Basic Parsing with Context-Free Grammarskathy/NLP/2017/ClassSlides/...Basic Parsing with Context-Free Grammars Some slides adapted from Julia Hirschberg and Dan Jurafsky 1 . ... Normal

BasicParsingwithContext-FreeGrammars

1 Some slides adapted from Julia Hirschberg and Dan Jurafsky

Announcementsbull HW2togoouttodayNextTuesdaymostimportantforbackgroundtoassignment

bull Signupforpolleverywhere

bull Todaywrap-upfromlastclassandstartonparsing

2

Wrap-uponsyntax

3

GrammarEquivalencebull Canhavedifferentgrammarsthatgeneratesamesetofstrings(weakequivalence)bull  Grammar1NPrarrDetPNandDetPrarra|thebull  Grammar2NPrarraN|NPrarrtheN

bull CanhavedifferentgrammarsthathavesamesetofderivaLontrees(strongequivalence)bull WithCFGspossibleonlywithuselessrulesbull  Grammar2NPrarraN|NPrarrtheNbull  Grammar3NPrarraN|NPrarrtheNDetPrarrmany

bull Strongequivalenceimpliesweakequivalence

NormalFormsampcbull Thereareweaklyequivalentnormalforms(ChomskyNormalFormGreibachNormalForm)

bull TherearewaystoeliminateuselessproducLonsandsoon

ChomskyNormalFormACFGisinChomskyNormalForm(CNF)ifallproducLonsareofoneoftwoforms

bull  ArarrBCwithABCnonterminalsbull  ArarrawithAanonterminalandaaterminal

EveryCFGhasaweaklyequivalentCFGinCNF

NobodyUsesSimpleCFGs(ExceptIntroNLPCourses)

bull AllmajorsyntacLctheories(ChomskyLFGHPSGTAG-basedtheories)representbothphrasestructureanddependencyinonewayoranother

bull AllsuccessfulparserscurrentlyusestaLsLcsaboutphrasestructureandaboutdependency

bull DerivedependencythroughldquoheadpercolaLonrdquoforeachrulesaywhichdaughterishead

MassiveAmbiguityofSyntaxbull Forastandardsentenceandagrammarwithwidecoveragethereare1000sofderivaLons

bull Examplebull  ThelargeportraitpaintertoldthedelegaLonthathesentmoneyordersinaleYeronWednesday

9

10

PennTreebank(PTB)bull SyntacLcallyannotatedcorpusofnewspapertexts(phrasestructure)

bull ThenewspapertextsarenaturallyoccurringdatabutthePTBisnot

bull PTBannotaLonrepresentsaparLcularlinguisLctheory(butafairlyldquovanillardquoone)

bull ParLculariLesbull  VeryindirectrepresentaLonofgrammaLcalrelaLons(needforheadpercolaLontables)

bull  CompletelyflatstructureinNP(brownbaglunchpink-and-yellowchildseat)

bull  HasflatSsflatVPs

ExamplefromPTB((S(NP-SBJIt)(VPs(NP-PRD(NP(NPthelatestinvestmentcraze) (VPsweeping (NPWallStreet))) (NP(NParash) (PPof (NP(NPnewclosed-endcountryfunds) (NP(NPthose (ADJPpubliclytraded) poraolios) (SBAR(WHNP-37that) (S(NP-SBJT-37) (VPinvest (PP-CLRin (NP(NPstocks) (PPof (NPasingleforeigncountry)))))))))))

SyntacticParsing

13

SyntacticParsingbull DeclaraLveformalismslikeCFGsFSAsdefinethelegalstringsofalanguage--butonlytellyoulsquothisisalegalstringofthelanguageXrsquo

bull Parsingalgorithmsspecifyhowtorecognizethestringsofalanguageandassigneachstringone(ormore)syntacLcanalyses

14

CFGExamplebull  ManypossibleCFGsforEnglishhereisanexample(fragment)

bull  SrarrNPVPbull  VPrarrVNPbull  NPrarrDetN|AdjNPbull  Nrarrboy|girlbull  Vrarrsees|likesbull  Adjrarrbig|smallbull  DetPrarra|the

bull  bigthesmallgirlseesaboybull  Johnlikesagirlbull  Ilikeagirlbull  Isleepbull  Theolddogthefootstepsoftheyoung

the small boy likes a girl

ModiMiedCFGS agrave NP VP VP agrave V S agrave Aux NP VP VP -gt V PP S -gt VP PP -gt Prep NP NP agrave Det Nom

