Context FreeGrammars

Reading: Chap 12-13, Jurafsky & Martin

This slide set was adapted from J. Martin, U. Colorado

Instructor: Paul Tarau, based on Rada Mihalcea’s original slides

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Syntax

Syntax = rules describing how words can connect to each other

* that and after year last I saw you yesterday colorless green ideas sleep furiously

• the kind of implicit knowledge of your native language that you had mastered by the time you were 3 or 4 years old without explicit instruction

• not necessarily the type of rules you were later taught in school.

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Syntax

Why should you care?Grammar checkersQuestion answering Information extractionMachine translation

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Context-Free Grammars

Capture constituency and orderingOrdering

What are the rules that govern the ordering of words and bigger units in the language

ConstituencyHow do words group into units and what we say about how the various kinds of units behave

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CFG Examples

S -> NP VPNP -> Det NOMINALNOMINAL -> NounVP -> VerbDet -> aNoun -> flightVerb -> left

these rules are defined independent of the context where they might occur -> CFG

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CFGs

S -> NP VPThis says that there are units called S, NP, and VP in this

languageThat an S consists of an NP followed immediately by a VPDoesn’t say that that’s the only kind of SNor does it say that this is the only place that NPs and VPs occur

GenerativityYou can view these rules as either analysis or synthesis

machinesGenerate strings in the languageReject strings not in the languageImpose structures (trees) on strings in the language

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Parsing

Parsing is the process of taking a string and a grammar and returning a (many?) parse tree(s) for that string

Other optionsRegular languages (expressions)

Too weakContext-sensitive

Too powerful

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Context?

The notion of context in CFGs is not the same as the ordinary meaning of the word context in language.

All it really means is that the non-terminal on the left-hand side of a rule is out there all by itselfA -> B CMeans that I can rewrite an A as a B followed by a C regardless

of the context in which A is found

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Key Constituents (English)

SentencesNoun phrasesVerb phrasesPrepositional phrases

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Sentence-Types

Declaratives: A plane leftS -> NP VP

Imperatives: Leave!S -> VP

Yes-No Questions: Did the plane leave?S -> Aux NP VP

WH Questions: When did the plane leave?S -> WH Aux NP VP

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Conjunctive Constructions

S -> S and SJohn went to NY and Mary followed him

NP -> NP and NPVP -> VP and VP…In fact the right rule for English is

X -> X and X

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Recursion

We’ll have to deal with rules such as the following where the non-terminal on the left also appears somewhere on the right (directly).NP -> NP PP [[The flight] [to Boston]]VP -> VP PP [[departed Miami] [at noon]]

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Recursion

Of course, this is what makes syntax interestingflights from DenverFlights from Denver to MiamiFlights from Denver to Miami in FebruaryFlights from Denver to Miami in February on a FridayFlights from Denver to Miami in February on a Friday under

$300Flights from Denver to Miami in February on a Friday under

$300 with lunch

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The Point

If you have a rule likeVP -> V NP

It only cares that the thing after the verb is an NP. It doesn’t have to know about the internal affairs of that NP

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The Point

VP -> V NPI hate

flights from DenverFlights from Denver to MiamiFlights from Denver to Miami in FebruaryFlights from Denver to Miami in February on a FridayFlights from Denver to Miami in February on a Friday under

$300Flights from Denver to Miami in February on a Friday under

$300 with lunch

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Potential Problems in CFG

AgreementSubcategorizationMovement

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Agreement

This dogThose dogs

This dog eatsThose dogs eat

*This dogs*Those dog

*This dog eat*Those dogs eats

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Subcategorization

Sneeze: John sneezedFind: Please find [a flight to NY]NPGive: Give [me]NP[a cheaper fare]NPHelp: Can you help [me]NP[with a flight]PPPrefer: I prefer [to leave earlier]TO-VPTold: I was told [United has a flight]S

…

*John sneezed the book*I prefer United has a flight*Give with a flight

Subcat expresses the constraints that a predicate (verb for now) places on the number and type of the argument it wants to take

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So?

So the various rules for VPs overgenerate.They permit the presence of strings containing verbs and

arguments that don’t go togetherFor exampleVP -> V NP therefore

Sneezed the book is a VP since “sneeze” is a verb and “the book” is a valid NP

Subcategorization frames can fix this problem (“slow down” overgeneration)

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Movement

• Core example– [[My travel agent]NP [booked [the flight]NP]VP]S

• I.e. “book” is a straightforward transitive verb. It expects a single NP arg within the VP as an argument, and a single NP arg as the subject.

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Movement

• What about?– Which flight do you want me to have the travel agent

book?

• The direct object argument to “book” isn’t appearing in the right place. It is in fact a long way from where its supposed to appear.

• And note that its separated from its verb by 2 other verbs.

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Formally…

To put all previous discussions/examples in a formal definition for CFG:

A context free grammar has four parameters:

1. A set of non-terminal symbols N2. A set of terminal symbols T3. A set of production rules P, each of the form A a, where A

is a non-terminal, and a is a string of symbols from the infinite set of strings (T N)*

4. A designated start symbol S

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Grammar equivalence and normal form

Strong equivalence:– two grammars are strongly equivalent if:

• they generate the same set of strings• they assign the same phrase structure to each sentence

– two grammars are weakly equivalent if:• they generate the same set of strings• they do not assign the same phrase structure to each sentence

Normal form – Restrict the form of productions– Chomsky Normal Form (CNF)– Right hand side of the productions has either one or two

terminals or non-terminals– e.g. A -> BC A -> a– Any grammar can be translated into a weakly equivalent CNF– A -> B C D <=> A-> B X X -> C D

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Building tree structures

Draw tree structures for the following phrases

Dallas from Denver arriving in Washington I need to fly between Philadelphia and Atlanta