Cross-framework Grammar Engineering using Constraint-driven Metagrammars

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Cross-framework Grammar Engineering using Constraint-driven Metagrammars

Denys Duchier, Yannick Parmentier, Simon Petitjean

To cite this version:

Denys Duchier, Yannick Parmentier, Simon Petitjean. Cross-framework Grammar Engineering using

Constraint-driven Metagrammars. 6th International Workshop on Constraint Solving and Language

Processing (CSLP’11), Sep 2011, Karlsruhe, Germany. pp.32-43. �hal-00614661�

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Constraint-driven Metagrammars

DenysDuhier,YannikParmentier,andSimonPetitjean

LIFO,Universitéd'Orléans,F-45067OrléansCedex2,Frane,

firstname.lastnameuniv-orleans. fr,

WWWhomepage:http://www.univ-orleans.fr/li fo/

Preprint

Abstrat. Inthis paper, we presentanabstrat onstraint-drivenfor-

malism for grammar engineering alled eXtensible MetaGrammar and

showhowtoextendittodeal withross-frameworkgrammarengineer-

ing. Asa ase study,we fous on the designof tree-adjoining, lexial-

funtional,andpropertygrammars(TAG/LFG/PG).

A partiularly interesting featureof this formalismis that it allows to

applyspeionstraintsonthelinguististruturesbeingdesribed.

Keywords: omputationallinguistis,formalgrammar,metagrammar,

onstraintsolving.

1 Introdution

Many grammatial frameworks have been proposed over the last deades to

desribethesyntaxofnaturallanguage.Amongthemostwidelyused,onemay

ite Tree-Adjoining Grammar (TAG) [1℄, Lexial-Funtional Grammar (LFG)

[2℄, or Head-driven Phrase StrutureGrammar(HPSG) [3℄. These frameworks

presenttheoretialandpratialinterests.Fromatheoretialpointofview,they

provide a formal devie for the linguist to experiment with her/his theories.

Fromapratialpoint of view,theymakeitpossibleto automatially proess

naturallanguageinappliationssuhasdialogsystems,mahinetranslation,et.

They dierin their expressivityand omplexity. Some reveal themselves more

adequateforthedesriptionofagiven languagethanothers. Still,formanyof

these frameworks,large resoures(i.e., grammars) havebeen designed,at rst

byhand,and laterviadediated tools(e.g.,integrated grammarenvironments

suhasXLEforLFG[4℄).Inthispaper,weareonernedwiththisomplextask

of grammar engineering, keepingin mind thetwoabove-mentionedtheoretial

andpratialinterests.

Severalapproaheshavebeenproposedforaomputer-aidedgrammarengi-

neering,mainlytoreduetheostsofgrammarextensionandmaintenane.The

main approahesare 1. theautomati aquisition from treebanks (see e.g., [5℄

forLFG),2.systemsbasedonanabstratdesriptionofthegrammar,eithervia

transformationrules,alsoknownasmetarules(seee.g,[6℄forTAG)orviaade-

sriptionlanguage,sometimesalled metagrammar(see e.g.,[7℄forTAG).The

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advantage of the desription-based approah (and espeially metagrammars )

overtheautomatiaquisitionapproahliesinthelinguistiontrolitprovides.

Indeed,thesedesriptionsapturelinguistigeneralizationsandmakeitpossible

toreasonaboutlanguageatanabstratlevel.Desribinglanguageatanabstrat

levelisnotonlyinterestingforstruturesharingwithin agivenframework,but

alsoforinformationsharingbetweenframeworksand /orlanguages.

This observation was already made by [9,10℄. In their papers, the authors

showedhowto extendanexisting metagrammarforTAGso that bothaTAG

and anLFG ouldbegenerated from it.TheyannotatedTAGmetagrammati-

alelementaryunits(so-alledlasses)withextrapieesofinformation,namely

(i) LFG's funtional desriptions and (ii) ltering information to distinguish

ommonlassesfromlassesspeitoTAGorLFG.Themetagrammarompi-

lationthengenerated anextended TAG,fromwhihLFGruleswereextrated.

