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1、INTENSIONALANDHIGHER-ORDERMODALLOGICInmemoryofRichardMontagueNORTH-HOLLANDMATHEMATICSSTUDIES19IntensionalandHigher-OrderModalLogicWithApplicationstoMontagueSemanticsDANIELGALLINDepartmentofMathematicsUniversityofSanFranciscoSanFrancisco,California,USA1975NORTH-HOLLANDPUB
2、LISHINGCOMPANY-AMSTERDAMOXFORDAMERICANELSEVIERPUBLISHINGCOMPANY,INC.-NEWYORK0NORTH-HOLLANDPUBLISHINGCOMPANY-AMSTERDAM,1975AllRightsReserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopy
3、ing,recordingorotherwise,withoutthepriorpermissionofthecopyrightowner.North-HollandISBN:072040360XAmericanElsevierISBN:044411002XPublishedby:NORTH-HOLLANDPUBLISHINGCOMPANY-AMSTERDAMNORTH-HOLLANDPUBLISHINGCOMPANY,LTD.-OXFORDDistributorsfortheU.S.A.andCanada:AmericanElsevi
4、erPublishingCompany,Inc.52VanderbiltAvenueNewYork,N.Y.10017PRINTEDINTHENETHERLANDSPREFACEInaseriesofpaperswrittenduringtheperiod1967-1971,RichardMontagueoutlinedahighlyoriginalapproachtotheproblemofprovidingapreciseaccountofnaturallanguagesyntaxandsemantics.Inasharpdepar
5、turefromthelinguisticmethodsoftheChomskyschool,Montagueintroducedapowerfulbodyoftechniquesfromthefieldofmathematicallogic,principallytheset-theoreticsemanticalmethodspioneeredbyhisteacherTarski.Montague'stragicdeathin1971cutshortwhatwascertainlythemostambitiousresearchun
6、dertakingofhiscareer,andoneforwhichhewasuniquelyqualified.Althoughhecompletedonlythreepapersdealingspe-cificallywithnaturallanguage,theideastheycontainhaveprovidedthebasisforanentirebranchofcurrentlinguisticresearch,andtheinterestinhisworkcontinuestogrowamongphilosophers
7、,linguistsandlogicians.ThepresentworkattemptstoprovidethetechnicalbackgroundnecessaryforathoroughunderstandingofMontagueSemantics,atthesametimeex-ploringsomeofthemathematicallyinterestingapplicationsofhigher-ordermodallogic.ThefocusofPartIisthelogicofintensions,denotedby
8、IL,whichMontagueintroducedinhispaper"UniversalGrammar.''ThissystemextendsChurch'sfunctionaltheoryoftype
