridge University Press. Radford, A. (1997). Syntactic Theory and the Structure of English: A Minimalist Approach. Cambridge University Press. Exercises 31 Sag, I. A., Wasow, T., and Bender, E. M. (Eds.). (2003). Syn- tactic Theory: A Formal Introduction. CSLI Publications, Stanford, CA. Steedman, M. (1989). Constituency and coordination in a combinatory grammar. In Baltin, M. R. and Kroch, A. S. (Eds.), Alternative Conceptions of Phrase Structure, pp. 201–231. University of Chicago. Steedman, M. (1996). Surface Structure and Interpretation. MIT Press. Linguistic Inquiry Monograph, 30. Steedman, M. (2000). The Syntactic Process. The MIT Press. Van Valin, Jr., R. D. and La Polla, R. (1997). Syntax: Struc- ture, Meaning, and Function. Cambridge University Press. Wundt, W. (1900). Völkerpsychologie: eine Untersuchung der Entwicklungsgesetze von Sprache, Mythus, und Sitte. W. Engelmann, Leipzig. Band II: Die Sprache, Zweiter Teil. Formal Grammars of English Constituency Context-Free Grammars Formal Definition of Context-Free Grammar Some Grammar Rules for English Sentence-Level Constructions Clauses and Sentences The Noun Phrase The Verb Phrase Coordination Treebanks Example: The Penn Treebank Project Treebanks as Grammars Heads and Head Finding Grammar Equivalence and Normal Form Lexicalized Grammars Combinatory Categorial Grammar Summary Bibliographical and Historical Notes Exercises

Related Posts