TomaximizethestruturesharingbetweentheirTAGandLFGmetagrammars,

theauthors denedlassesontainingtree fragmentsofdepth one.Thesefrag-

mentswereeitherombinedtoprodueTAGtreesorassoiatedwithfuntional

desriptions to produe LFG rules. This ross-framework experiment was ap-

pliedtothedesignofaFrenh/Englishparallelmetagrammar,produingboth

a TAG and a LFG. This work was still preliminary. Indeed (i) it onerned

a limited metagrammar(the target TAG was omposed of 550 trees, and the

assoiated LFG of 140rules) (ii) moreimportantly, there is no lear evidene

whether ageneralizationtootherframeworksand/orlanguagesouldbepos-

sible(metagrammarimplementationhoies, suhastreefragmentdepth,were

notindependentfrom thetargetframeworks).

Here,wehosetoadoptamoregeneralizedapproahbydesigninganextensi-

blemetagrammatiallanguage,thatanhandleanarbitrarynumberofdistint

targetframeworks.Thelinguistanthususethesameformalismtodesribedif-

ferentframeworksandgrammars.Nonetheless,ifonewantstoexperimentwith

multi-formalism, e.g., by designing a parallel TAG / LFG grammar, nothing

prevents her/him from dening universal lasses, whih ontain metagram-

matial desriptionsbuilt onaommon sublanguage. Ratherthan designinga

newmetagrammatiallanguagefrom srath,weproposetoextendanexisting

formalism,namelyeXtensible MetaGrammar(XMG)[11℄,whihseemspartiu-

larlyadequatethankstoitsmodularityandextensibility.

The paper is organizedas follows. In setion 2, we briey introdue TAG,

aswellastheredundanyissues raisingwhile developinglargeTAGgrammars

(whihmotivatedmetagrammars).WethenintroduetheXMGmetagrammat-

ial languageand show how it an be used to design TAG grammars. In se-

tion3,webriey introdue LFGand presentanextensionof XMGto desribe

LFGgrammars. In setion 4,we introdueProperty Grammar(PG) [12℄, and

presentaseondextensionofXMGtogeneratePGgrammars.Insetion5,we

willgeneralizeoverthesetwoextensions,anddenealayoutforross-framework

grammarengineering.Finally,weonludeandgiveperspetivesin setion6.

1

Inrule-baseddesriptions,onehastoarefullydenetheorderingoftheappliations

ofrules[8℄,whihmakesithardtodesignlargegrammars.

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Grammars with a metagrammar

2.1 Tree-AdjoiningGrammar

TAG 2

is atree rewriting system,where elementary treesan be ombinedvia

tworewritingoperations,namelysubstitutionandadjuntion.Substitution on-

sistsinreplaingaleafnodelabelledwith↓^with^a^tree^whose^root^has^the^same

syntatiategoryasthisleafnode.Adjuntiononsistsinreplainganinternal

node witha treewhere boththeroot nodeand one of theleafnodes (labelled

with ⋆⁾ ^have^the^same^syntatiâtegoryâs^this înternal ^node. Âs ânîllustra-

tion,onsider Fig.1below.Itshows(i) thesubstitutionoftheelementarytree

assoiatedwiththenounJohnintotheelementarytreeassoiatedwiththeverb

sleeps,and(ii)theadjuntionoftheelementarytreeassoiatedwiththeadverb

deeplyinto thetreeassoiatedwithsleeps.

S

NP↓ ^VP ^VP

NP V VP⋆ ^ADV

John sleeps deeply

→

S

NP VP

John VP ADV

V deeply

sleeps

(derivedtree)

Fig.1.TreerewritinginTAG

Basially,areal sizeTAGismadeof thousandsofelementarytrees[14,15℄.

Due to TAG's extendeddomain ofloality,many ofthese treesshare ommon

sub-trees,asforinstanetherelationbetweenaanonialsubjetandits verb,

as shownin Fig. 2.To dealwith thisredundany, themetagrammar approah

(in partiular XMG) proposes todesribelargeTAG grammarsin an abstrat

andfatorizedway.

2.2 eXtensible MetaGrammar(XMG)

XMGisametagrammatiallanguageinspiredby logiprogramming.Theidea

behindXMGisthatametagrammarisadelarativelogialspeiationofwhat

agrammaris.Thisspeiationreliesonthefollowingthreemainonepts:

•^several^dimensions ^of^language^(e.g.^syntax,^semantis)^an^be^desribed;

•^for^eah ^of^these dimensions,desriptionsare madeofnon-deterministi om- binationsofelementaryunits;

•^for^some^of^thesedimensions,desriptionsmustbesolvedtoproduemodels.