N agrave old | dog | footsteps | young | flight

NP agravePropN V agrave dog | include | prefer | book

NP -gt Pronoun Nom -gt Adj Nom Aux agrave does Nom agrave N Prep agravefrom | to | on | of Nom agrave N Nom PropN agrave Bush | McCain |

Obama Nom agrave Nom PP Det agrave that | this | a| the VP agrave V NP Adj -gt old | green | red

Parse Tree for lsquoThe old dog the footsteps of the youngrsquo for Prior CFG

S

NP VP

NP V

DET NOM

N PP

DET NOM

N

The old dog the

footsteps of the young

ParsingasaFormofSearchbull SearchingFSAs

bull  Findingtherightpaththroughtheautomatonbull  SearchspacedefinedbystructureofFSA

bull SearchingCFGsbull  Findingtherightparsetreeamongallpossibleparsetrees

bull  Searchspacedefinedbythegrammar

bull Constraintsprovidedbytheinputsentenceandtheautomatonorgrammar 18

Top-DownParserbull BuildsfromtherootSnodetotheleavesbull ExpectaLon-basedbull Commonsearchstrategy

bull  Top-downlei-to-rightbacktrackingbull  TryfirstrulewithLHS=Sbull  NextexpandallconsLtuentsinthesetreesrulesbull  ConLnueunLlleavesarePOSbull  BacktrackwhencandidatePOSdoesnotmatchinputstring 19

RuleExpansionbull ldquoTheolddogthefootstepsoftheyoungrdquo

bull Wheredoesbacktrackinghappen

bull WhatarethecomputaLonaldisadvantages

bull Whataretheadvantages

20

21

Bottom-UpParsingbull ParserbeginswithwordsofinputandbuildsuptreesapplyinggrammarruleswhoseRHSmatches DetNVDetNPrepDetN TheolddogthefootstepsoftheyoungDetAdjNDetNPrepDetN TheolddogthefootstepsoftheyoungParseconLnuesunLlanSrootnodereachedornofurthernodeexpansionpossible

22

DetNVDetNPrepDetNTheolddogthefootstepsoftheyoungDetAdjNDetNPrepDetN

23

Bottom-upparsingbull WhendoesdisambiguaLonoccur

bull WhatarethecomputaLonaladvantagesanddisadvantages

24

25

Whatrsquosrightwrongwithhellip

bull  Top-Downparsersndashtheyneverexploreillegalparses(egwhichcanrsquotformanS)--butwasteLmeontreesthatcannevermatchtheinput

bull  BoYom-Upparsersndashtheyneverexploretreesinconsistentwithinput--butwasteLmeexploringillegalparses(withnoSroot)

bull  Forbothfindacontrolstrategy--howexploresearchspaceefficientlybull  Pursuingallparsesinparallelorbacktrackorhellipbull  Whichruletoapplynextbull  Whichnodetoexpandnext 26

SomeSolutionsDynamicProgrammingApproachesndashUseacharttorepresentparltalresults

bull CKYParsingAlgorithmbull  BoYom-upbull  GrammarmustbeinNormalFormbull  TheparsetreemightnotbeconsistentwithlinguisLctheory

bull EarlyParsingAlgorithmbull  Top-downbull  ExpectaLonsaboutconsLtuentsareconfirmedbyinputbull  APOStagforawordthatisnotpredictedisneveradded

bull ChartParser 27

EarleyParsingbull AllowsarbitraryCFGsbull Fillsatableinasinglesweepovertheinputwordsbull  TableislengthN+1Nisnumberofwordsbull  Tableentriesrepresent

bull  CompletedconsLtuentsandtheirlocaLonsbull  In-progressconsLtuentsbull  PredictedconsLtuents 28

Statesbull Thetable-entriesarecalledstatesandarerepresentedwithdoYed-rulesS-gtVP AVPispredicted

NP-gtDetNominal AnNPisinprogress

VP-gtVNP AVPhasbeenfound

29

StatesLocationsbull ItwouldbenicetoknowwherethesethingsareintheinputsohellipS-gtVP[00] AVPispredictedatthe

startofthesentence

NP-gtDetNominal[12] AnNPisinprogressthe Detgoesfrom1to2

VP-gtVNP [03] AVPhasbeenfound starLngat0andendingat3

30

Graphically

31

Earleybull Aswithmostdynamicprogrammingapproachestheanswerisfoundbylookinginthetableintherightplace

bull InthiscasethereshouldbeanSstateinthefinalcolumnthatspansfrom0ton+1andiscomplete

bull Ifthatrsquosthecaseyoursquoredonebull  Sndashgtα[0n+1]

