context free grammars reading: chap 12-13, jurafsky & martin

Context FreeGrammars

Reading: Chap 12-13, Jurafsky & Martin

This slide set was adapted from J. Martin and Rada Mihalcea

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.

Syntax

Why should you care?Grammar checkersQuestion answering Information extractionMachine translation

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Speech and Language Processing - Jurafsky and Martin

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Constituency

The basic idea here is that groups of words within utterances can be shown to act as single units.

And in a given language, these units form coherent classes that can be be shown to behave in similar ways

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Constituency

For example, it makes sense to the say that the following are all noun phrases in English...

The person I ate dinner with yesterdayThe car that I drove in college

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Grammars and Constituency

However, it isn’t easy or obvious how we come up with the right set of constituents and the rules that govern how they combine...

That’s why there are so many different theories of grammar and competing analyses of the same data.

The approach to grammar, and the analyses, adopted here are very generic (and don’t correspond to any modern linguistic theory of grammar).

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Context-Free Grammars

Context-free grammars (CFGs)Also known as

Phrase structure grammarsBackus-Naur form

Consist ofRules TerminalsNon-terminals

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Context-Free Grammars

TerminalsWe’ll take these to be words

Non-TerminalsThe constituents in a language

Like noun phrase, verb phrase and sentenceRules

Rules are equations that consist of a single non-terminal on the left and any number of terminals and non-terminals on the right.

CFG Example

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 weak – not expressive enoughContext-sensitive

Too powerful – parsing is not efficient

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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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Some NP Rules

Here are some rules for our noun phrases

Together, these describe two kinds of NPs.One that consists of a determiner followed by a nominalAnd another that says that proper names are NPs.The third rule illustrates two things

An explicit disjunctionTwo kinds of nominals

A recursive definitionSame non-terminal on the right and left-side of the

rule

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Grammar

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Derivations

A derivation is a sequence of rules applied to a string that accounts for that stringCovers all the elements in the

stringCovers only the elements in the

string

Practice: Another Recursion Example

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 Example

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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Sentence Types

Declaratives: A plane left.

S NP VPImperatives: Leave!

S VPYes-No Questions: Did the plane leave?

S Aux NP VPWH Questions: When did the plane leave?

S WH-NP Aux NP VP

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Noun Phrases

Let’s consider the following rule in more detail...NP Det Nominal

Consider the derivation for the following exampleAll the morning flights from Denver to Tampa leaving before 10

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Noun Phrases

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NP Structure

Clearly this NP is really about flights. That’s the central criticial noun in this NP. It is the head.

We can dissect this kind of NP into the stuff that can come before the head, and the stuff that can come after it.

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Determiners

Noun phrases can start with determiners...Determiners can be

Simple lexical items: the, this, a, an, etc.A car

Or simple possessivesJohn’s car

Or complex recursive versions of thatJohn’s sister’s husband’s son’s car

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Nominals

Contains the head and any pre- and postmodifiers of the head.Pre-

Quantifiers, cardinals, ordinals...Three cars

Adjectiveslarge cars

Note: there are ordering constraintsThree large cars?large three cars

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Postmodifiers

Three kindsPrepositional phrases

From SeattleNon-finite clauses

Arriving before noonRelative clauses

That serve breakfastRecursive rules to handle these

Nominal Nominal PPNominal Nominal GerundVPNominal Nominal RelClause

Agreement

This dogThose dogs

This dog eatsThose dogs eat

*This dogs*Those dog

*This dog eat*Those dogs eats

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Verb Phrases

English VPs consist of a head verb along with 0 or more following constituents which we’ll call arguments.

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 places on the number and type of the argument it wants to take

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Overgeneration

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

In lecture: go over the grammar for assignment 3

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Possible CFG Solution

Possible solution for agreement.Can use the same trick for all the verb/VP classes.

(Like propositionalizing a first-order knowledge base – the KB gets very large, but the inference algorithms are very efficient)

SgS -> SgNP SgVPPlS -> PlNp PlVPSgNP -> SgDet SgNomPlNP -> PlDet PlNomPlVP -> PlV NPSgVP ->SgV Np…

Movement

• Core example (no movement yet)– [[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.

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 it’s 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

Grammar equivalence and normal form

Strong equivalence:– two grammars are strongly equivalent if:

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

– two grammars are weakly equivalent if:• they generate/accept 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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Treebanks

Treebanks are corpora in which each sentence has been paired with a parse tree (presumably the right one).

These are generally created By first parsing the collection with an automatic

parserAnd then having human annotators correct each

parse as necessary.This generally requires detailed annotation guidelines that provide a POS tagset, a grammar and instructions for how to deal with particular grammatical constructions.

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Penn Treebank

Penn TreeBank is a widely used treebank.

Most well known is the Wall Street Journal section of the Penn TreeBank.

1 M words from the 1987-1989 Wall Street Journal.

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Treebank Grammars

Treebanks implicitly define a grammar for the language covered in the treebank.

Simply take the local rules that make up the sub-trees in all the trees in the collection and you have a grammar.

Not complete, but if you have decent size corpus, you’ll have a grammar with decent coverage.

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Treebank Grammars

Such grammars tend to be very flat due to the fact that they tend to avoid recursion.

For example, the Penn Treebank has 4500 different rules for VPs. Among them...

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Heads in Trees

Finding heads in treebank trees is a task that arises frequently in many applications.Particularly important in statistical parsing

We can visualize this task by annotating the nodes of a parse tree with the heads of each corresponding node.

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Lexically Decorated Tree

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Head Finding

The standard way to do head finding is to use a simple set of tree traversal rules specific to each non-terminal in the grammar.

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Noun Phrases

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Treebank Uses

Treebanks (and headfinding) are particularly critical to the development of statistical parsersChapter 14

Also valuable to Corpus Linguistics Investigating the empirical details of various constructions in a

given language

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Dependency Grammars

In CFG-style phrase-structure grammars the main focus is on constituents.

But it turns out you can get a lot done with just binary relations among the words in an utterance.

In a dependency grammar framework, a parse is a tree where the nodes stand for the words in an utteranceThe links between the words represent dependency relations

between pairs of words.Relations may be typed (labeled), or not.

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Dependency Relations

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Dependency Parse

They hid the letter on the shelf

See the Stanford parser on line

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Dependency Parsing

The dependency approach has a number of advantages over full phrase-structure parsing.Deals well with free word order languages where the constituent

structure is quite fluidParsing is much faster than CFG-bases parsersDependency structure often captures the syntactic relations

needed by later applicationsCFG-based approaches often extract this same information

from trees anyway.

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Dependency Parsing

There are two modern approaches to dependency parsingOptimization-based approaches that search a space of trees for

the tree that best matches some criteriaShift-reduce approaches that greedily take actions based on the

current word and state.

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Summary

Context-free grammars can be used to model various facts about the syntax of a language.

When paired with parsers, such grammars consititute a critical component in many applications.

Constituency is a key phenomena easily captured with CFG rules.But agreement and subcategorization do pose

significant problemsTreebanks pair sentences in corpus with their corresponding trees.

context free grammars reading: chap 12-13, jurafsky & martin

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