2

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S

N↓ V⋄ ^N↓

Jeanmangeunepomme

Johneatsanapple

N⋆ ^S

C

que

S

N↓ ^V⋄

LapommequeJeanmange

TheapplethatJohneats

Fig.2.StruturalredundanyinTAG

XMG'sextensibility omes from theonept of dimensions.These allow to

desribeanarbitrarynumberoftypesoflinguististrutures.Non-determinism

allowsforfatorization,anddesriptionsolvingforassemblyandvalidation(i.e.,

well-formednessof thedesriptionaording tosome targetframework). Here-

after,wewillrstuseXMGtodesribeTAG.Then,wewillapplyXMG'sexten-

sibilitytothedesriptionofotherframeworks,namelyLFGandPG.Eventually,

wewillgeneralizeoverthese appliations.

WhendesribingTAGtreeswithXMG,onedenesboth(i)treefragments

and (ii) onstraintsthat express how these fragments haveto be ombined to

produethegrammar.Twolanguagesarethusused:adesriptionlanguageLD^to

speifyfragments,andaontrollanguageLC^to^speify^ombinationonstraints.

LD îs^basedôn^the^preedeneând^dominane^relations.Furthermore,sine TAGallowsforthelabellingofsyntatinodeswithfeature strutures,sodoes

LD^.Â ^desriptionⁱⁿ LD îsâ^formula^builtâs^follows:

Desc :=x→y | x→⁺y | x→^∗y | x≺y | x≺⁺y | x[f:E] | x(p:E) | Desc ∧ Desc

where x, y ^refer^to ^node ^variables, →^(resp. ≺⁾ ^to ^the^dominane ^(resp.^pree-

dene)relation,and+^(resp.∗⁾^are^used^to^denote^the^transitive^(resp.^reexive

andtransitive)losureofthisrelation.Thesquarebraketsareusedtoassoiate

anodevariablewithsomefeaturestruture.Parenthesisareusedtoassoiatea

nodevariable withsomeproperty(suhastheTAG⋆^property^seenⁱⁿ ^Fig.^1).

Notethatnodevariablesarebydefault loaltoadesription.Ifanodevariable

needsto beaessedfrom outsideitsdesription,itis possibleto usesomeex-

portmehanism.Oneavariableis exported,it beomesaessibleusing adot

operator. For instane, to refer to the variable xⁱⁿ ^the^desription Desc^, ^one

writesDesc.x^.^Here^is^anillustrationofafragmentdesriptionin XMG(onthe right,oneanseeaminimalmodelofthisdesription):

(x[cat:S] →y[cat:V] ) ∧ (x→z(mark:subst) [cat:N] ) ∧ (z ≺ y)

x[at:S℄

z↓^[at:N℄ ^y^[at:V℄

LC ^oers^three^mehanisms^to^handle^fragments:^abstration^via^parameter-

izedlasses(assoiationofanameandzeroormoreparameterswithaontent),

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umulationofontents).AformulainLC ^is^built^as^follows:

Class := Name[p1, . . . ,pn]→Content

Content := Desc | Name[. . .] | Content∨Content | Content∧Content

As an illustration of LC^, ^let ûs ônsider ^dierent ôbjet realizations. One ouldforinstanedenethe4fragments:(i)anonialsubjet,(ii)verbalmor-

phology, (iii)anonial,and (iv)relativizedobjet, andthefollowingombina-

tions,thus produingthetwotreesofFig.2:

Object →CanObj ∨ RelObj

Transitive →CanSubj ∧ VerbMorph ∧ Object

Metagrammarompilation. ToprodueagrammarfromanXMGmetagrammar,

weletthelogialspeiationgenerate,inanon-deterministiway,desriptions.