32

EarleyAlgorithmbull Marchthroughchartlei-to-rightbull Ateachstepapply1of3operators

bull Predictorbull  CreatenewstatesrepresenLngtop-downexpectaLons

bull  Scannerbull  MatchwordpredicLons(rulewithwordaierdot)towords

bull Completerbull WhenastateiscompleteseewhatruleswerelookingforthatcompletedconsLtuent

33

Predictorbull Givenastate

bull Withanon-terminaltorightofdot(notapart-of-speechcategory)

bull  Createanewstateforeachexpansionofthenon-terminalbull  PlacethesenewstatesintosamechartentryasgeneratedstatebeginningandendingwheregeneraLngstateends

bull  Sopredictorlookingatbull  S-gtVP[00]

bull  resultsinbull  VP-gtVerb[00]bull  VP-gtVerbNP[00]

34

Scannerbull Givenastate

bull Withanon-terminaltorightofdotthatisapart-of-speechcategory

bull  IfthenextwordintheinputmatchesthisPOSbull  Createanewstatewithdotmovedoverthenon-terminalbull  SoscannerlookingatVP-gtVerbNP[00]bull  Ifthenextwordldquobookrdquocanbeaverbaddnewstate

bull  VP-gtVerbNP[01]bull  Addthisstatetochartentryfollowingcurrentonebull  NoteEarleyalgorithmusestop-downinputtodisambiguatePOSOnlyPOSpredictedbysomestatecangetaddedtochart

35

Completerbull  Appliedtoastatewhenitsdothasreachedrightendofrole

bull  Parserhasdiscoveredacategoryoversomespanofinput

bull  Findandadvanceallpreviousstatesthatwerelookingforthiscategorybull  copystatemovedotinsertincurrentchartentry

bull  Givenbull  NP-gtDetNominal[13]bull  VP-gtVerbNP[01]

bull  Addbull  VP-gtVerbNP[03] 36

Howdoweknowwearedonebull FindanSstateinthefinalcolumnthatspansfrom0ton+1andiscomplete


37

Earleybull  Morespecificallyhellip

1  Predictallthestatesyoucanupfront

2  Readaword

1  Extendstatesbasedonmatches2  AddnewpredicLons3  Goto2

3  LookatN+1toseeifyouhaveawinner 38

Examplebull Bookthatflightbull WeshouldfindhellipanSfrom0to3thatisacompletedstatehellip

39

CFGforFragmentofEnglishS agrave NP VP VP agrave V S agrave Aux NP VP PP -gt Prep NP NP agrave Det Nom



Nom -gt Adj Nom Aux agrave does Nom agrave N Prep agravefrom | to | on | of Nom agrave N Nom PropN agrave Bush | McCain |


S agrave NP VP S -gt VP VP agrave V S agrave Aux NP VP PP -gt Prep NP NP agrave Det Nom


NP agravePropN NP -gt Pro

V agrave dog | include | prefer | book Aux agrave does

Nom agrave N Prep agravefrom | to | on | of Nom agrave N Nom PropN agrave Bush | McCain |

Obama Nom agrave Nom PP Det agrave that | this | a| the VP agrave V NP VP -gt V NP PP VP -gt V PP VP -gt VP PP

Adj -gt old | green | red








Example

43

Example

44

Completer

Example

45

Completer

Example

46

Detailsbull Whatkindofalgorithmsdidwejustdescribebull Notparsersndashrecognizers

bull  ThepresenceofanSstatewiththerightaYributesintherightplaceindicatesasuccessfulrecogniLon

bull  Butnoparsetreehellipnoparserbull  Thatrsquoshowwesolve(not)anexponenLalprobleminpolynomialLme

47

ConvertingEarleyfromRecognizertoParserbull WiththeaddiLonofafewpointerswehaveaparser

bull AugmenttheldquoCompleterrdquotopointtowherewecamefrom

48

Augmentingthechartwithstructuralinformation

S8 S9

S10

S11

S13 S12

S8

S9 S8

RetrievingParseTreesfromChartbull  Allthepossibleparsesforaninputareinthetable

bull WejustneedtoreadoffallthebackpointersfromeverycompleteSinthelastcolumnofthetable

bull  FindalltheS-gtX[0N+1]

bull  FollowthestructuraltracesfromtheCompleter

bull  OfcoursethiswonrsquotbepolynomialLmesincetherecouldbeanexponenLalnumberoftrees

bull Wecanatleastrepresentambiguityefficiently 50

LeftRecursionvsRightRecursion

bull Depth-firstsearchwillneverterminateifgrammarisle9recursive(egNP--gtNPPP)

