Montague Grammar.docx
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Montague Grammar.docx
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MontagueGrammar
MontagueGrammar
AmyH.Kao
EECS595
Fall2004
“Thereisinmyopinionnoimportanttheoreticaldifferencebetweennaturallanguagesandtheartificiallanguagesoflogicians;indeed,Iconsideritpossibletocomprehendthesyntaxandsemanticsofbothkindsoflanguageswithinasinglenaturalandmathematicallyprecisetheory”(Montague1970)
Abstract
In1970,RichardMontague’sradicaltheoriesofhowformallogiccouldbeusedtodescribenaturallanguagechangedthewaylogiciansandlinguistsperceivedtheconnectionsbetweentheirfields.Usingformallogicandamodel-theoreticview,Montaguecreatesasystemwherethesyntacticstructureandsemanticstructureofnaturallanguageareconnectedinamannerthatallowsforabetterunderstandingofthesemanticmeaningsofsentences.ThesetheoriesareexemplifiedinwhathasbeentermedMontagueGrammar.Inthispaper,wegainabetterunderstandingofMontagueGrammar’simpactonlogiciansandlinguistsbyunderstandingthemanycomponentsofMontagueGrammar,includingsyntacticandsemantichandling,intensionallogic,generalquantification,andmodeltheory.
History
RichardMontague(1930-1971),bothalogicianandphilosopheroflanguage,wasastudentofAlfredTarski,alogicianoftencomparedwiththelikesofAristotleandGödel.In1993,Tarski’spaperTheconceptoftruthinformalizedlanguagebeganthedevelopmentofmodeltheory,whichprovidedthefoundationformuchofMontague’sworkinsemantics.Modeltheorydescribesthemeaningsofformalandnaturallanguagesbydefiningtheclassesofobjectsreferredtobytheexpressions.Inthismanner,modeltheoryexaminesthetruthofanexpression(usingTarski’sTruthdefinitions)byexaminingthetruthoftheexpression’scorrespondingclasselements.Tarski’sinfluencemaybeseeninmuchofMontague’sapproachessemantics,allowingforalogicalmodeltheoreticapproachthatwasradicalforMontague’stime.
InUniversalGrammar(1970),Montagueintroducedhistheoryofformalsyntaxandsemanticsasappliedtobothformalandnaturallanguage.UniversalGrammarissignificantbecauseitwasthefirstattemptatapplyingformalsemanticstonaturallanguage.LogicianspriortoMontagueregardednaturallanguageastooambiguousandunstructuredforformallogicalanalysiswhilelinguistsfeltthatformallanguageswereunabletocapturethestructuresofnaturallanguages.MontaguemoreexplicitlyarguesforthesimilaritiesofnaturalandformallanguageinEnglishasaformallanguage(1970)wherehewrites“Irejectthecontentionthatanimportanttheoreticaldifferenceexistsbetweenformalandnaturallanguages.”
MontaguedemonstratestheapplicationofhistheoriesinTheProperTreatmentofQuantificationinOrdinaryEnglish(1973),mostcommonlyreferredtoasPTQ,wherehedefinesthesyntaxandsemanticsforalargefragmentofEnglish.Inthetext,Englishphrasesaretranslatedintologicalexpressionsbasedonintensionallogic,whicharetheninterpretedwithTarski’smodeltheory.ThetermMontaguegrammargenerallyreferstothetheoriesoutlinedinUniversalGrammar,Englishasaformallanguage,andPTQ,butbecausesomuchofMontague’sworkisexplainedinPTQ,MontaguegrammarisoftenalsoreferredtoasPTQ.
Montague’sworkcameatatimewhenlinguistsweredevelopingdifferentapproachestosemanticsinrelationtoChomsky’sgenerativegrammar.Thetwomainapproaches,generativesemantics(Lakoff,Ross,McCawley,Postal)andinterpretivesemantics(Jackendoff,Chomsky),wereatoddswitheachother.Generativesemanticsdidnotseparatesemanticandsyntacticruleswhileinterpretivesemanticscontainedadistinctionbetweenthetwotypesofrules.Montague’sapproachofferedaperspectiveofhowthestructuresofsemanticandsyntacticrulescanbeconnectedtoeachotherbutnotrequiredtobethesamerules.LinguistshopedthatMontague’sworkwouldmerge“thebestaspectsofbothofthewarringapproaches,withsomeaddedadvantagesofitsown”(Partee2001).
MontaguewasnottheonlylinguistawareoftherelevantadvancesinlogicandphilosophyoflanguagebutbeforeMontague’sworkbecamepopular,linguistandlogiciansdidnotactivelyworktogether.Manyattributethelackofcommunicationbetweenthefieldstothepersonalitiesofgenerativesemanticists.TheclashofthesetwofieldswasdemonstratedinAugustof1969duringacolloquiumoflogiciansandlinguists.ThecolloquiumwasaimedatfosteringcollaborationsbetweenthetwofieldsbutwasdeemedafailurebyW.V.Quine,whodeclaredit“afiascoatbridgebuilding”(Abbott,1999).Thoughunsuccessfulingeneratingnewinteractionsbetweenpeople,thepapersfromthecolloquium,includingarticlesbyMontague,werereadbymanylinguistsandlogicians.Thesearticleswerekeyinsettingthegroundsforfuturecollaborationsbetweenthetwofields.
