Syntax380L
September12,2003
Phrase Structure Rules
Structure within the NP 1Definitions
(1)a tree for‘the brown fox sings’
A
B
D the
E
F
brown
G
fox
C
sings
Linguistic trees have nodes.The nodes in(1)are A,B,C,D,E,F,and G.
There are two kinds of nodes:internal nodes and terminal nodes.The internal nodes in(1)are A,B,and E.The terminal nodes are C,D,F,and G.Terminal nodes are so called because they are not expanded into anything further.The tree ends there.
Terminal nodes are also called leaf nodes.The leaves of(1)are really the words that constitute the sentence‘the brown fox sings’i.e.‘the’,‘brown’,‘fox’,and‘sings’.
sort out the facts(2)  a.A set of nodes form a constituent iff they are exhaustively dominated by a common
node.
b.X is a constituent of Y iff X is dominated by Y.
c.X is an immediate constituent of Y iff X is immediately dominated by Y.
Notions such as subject,object,prepositional object etc.can be defined structurally.So a subject is the NP immediately dominated by S and an object is an NP immediately dominated by VP etc.
(3)  a.If a node X immediately dominates a node Y,then X is the mother of Y,and Y is the
daughter of X.
b.A set of nodes are sisters if they are all immediately dominated by the same(mother)
node.
We can now define a host of relationships on trees-grandmother,granddaughter,descendant, ancestor etc.
Another important relationship that is defined in purely structural terms is c-command.
(4)A c-commands B if and only if A does not dominate B and the node that immediately
dominates A dominates B.
c-command is used in the formulation of Condition C,a principle used to determine what a pro-noun may not refer to.
C ONDITION C
(5)A pronoun cannot refer to a proper name it c-commands.
Note that Condition C is a negative condition.It never tells you what a particular pronoun must refer to.It only tells you what it cannot refer to.
In general,if a pronoun cannot refer to a proper name(despite agreeing in gender and number), you can conclude that the pronoun c-commands the proper name.
The N O C ROSSING B RANCHES C ONSTRAINT
(6)If one node X precedes another node Y,then all descendants of X must also precede Y and
all descendants of Y.
2How to grow trees
Where do the trees that we use to analyze linguistic structure come from?
In a way,they are just representations of facts that exist out in the world-the facts that we can discover using constituency test.So one way to make trees is by doing empirical work-taking a sentence,applying various constituency tests to the words in the sentence,and then drawing a tree based on the results of our tests.
This empirical method is ultimately the only correct way to deduce‘tree structure’.However,in most cases,we can simplify things considerably by using Phrase Structure Rules.
Phrase Structure Rules are rules of the sort
X Y Z
This rule says‘take the node X and expand it into the nodes Y and Z’.Alternately,going from right to left(or from below),it says‘if you have a Y and a Z next to each other,you can combine them to make an X’.1
Phrase structure rules can be ules that expand categories into other categories,or they can also be ules that expand category labels by word(lexical items).2
A grammar can then be thought of as a set of phrase structure rules(categorial rules plus lexical rules).
The categorial rules can be thought of as(part of)the syntax and the lexical rules as(part of)the lexicon.
2.1Some Phrase Structure Rules for English
(7)Categorial Rules
a.S NP Modal VP
b.VP V AP PP
c.AP ADVP A
d.ADVP ADV
e.PP P NP
f.NP D N
(8)Lexical Rules
a.N girl
b.N boy
c.Adv incredibly
d.A conceited
e.V seem
f.Modal must
g.P to
h.D that
i.D this
Some sentences these rules will generate:
(9)  a.This boy must seem incredibly conceited to that girl.
b.This boy must seem incredibly conceited to this girl.
c.This boy must seem incredibly conceited to that boy.
d.This boy must seem incredibly conceited to this boy.
e.This girl must seem incredibly conceited to that girl.
f.This girl must seem incredibly conceited to this girl.
g.This girl must seem incredibly conceited to that boy.
h.This girl must seem incredibly conceited to this boy.
How many more sentences will these rules generate?
Optional constituents
How do we handle cases like:
(10)This boy must seem incredibly stupid.
2.2Introducing infinity
We know that human languages can contain sentences of arbitrary length.Consider(11)which stands for an infinite number of sentences.
(11)He believes that he believes that he believes that he believes that he ate pizza.
So if all of human language is to be generated by a set of phrase structure rules,the relevant set of phrase structure rules should generate an infinite number of sentences.
How can that be done?
Let us try to analyze(11),starting with a more manageable(12).
(12)He believes that he ate pizza.
We start with the following categorial rules:
(13)  a.S NP VP
b.VP V¯S
c.¯S COMP S
d.VP V NP
We need the following lexical rules:
(14)  a.NP he
b.NP pizza
c.V ate
d.V believes
e.COMP that
Now we can generate(12).This is shown in(15). (15)
S
NP
he
VP
V
believes
¯S
COMP that
S
NP
he
VP
V
ate
NP
pizza
But is(12)all that the rules in(13)and(14)will generate?
How many sentences will(13)and(14)generate?
2.2.1Overgeneration
The rules in(13)and(14)will also generate sentences(see the structure below)like: (16)*He ate that he believes pizza.
S
NP
he
VP
V
ate
¯S
COMP
that
S
NP
he
VP
V believes
NP pizza
How can we constrain phrase structure rules so that such overgeneration does not take place?
3Noun Phrases
So far,we have seen two kinds of categories:
word-level categories such as N,V,A,P etc.(somewhat imprecisely,words)and
phrase-level categories such as NP,VP,AP,PP etc.(somewhat imprecisely,sequences of words which can‘stand on their own’).
We will now investigate if these two kinds of categories are all we need a third category which lies in between words and full phrases.
Consider the following NP:
(17)the king of England
We feel quite confident saying that‘the king of England’is an NP.What else can we say about its structu
re?
There seems to be a lot of evidence that of England is a PP.It can be co-ordinated,shared in shared constituent co-ordination.It can also function as a sentence fragment and be preposed.
(18)  a.the king[of England]and[of the empire].(coordination)
b.He is the king,and she is the queen,[of England].(shared constituent coordination)
c.A:Was he the king of Livonia?
B:No,[of England].(sentence fragment)
d.[Of which country]was he the king?
At this point we have two options:
(19)
NP

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