51

)( εαα ⎯rarr⎯ΑΒ⎯rarr⎯Α

bull SoluLonsbull Rewritethegrammar(automaLcally)toaweaklyequivalentonewhichisnotlei-recursiveegThemanonthehillwiththetelescopehellipNPagraveNPPP(wantedNomplusasequenceofPPs)NPagraveNomPPNPagraveNomNomagraveDetNhellipbecomeshellipNPagraveNomNPrsquoNomagraveDetNNPrsquoagravePPNPrsquo(wantedasequenceofPPs)NPrsquoagraveebull  Notsoobviouswhattheserulesmeanhellip

bull Hardertodetectandeliminatenon-immediatele9recursion

bull  NP--gtNomPPbull  Nom--gtNP

bull  Fixdepthofsearchexplicitly

bull Ruleorderingnon-recursiverulesfirstbull  NP--gtDetNombull  NP--gtNPPP

53

AnotherProblemStructuralambiguity

bull MulLplelegalstructuresbull AYachment(egIsawamanonahillwithatelescope)

bull CoordinaLon(egyoungercatsanddogs)bull NPbrackeLng(egSpanishlanguageteachers)

54

55

56

NP vs VP Attachment

bull SoluLonbull Returnallpossibleparsesanddisambiguateusingldquoothermethodsrdquo

57

SummingUpbull Parsingisasearchproblemwhichmaybeimplementedwithmanycontrolstrategiesbull  Top-DownorBoYom-Upapproacheseachhaveproblemsbull  Combiningthetwosolvessomebutnotallissues

bull  Leirecursionbull  SyntacLcambiguity

58

Announcementsbull HW2togoouttodayNextTuesdaymostimportantforbackgroundtoassignment

