Lecture CFG

7/30/2019 Lecture CFG

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1

CONTEXT-FREE GRAMMARS


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NLE2

Syntactic analysis (Parsing)

S

NP VP

AT NNS VBD NP

AT NNthe children ate

the cake


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NLE4

Beyond regular languages:

Context-Free Grammars

S NP VPNP Det Nominal

Nominal Noun

VP V

Det theDet a

Noun flight

V left


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NLE5

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

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 stringsderivable from the start symbol S (for Sentence)


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NLE6

Derivations and parse trees


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NLE7

A more formal definition

A CFG is a 4-tuple

consisting of


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NLE8

What `context free means


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NLE9

Derivations and languages

The language LG GENERATED by a CFG

grammar G is the set of strings of TERMINALsymbols that can be derived from the start

symbol S using the production rules in G

LG = {w | w is in * and S derives w}

The strings in LG are called GRAMMATICAL The strings not in LG are called

UNGRAMMATICAL


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NLE10

Grammar development

One of the most basic skills in NLE is the ability

to write a CFG for some fragment of alanguage (e.g., the dates)

Well briefly cover some of the issues to be

addressed when writing small CFG grammars


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NLE11

An example lexicon


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NLE12

An example grammar


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NLE13

A simple parse tree


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NLE14

Basic types of phrases

Sentences

Noun Phrases Verb phrases

Prepositional phrases


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NLE15

Basic types of sentences


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NLE16

Noun phases: premodifiers

NP (Det) (Card) (Ord) (Quant) (AP) Nominal

Det: Determiners

a flight

Optional: Im looking forflights 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


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NLE17

Noun phases: postmodifiers

Nominal Noun

Nominal Nominal PP (PP) (PP) Nominal Nominal GerundVP

Nominal Nominal RelClause


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NLE18

Types of postnominal modifiers


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NLE19

Recursion

Nominal Nominal PP (PP) (PP)

Is an example of RECURSIVE rule Other examples:

NP NP PP

VP VP PP

Recursion a powerful device, but could havebad consequences (see lectures on parsing)


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NLE20

Recursion and VP attachment


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NLE21

Coordination

NP NP and NP

John and Mary left

VP VP and VP

John talks softly and carries a big stick

S S and / but / S

Kim is a lawyer but Sandy is reading medicine.

In fact, probably English has a

XP XP and XP

rule


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NLE22

Agreement

This dog

Those dogs *This dogs

*Those dogs

This dog is smart *This dog are smart

*Those dogs is smart


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NLE24

CFGs vs Regular languages

For many applications, finite state languages

(the languages defined by FA) are appropriate Limitation of FAs: cannot count

I.e., cannot check A n B n

Example of construction showing that English

is CF: long-distance dependencies Which film did Kim say the directorwho we just met

_recommended_?


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NLE25

The Chomsky Hierarchy

Finite-state languages (type 3)

A bC | Cb (a single NT on the right)

Context-free languages (type 2)

A BB

Context-sensitive languages (type 1)

CAC BB

Recursively enumerable languages

Every language that can be specified by a finite algorithm


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NLE26

Readings

Jurafsky and Martin, chapter 9

The chapters on context-free languages in The Free Dictionary:

http://encyclopedia.thefreedictionary.com/Context-

free%20language

Wikipedia:http://en.wikipedia.org/wiki/Context-free_grammar
http://encyclopedia.thefreedictionary.com/Context-free%20languagehttp://encyclopedia.thefreedictionary.com/Context-free%20languagehttp://en.wikipedia.org/wiki/Context-free_grammarhttp://en.wikipedia.org/wiki/Context-free_grammarhttp://en.wikipedia.org/wiki/Context-free_grammarhttp://en.wikipedia.org/wiki/Context-free_grammarhttp://encyclopedia.thefreedictionary.com/Context-free%20languagehttp://encyclopedia.thefreedictionary.com/Context-free%20languagehttp://encyclopedia.thefreedictionary.com/Context-free%20language

Documents

Lecture CFG