Inother words,theombination onstraintsareproessed to generatedesrip-

tions(oneperdimension).Forsomedimensions,desriptionsneedtobesolved

to produe models. This is thease for TAG,a onstraint-basedtree desrip-

tion solveris thus usedto omputetrees [11℄. Note this solveratually heks

several typesof onstraints[16℄: treewell-formednessonstraints,TAG-related

onstraints(e.g.,uniquenodelabelled⋆^),^andlanguage-relatedonstraints(e.g., uniquenessand orderoflitisinFrenh).

AsoneoftherstambitionsofXMGismulti-formalism,dimensionsarean

eientwayto denedierenttypesof desriptionlanguageadaptedto target

frameworks.Letus seehowtodenedimensionsforLFGandPG.

3 Generating Lexial-Funtional Grammars with a

metagrammar

3.1 Lexial-Funtional Grammar

Alexial-funtionalgrammar(LFG)onsistsofthreemainomponents:1.ontext-

freerulesannotatedwith funtionaldesriptions,2.well-formednesspriniples,

and 3. a lexion. From these omponents, twomain interonneted strutures

an be built 3

: a (onstituent)-struture, and a f(untional)-struture. The -

struturerepresentsasyntatitree, andthef-struturegrammatialfuntions

in the form of reursiveattribute-value matries. Asan exampleof LFG, on-

sidertheFig.3below.Itontainsatoygrammarandthe-andf-struturesfor

thesenteneJohnlovesMary.Inthisexample,oneanseefuntionaldesrip-

tionslabellingontext-freerules(see(1) and(2)).Thesedesriptionsaremade

ofequations.Forinstane,inrule(1),theequation(↑SU BJ) =↓ônstrains^the SU BJ ^feature ôf ^the ^funtional ^desription âssoiated^with ^the ^left-hand ^side

oftheontext-freeruleto unifywiththefuntionaldesriptionassoiatedwith

3

Thisonnetionisoftenreferredtoasfuntionalprojetionorfuntionalmapping.

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tionsareuniation onstraintsbetweenattribute-valuematries. Nonetheless,

theseonstraintsmaynotprovideenoughontrolonthef-struturesliensedby

thegrammar,LFGheneomeswiththreeadditionalwell-formednesspriniples

(ompleteness,ohereneanduniqueness)[2℄.

Toygrammar:

(1)S → ^NP ^VP

↑=↓ (↑SU BJ) =↓ ↑=↓

(2)VP → ^V ^NP

↑=↓ ↑=↓ (↑OBJ) =↓

(3)John NP,(↑P RED) =^′JOHN^′,(↑N U M) =SG,(↑P RES) = 3

(4)Mary NP,(↑P RED) =^′M ARY^′,(↑N U M) =SG,(↑P RES) = 3

(5)loves V,(↑P RED) =^′LOV Eh(↑SU BJ) (↑OBJ)i^′,(↑T EN SE) =P RESEN T

-struture: f-struture:

S

↑=↓

NP

(↑SU BJ) =↓

VP

↑=↓

John

V

↑=↓

NP

(↑OBJ) =↓

loves Mary

f1^:







PRED 'LOVE

D(↑SU BJ) (↑OBJ)E

'

SUBJ f2^:







PRED 'JOHN'

NUM SG

PERS 3







OBJ f3^:







PRED 'MARY'

NUM SG

PERS 3







TENSE PRESENT







Fig.3.LFGgrammarand-andf-struturesforthesenteneJohnlovesMary

3.2 Extending XMGfor LFG

In the previous setion, we dened the XMG language, and applied it to the

desriptionofTAG.Letusreallthatoneofthemotivationsofmetagrammars

ingeneral(andofXMGinpartiular)istheredundanywhihaetsgrammar

extensionandmaintenane.InTAG,theredundanyishigherthaninLFG.Still,

asmentioned in [9℄, in LFG there are redundanies at dierent levels, namely

within the rewriting rules,the funtionalequations and thelexion.Thus, the

metagrammarapproahan provehelpful inthisontext.Letus nowsee what

typeoflanguageouldbeusedto desribeLFG.

4

TodesribeLFGat an abstrat level, oneneedsto desribeitselementary

units,whih areontext-freerulesannotatedwithfuntionaldesriptions(e.g.,

equations)andlexialentries usingattribute-valuematries.Context-freerules

4

AspeiationlanguageforLFGhasbeenproposedby[17 ℄,butitorrespondsmore

toamodel-theoretidesriptionofLFGthantoametagrammar.

