Transcript CONTEXT-FREE GRAMMARS

CONTEXT-FREE GRAMMARS
1
Syntactic analysis (Parsing)
S
NP
AT
the
VP
NNS
VBD
children
ate
NP
AT
the
2
NLE
NN
cake
Beyond regular languages:
Context-Free Grammars
S  NP VP
NP  Det Nominal
Nominal  Noun
VP  V
4
Det  the
Det  a
Noun  flight
V  left
NLE
Derivations

A DERIVATION of a string is a sequence of rule
applications
–
E.g., the string “a flight” can be derived from the grammar
above and symbol NP by the (leftmost first) derivation



5
NP => Det Nominal => a Nominal => a Noun => a flight
Derivations can be visualized as PARSE TREES
The LANGUAGE defined by a CFG is the set of strings
derivable from the start symbol S (for Sentence)
NLE
Derivations and parse trees
6
NLE
A more formal definition

7
A CFG is a 4-tuple
<N,,P, S> consisting of
NLE
What `context free’ means
8
NLE
Derivations and languages

The language LG GENERATED by a CFG
grammar G is the set of strings of TERMINAL
symbols that can be derived from the start
symbol S using the production rules in G
–


9
LG = {w | w is in * and S derives w}
The strings in LG are called GRAMMATICAL
The strings not in LG are called
UNGRAMMATICAL
NLE
Grammar development


10
One of the most basic skills in NLE is the ability
to write a CFG for some fragment of a
language (e.g., the dates)
We’ll briefly cover some of the issues to be
addressed when writing small CFG grammars
NLE
An example lexicon
11
NLE
An example grammar
12
NLE
A simple parse tree
13
NLE
Basic types of phrases




14
Sentences
Noun Phrases
Verb phrases
Prepositional phrases
NLE
Basic types of sentences
15
NLE
Noun phases: premodifiers


NP  (Det) (Card) (Ord) (Quant) (AP) Nominal
Det: Determiners
–
–




16
a flight
Optional: I’m looking for flights to Denver
Card: Cardinal numbers (one stop)
Ord: Ordinal numbers (the first flight)
Quantifiers: most flights to Denver leave in the morning
AP (Adjectives): three very expensive seats
NLE
Noun phases: postmodifiers




17
Nominal  Noun
Nominal  Nominal PP (PP) (PP)
Nominal  Nominal GerundVP
Nominal  Nominal RelClause
NLE
Types of postnominal modifiers
18
NLE
Recursion

Nominal  Nominal PP (PP) (PP)
–

Other examples:
–
–

19
Is an example of RECURSIVE rule
NP  NP PP
VP  VP PP
Recursion a powerful device, but could have
bad consequences (see lectures on parsing)
NLE
Recursion and VP attachment
20
NLE
Coordination

NP  NP and NP
–

VP  VP and VP
–

John talks softly and carries a big stick
S  S and / but / S
–

John and Mary left
Kim is a lawyer but Sandy is reading medicine.
In fact, probably English has a
XP  XP and XP
rule
–
21
NLE
Agreement







22
This dog
Those dogs
*This dogs
*Those dogs
This dog is smart
*This dog are smart
*Those dogs is smart
NLE
CFGs vs Regular languages


For many applications, finite state languages
(the languages defined by FA) are appropriate
Limitation of FAs: cannot count
–

Example of construction showing that English
is CF: long-distance dependencies
–
24
I.e., cannot check A n B n
Which film did Kim say the director who we just met
_ recommended _?
NLE
The Chomsky Hierarchy

Finite-state languages (type 3)
–

Context-free languages (type 2)
–

CAC  BB
Recursively enumerable languages
–
25
A  BB
Context-sensitive languages (type 1)
–

A  bC | Cb (a single NT on the right)
Every language that can be specified by a finite algorithm
NLE
Readings


Jurafsky and Martin, chapter 9
The chapters on context-free languages in
–
–
26
The Free Dictionary:
http://encyclopedia.thefreedictionary.com/Contextfree%20language
Wikipedia:
http://en.wikipedia.org/wiki/Context-free_grammar
NLE