Graphs and trees
Graphs and trees
Sentences
The sentence as a string of words
E.g
I saw the lady with the binoculars
string = a b c d e b f
However, the relations of parts of a
string to each other may be different
I saw the lady with the binoculars
is stucturally ambiguous
Who has the binoculars?
[ I ] saw the lady [ with the binoculars ]
= [a] b c d [e b f]
I saw [ the lady with the binoculars]
= a b [c d e b f]
Other examples
I read the paper on the sofa
I wrote an article on the ship
How can we represent the difference?
By assigning them different structures.
We can represent structures with 'trees'.
I
read
the
book
•Trees show us the
•structure (hierarchical relations)
•as well as the order (linear relation)
•of the elements of a sentence.
Sentence: I read the book
simple concatenation:
a) graphemes
I + r + e +a + d + t + h + e + b + o + o + k
b) words
I + read + the + book
Graphs and trees
Sentence: I read the book
concatenation of 'parts' (constituents)
[I]
subject
[ read ]
verb
=[I]
Graphs and trees
[ read the book ]
predicate
[ the book ]
object
[ [ read ] [ the book ] ]
Tree representation of nested structures or
herarchical structure
I
read
the
book
We can label the trees using category names
S
NP
VP
V
I
hierarchical
relations
NP
DET
read the
linear relations
N
book
Now we can disambiguate the sentence, which is
actually two sentences
a. I saw the lady with the binoculars
S
NP
VP
V
NP
NP
I
saw
PP
the lady with the binoculars
I saw [the lady with the binoculars]
b. I saw the lady with the binoculars
S
NP
VP
VP
I
saw the lady
PP
with the binoculars
I [ saw the lady ] with the binoculars
We can 'generate' the trees using phrase
structure rules
S  NP VP
S
NP
VP
VP  V
NP
VP
V
NP
NP  NP PP
NP
NP
PP
VP  VP
PP
VP
VP
PP
NP  DET N
NP
DET
N
Grammar
S 
VP 
NP 
VP 
NP 
NP
V
NP
VP
DET
VP
NP
PP
PP
N
These rules generate syntactic or phrasestructure trees
PHRASE STRUCTURE
RULES
LEXICON
S  NP VP ADV
VP  V NP
NP  Det (A) N
NP  Det N (PP)
PP  P NP
Det: a, the
N: man, article, newspaper
V: read
A: young
ADV: quickly
P: in
Graphs and trees
Merging (nested concatenation)
Take D (the) and N (article) and concatenate into
NP1 (the man)
Take V (read) and NP1 (the article) and
concatenate into VP (read the article)
Take D (the) and N (man) and concatenate into
NP2 (the man)
Take NP2 (the man) and VP (read the article)
and concatenate into S (the man read the article)
Graphs and trees
S
NP
DET
N
the man
VP
V
read
NP
DET
the
N
book
A simple phrase structure tree
birds fly
S
NP
VP
N
birds
V
fly
a phrase structure tree
Graphs and trees
CP
A complex phrase structure tree:
Peter met the teacher of ...
C‘
C
AGRP
DP1
AGR'
D' AGR
TP
D NP
t1
N'
T2
N
met
Peter
T'
VP
t1
V'
V
t2
DP
D'
D
the
NP
N'
N
PP
teacher
P'
P
DP
of
D‘
Graphs and trees
D......etc
Some exercises on trees
See handout
Graphs and trees