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XMGusingadesriptionlanguagesimilartotheoneforTAG,i.e.,usingthe→

(dominane)and≺^(preedene)^relations.Ôneân^forînstane^dene^dierent

ontext-free bakbones aordingto the numberof elementsin theright-hand

sidesoftheLFGrules.ThesebakbonesareenapsulatedinparameterizedXMG

lasses,wheretheparametersareusedtoassignasyntatiategorytoagiven

elementoftheontext-freerule,suhasinthelassBinaryRulebelow.

BinaryRule[A, B, C] → (x[cat:A]→y[cat:B])∧(x→z[cat:C])∧(y≺⁺z)

exports hx, y, zi

Wealsoneedtoannotatethenodevariablesx, y, z^with^funtionaldesriptions.

Letusseehowthese funtionaldesriptionsFDesc^are^built:⁵

where g ^refers ^to ân attribute-value matrix, F EAT ^to â ^feature, V AL ^to â

(possiblyomplex)value,CON ST^toâônstraintôperator⁽=^forûniation,=c

foronstraininguniation,∈^for^setmembership,6=^for^dierene),(FDesc)^to

optionality,and∗^to^LFG's^funtionalûnertainty^.^Note^thatgân^beômplex,

that is, it an orrespond to a (relative using ↑ ând ↓ ôr âbsolute) ^path

pointingtoasub-attribute-valuematrix.

Tospeifysuhfuntionaldesriptions,weanextendXMGinastraightfor-

wardmanner,withadediateddimensionandadediateddesriptionlanguage

LLF G ^dened^as^follows:

DescLFG := x→y | x≺y | x≺⁺y | x = y | x[f:E] | xhFdi | DescLFG ∧ DescLFG

Fd := g| ∃g.f | g.f=v| g.f =cv| g.f ∈v| ¬Fd| Fd∨Fd| (Fd)| Fd∧Fd

g,h := ↑ | ↓ | h.f | f ∗i

where g, h^are^variables^denotingattribute-valuematries, f, i^(atomi)^feature

names,v ^(possiblyômplex) ^values,ândh. . .iôrresponds^to ^LFG's^funtional

mappingintrodued above. With suh alanguage,it nowbeomes possible to

deneanXMGmetagrammarforourtoyLFGasfollows.

6

Srule →br=BinaryRule[S,NP,VP] ∧br.xh↑=↓i ∧br.yh(↑.SUBJ) =↓i

∧ br.zh↑=↓i

V P rule →br=BinaryRule[VP,V,NP]∧ br.xh↑=↓i ∧br.yh↑=↓i

∧ br.zh(↑.OBJ) =↓i

5

Wedonotonsiderhereadditional LFGoperators, whihhavebeenintroduedin

speiLFGenvironments,suhasshue,insertorignore,et.

6

Here, we do not desribe the lexial entries, these anbe dened using the same

languageastheLFGontext-freerules,omittingtheright-and-side.

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done,letushavealookataslightlymoreomplexexampletakenfrom [9℄:

V P → V (N P) P P (N P)

↑=↓ (↑OBJ) =↓ (↑SecondOBJ) =↓ (↑OBJ) =↓

Here,wehavetwopossiblepositionsfortheNPnode,eitherbeforeorafterthe

PP node.SuhansituationanbedesribedinXMGasfollows:

V P rule2 →br=BinaryRule[VP,V,PP] ∧ u[cat:NP] ∧ br.y≺⁺u

∧ br.yh↑=↓i ∧ br.zh(↑.SecondOBJ) =↓i ∧ uh(↑.OBJ) =↓i

Here, we do not speify the preedene between the NP and PP nodes. We

simply speify that the NP node is preeded by the V node (denoted by y^).

When ompiling this desription with a solver suh as the one for TAG, two

solutions(LFG rules)will beomputed.Inother terms,theoptionalityanbe

expresseddiretlyatthemetagrammatiallevel,andthemetagrammarompiler

andiretlyapplyLFG'suniqueness priniple.

Inotherwords,themetagrammarherenotonlyallowsforstruturesharing

via the (onjuntive or disjuntive) ombination of parameterized lasses,but

it also allows to apply well-formedness priniples to the desribed strutures.