Oneoftheimportantissuesbroughttotheattentionoflinguistsatthe1969colloquiumwasthedifferentiationbetweensemanticrepresentationandsemanticmeaning.PhilosopherDavidLewiscondemnedtheexistingsystemsofsemanticrepresentationbecausetheylackedthetreatmentoftruthconditions.Atthetime,expressionswerecommonlygivenacorrespondingmarkingtodenotethesemanticmeaning.LewisclaimedthatthesemarkingssimplytranslatedsentencesintoanartificiallanguageonecouldcallSemanticMarkerseswithoutregardtothemeaningofthesentence.Montague’sworkintheyearsfollowingthatcolloquiumcouldbedeemedananswertoLewis’scriticismswithsemanticanalysis.HismodeltheoreticanalysisofsemanticsinnaturallanguageprovidedatreatmentofmeaningsthatLewishadfoundlackinginsemanticrepresentations.
Montague’sworkinnaturallanguageisdescribedinonlythreepublications(UniversalGrammar,Englishasaformallanguage,andTheProperTreatmentofQuantificationinOrdinaryEnglish)butmostfoundhiswritingtobe“highlyformalandcondensed,verydifficultforordinaryhumans(evenlogicians!
)toreadwithcomprehension.”(Abbott1999)TheproliferationofMontague’sworkisthereforeoftenattributedtoBarbaraParteewhopresentedMontague’sworkinamoreunderstandablefashion.
ParteegraduatedMIT(1965)withaPhDinLinguisticsunderChomskyandbecamefamiliarwithMontague’sworkwhenshebeganteachingatUCLA(1965-1972)wherehewasaprofessor.Partee’sMontagueGrammarandTransformationalGrammar(LinguisticInquiry1975)wasseenasthefirstintroductorytextonMontagueGrammar.Dowty,Wall&Peterslaterpublishedanothercomprehensivetextcalled“WordMeaningandMontagueGrammar”(1981).WhenParteebecameafacultymemberattheUniversityofMassachusettsatAmherst,herclassesonMontagueGrammarbecameanattractiontomanyprominentlinguistsandlogicians.
Montague’sgroundbreakingworkinformalsemanticscreatednewareasofresearchthatwereofinteresttobothlinguistsandlogicians,helpingtoproliferateinteractionsbetweenthefields.BarbaraPartee’sjointappointmentinthelinguisticsandphilosophydepartmentsatUniversityofMassachusettsisoneofmanysignsthatlinguistsandlogiciansarecollaboratingmoreclosely.In1977,thejournalLinguisticsandPhilosophypublisheditsfirstissueandtothisday,continuestofostercommunicationsbetweenthetwocommunities.
MontagueGrammar
Montague’sUniversalGrammar(UG)isageneraltheoryoflanguagedevelopedtoencompassthesyntaxandsemanticsofknownartificiallanguagesaswellasnaturallanguagesand“unnatural”languages.UGrelatessyntaxandsemanticsbycreatingaformalinterpretationofFrege’sphilosophythatanexpression’smeaningisafunctionofthemeaningofitsconstituentsanditssyntax.ThecharacteristicsofUGaremeanttobemoregeneralsoastoserveasthereferenceframeworkforcomparingformalandnaturallanguages.
ThetheoriesofUniversalGrammarareappliedinMontagueGrammarasdescribedinTheProperTreatmentofQuantificationinOrdinaryEnglish(PTQ).ItisworthnotingthatthetermsUniversalGrammar(UG),MontagueGrammar,andPTQmaybefoundinterchangeablyinvarioustextsregardingMontague’swork.Ingeneral,UGreferstoMontague’stheoriesofsyntaxandsemanticsfoundinUniversalGrammarwhereasPTQiscommonlyusedtodenotetheapplicationandprocessofthetheory.ThetermMontagueGrammarismoregeneralandiscommonlyusedtorefertoanythingwithinMontague’sthreemaintextsconcerningsyntaxandsemantics.ThefollowingsectionsofthispaperwillexaminesyntaxandsemanticsashandledinMontagueGrammar.
Syntax
SyntaxinMontaguegrammarconsistsofsyntacticrulesandsyntacticoperationsasdescribedinUniversalGrammar.Therulesarecomposedofsyntacticcategoriesdefinedasbasicorrecursiveclauseswhilesyntacticoperationsarefunctionssuchasconcatenationthatdefinehowcategoriesformnewphrases.Theserulesandoperationsmaybeappliedtoalexicontodefinethesyntaxofa‘fragment’ofEnglish.
Syntacticcategoriesarebasedupontwoprimitivecategories:
sentenceandentitycategoriesasdenotedbytanderespectively.Thetcategorydoesnotcontainlexicalitems.Itiscomposedofsentencesbuiltbyrecursiverules.Thelabeltrepresentsthefactthatallmembersofthecategorycontainatruth-value.Theprimitivecategoryedoesnotactuallycontainanyentities.Itsusageliesnotincategorizationofphrasesbutinrepresentingsemanticinformation.Forexample,phrasescategorizedast/eimpliestheusageofafunctionthattakesthesensesofentities(e)intotruth-values(t).
Usingtheprimitivecategoriestande,anindefinitenumberofcategoriesmaybeconstructedintheformX/YwhereXandYarecategories
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