bull Signupforpolleverywhere

bull Todaywrap-upfromlastclassandstartonparsing

2

Wrap-uponsyntax

3















9

10








SyntacticParsing

13



14











S

NP VP

NP V

DET NOM

N PP

DET NOM

N

The old dog the













20

21


22


23



24

25














29


startofthesentence



30

Graphically

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2  Readaword




39




















Example

43

Example

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Completer

Example

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Completer

Example

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S8 S9

S10

S11

S13 S12

S8

S9 S8









51







53




54

55

56

NP vs VP Attachment


57



58

Wrap-uponsyntax

3















9

10








SyntacticParsing

13



14











S

NP VP

NP V

DET NOM

N PP

DET NOM

N

The old dog the













20

21


22


23



24

25














29


startofthesentence



30

Graphically

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2  Readaword




39




















Example

43

Example

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Completer

Example

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Completer

Example

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47



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S8 S9

S10

S11

S13 S12

S8

S9 S8









51







53




54

55

56

NP vs VP Attachment


57



58















9

10








SyntacticParsing

13



14











S

NP VP

NP V

DET NOM

N PP

DET NOM

N

The old dog the













20

21


22


23



24

25














29


startofthesentence



30

Graphically

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2  Readaword




39




















Example

43

Example

44

Completer

Example

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Completer

Example

46




47



48


S8 S9

S10

S11

S13 S12

S8

S9 S8









51







53




54

55

56

NP vs VP Attachment


57



58












9

10








SyntacticParsing

13



14











S

NP VP

NP V

DET NOM

N PP

DET NOM

N

The old dog the













20

21


22


23



24

25














29


startofthesentence



30

Graphically

31




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33






34





35








37



2  Readaword




39




















Example

43

Example

44

Completer

Example

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Completer

Example

46




47



48


S8 S9

S10

S11

S13 S12

S8

S9 S8









51







53




54

55

56

NP vs VP Attachment


57



58










9

10








SyntacticParsing

13



14











S

NP VP

NP V

DET NOM

N PP

DET NOM

N

The old dog the













20

21


22


23



24

25














29


startofthesentence



30

Graphically

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2  Readaword




39




















Example

43

Example

44

Completer

Example

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Completer

Example

46




47



48


S8 S9

S10

S11

S13 S12

S8

S9 S8









51







53




54

55

56

NP vs VP Attachment


57



58







9

10








SyntacticParsing

13



14











S

NP VP

NP V

DET NOM

N PP

DET NOM

N

The old dog the













20

21


22


23



24

25














29


startofthesentence



30

Graphically

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2  Readaword




39




















Example

43

Example

44

Completer

Example

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Completer

Example

46




47



48


S8 S9

S10

S11

S13 S12

S8

S9 S8









51







53




54

55

56

NP vs VP Attachment


57



58



9

10








SyntacticParsing

13



14











S

NP VP

NP V

DET NOM

N PP

DET NOM

N

The old dog the













20

21


22


23



24

25














29


startofthesentence



30

Graphically

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2  Readaword




39




















Example

43

Example

44

Completer

Example

45

Completer

Example

46




47



48


S8 S9

S10

S11

S13 S12

S8

S9 S8









51







53




54

55

56

NP vs VP Attachment


57



58

9

10








SyntacticParsing

13



14











S

NP VP

NP V

DET NOM

N PP

DET NOM

N

The old dog the













20

21


22


23



24

25














29


startofthesentence



30

Graphically

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2  Readaword




39




















Example

43

Example

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Completer

Example

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Completer

Example

46




47



48


S8 S9

S10

S11

S13 S12

S8

S9 S8









51







53




54

55

56

NP vs VP Attachment


57



58

10








SyntacticParsing

13



14











S

NP VP

NP V

DET NOM

N PP

DET NOM

N

The old dog the













20

21


22


23



24

25














29


startofthesentence



30

Graphically

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2  Readaword




39




















Example

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Example

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Completer

Example

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Completer

Example

46




47



48


S8 S9

S10

S11

S13 S12

S8

S9 S8









51







53




54

55

56

NP vs VP Attachment


57



58








SyntacticParsing

13



14











S

NP VP

NP V

DET NOM

N PP

DET NOM

N

The old dog the













20

21


22


23



24

25














29


startofthesentence



30

Graphically

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2  Readaword




39




















Example

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Example

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Completer

Example

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Completer

Example

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S8 S9

S10

S11

S13 S12

S8

S9 S8









51







53




54

55

56

NP vs VP Attachment


57



58


SyntacticParsing

13



14











S

NP VP

NP V

DET NOM

N PP

DET NOM

N

The old dog the













20

21


22


23



24

25














29


startofthesentence



30

Graphically

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2  Readaword




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Example

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Example

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Completer

Example

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Completer

Example

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S8 S9

S10

S11

S13 S12

S8

S9 S8









51







53




54

55

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NP vs VP Attachment


57



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SyntacticParsing

13



14











S

NP VP

NP V

DET NOM

N PP

DET NOM

N

The old dog the













20

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22


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startofthesentence



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Graphically

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2  Readaword




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Example

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S8 S9

S10

S11

S13 S12

S8

S9 S8









51







53




54

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NP vs VP Attachment


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14











S

NP VP

NP V

DET NOM

N PP

DET NOM

N

The old dog the













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startofthesentence



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2  Readaword




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Example

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Example

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Example

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Completer

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S8 S9

S10

S11

S13 S12

S8

S9 S8









51







53




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NP vs VP Attachment


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S

NP VP

NP V

DET NOM

N PP

DET NOM

N

The old dog the













20

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startofthesentence



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Graphically

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2  Readaword




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Example

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Example

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Completer

Example

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S8 S9

S10

S11

S13 S12

S8

S9 S8









51







53




54

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NP vs VP Attachment


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S

NP VP

NP V

DET NOM

N PP

DET NOM

N

The old dog the













20

21


22


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24

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29


startofthesentence



30

Graphically

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2  Readaword




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Example

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Example

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Completer

Example

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Completer

Example

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S8 S9

S10

S11

S13 S12

S8

S9 S8









51







53




54

55

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NP vs VP Attachment


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S

NP VP

NP V

DET NOM

N PP

DET NOM

N

The old dog the













20

21


22


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24

25














29


startofthesentence



30

Graphically

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2  Readaword




39




















Example

43

Example

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Completer

Example

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Completer

Example

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S8 S9

S10

S11

S13 S12

S8

S9 S8









51







53




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NP vs VP Attachment


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20

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startofthesentence



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Graphically

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2  Readaword




39




















Example

43

Example

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Completer

Example

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Completer

Example

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S8 S9

S10

S11

S13 S12

S8

S9 S8









51







53




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NP vs VP Attachment


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20

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startofthesentence



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2  Readaword




39




















Example

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Example

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Completer

Example

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Completer

Example

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S8 S9

S10

S11

S13 S12

S8

S9 S8









51







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NP vs VP Attachment


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startofthesentence



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Graphically

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2  Readaword




39




















Example

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Example

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Completer

Example

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Completer

Example

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S8 S9

S10

S11

S13 S12

S8

S9 S8









51







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NP vs VP Attachment


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startofthesentence



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Documents

Basic Parsing with Context-Free Grammarskathy/NLP/2017/ClassSlides/...Basic Parsing with Context-Free Grammars Some slides adapted from Julia Hirschberg and Dan Jurafsky 1 . ... Normal