In the example above with the two NP nodes, this well-formedness priniple

is heked on the onstituent struture and indiretly impats the funtional

struture(whih isthestruture onernedwiththese priniples).Ifweseethe

funtionalstruturesasgraphsandequationsasonstraintsonthese,oneould

imagine to develop a spei onstraint solver. This would allow to turn the

metagrammar ompiler into an LFG parser, whih would, while solving tree

desriptions for theonstituent struture, solvegraph-labelling onstraints for

thefuntionalstruture.

Note that asimilar approah of struture sharing within an LFG through

ombinationsofelementaryunitshasbeenproposedby[18℄.Intheirpaper,the

authorsdesribehowtoshare informationbetweenLFGstrutures bydening

nameddesriptions,alledtemplates.Thesetemplatesanabstratoveronjun-

tionordisjuntionoftemplates,theyarethusomparabletoourmetagrammar

lasses. The main dierene with our approah, is that nothing is said about

aninterpretationofthesetemplates (theyatinamaro-likefashion),whilein

XMG,oneouldapplysomespeitreatments(e.g.onstraintsolving)onthe

metagrammarlasses.

4 Generating Property Grammars with a metagrammar

4.1 Property Grammar

PropertyGrammar(PG)[12℄ diersfromTAGorLFGin sofarasitdoesnot

belong tothe generativesyntaxfamily,but to the model-theoretisyntaxone.

In PG, one denes the relations between syntati onstituents not in terms

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of rewriting rules, but in termsof loal onstraints (the so-alled properties).

The properties liensed bythe framework relyon linguisti observations, suh

aslinearpreedenebetweenonstituents,oourreny,mutualexlusion,et.

Here,wewillonsiderthefollowing6properties,thatonstraintherelations

betweenaonstituent (i.e., thenodeof asyntatitree), withategoryA ^and

itssub-onstituents(i.e., thedaughter-nodesofA):

8

Obligation A:△B ^at ^least^oneB ^hild

Uniqueness A:B! ^at ^most^oneB ^hild

Linearity A:B≺C B ^hild^preedesC ^hild

Requirement A:B⇒C îfâB ^hild,^thenâlsoâC ^hild

Exlusion A:B6⇔C B ândC ^hildrenâre^mutuallyêxlusive

Constitueny A:S ^hildren^must^have^ategoriesⁱⁿS

InarealsizePG,suhastheFrenhPGof[19℄,thesepropertiesareenapsulated

(togetherwithsomesyntatifeatures)within linguistionstrutions,andthe

latterarrangedin aninheritane hierarhy 9

.Anextrat ofthehierarhyof[19℄

ispresentedinFig.4(fragmentorrespondingto basiverbalonstrutions).

V(Verb)

INTR

ID|NATURE

h

SCAT

1

.SCAT

i

onst.:V^:

1

CATV

SCAT¬^(aux-etre∨^aux-avoir)

V-n(Verbwithnegation)inheritsV

INTR



^SYN



^NEGA

"

RECT

1

DEP Adv-n

#







uniqueness: ^Adv-ng

Adv-np

!

requirement: ¹ ⇒^Adv-n

linearity:Âdv-ng≺ ¹ :Âdv-ng≺Âdv-np

:^Adv-np≺ ¹.[M ODE inf]

: ¹.[M ODE ¬inf]≺^Adv-np

V-m(Verbwithmodality)inheritsV;V-n

INTR



^SYN



^INTRO

"

RECT

1

DEP Prep

#







uniqueness:^Prep!

requirement: ¹ ⇒^Prep

linearity: ¹ ≺^Prep

Fig.4.FragmentofaPGforFrenh(basiverbalonstrutions)

LetusforinstanehavealoserlookatthepropertiesoftheV-nonstrution

ofFig.4.ItsaysthatinFrenh,forverbswithanegation,thisnegationismade

7

Aninterestingharateristioftheseonstraintsisthattheyanbeindependently

violated,andthusprovideawaytoharaterizeagrammatialsentenes.

8

Here,weomitlexialproperties,suhascat(apple) =^{N .}

9

Note that this hierarhy is a disjuntive inheritane hierarhy, i.e., whenthere is

multipleinheritane,thesublassinheritsoneofitssuper-lasses.