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1、AndrásKornaiMathematicalLinguisticsABCAndrsKornaiáMetaCartaInc.350MassachusettsAve.Cambridge,MA02139USAISBN:978-1-84628-985-9e-ISBN:978-1-84628-986-6DOI:10.1007/978-1-84628-986-6BritishLibraryCataloguinginPublicationDataAcataloguerecordforthisbookisavailablefromt
2、heBritishLibraryLibraryofCongressControlNumber:2007940401©Springer-VerlagLondonLimited2008Apartfromanyfairdealingforthepurposesofresearchorprivatestudy,orcriticismorreview,aspermittedundertheCopyright,DesignandPatentsAct1988,thispublicationmayonlyberepro-duced,st
3、oredortransmitted,inanyformorbyanymeans,withthepriorpermissioninwritingofthepublishers,orinthecaseofreprographicreproductioninaccordancewiththetermsoflicensesissuedbytheCopyrightLicensingAgency.Enquiriesconcerningreproductionoutsidethosetermsshouldbesenttothepubl
4、ishers.Theuseofregisterednames,trademarks,etc.,inthispublicationdoesnotimply,evenintheab-senceofaspecificstatement,thatsuchnamesareexemptfromtherelevantlawsandregulationsandthereforefreeforgeneraluse.Thepublishermakesnorepresentation,expressorimplied,withregardto
5、theaccuracyoftheinforma-tioncontainedinthisbookandcannotacceptanylegalresponsibilityorliabilityforanyerrorsoromis-sionsthatmaybemade.Printedonacid-freepaper987654321SpringerScience+BusinessMediaSpringer.comTomyfamilyPrefaceMathematicallinguisticsisrootedbothinEuc
6、lid’s(circa325–265BCE)axiomaticmethodandinPan¯.ini’s(circa520–460BCE)methodofgrammaticaldescription.Tobesure,bothEuclidandPan¯.inibuiltuponaconsiderablebodyofknowledgeamassedbytheirprecursors,butthesystematicity,thoroughness,andsheerscopeoftheElementsandtheAsht.a
7、dhy¯ay¯¯ıwouldplacethemamongthegreatestlandmarksofallintellectualhistoryevenifwedisregardedthekeymethodologicaladvancetheymade.Asweshallsee,thetwomethodsarefundamentallyverysimilar:theaxiomaticmethodstartswithasetofstatementsassumedtobetrueandtransferstruthfromth
8、eaxiomstootherstatementsbymeansofafixedsetoflogicalrules,whilethemethodofgrammaristostartwithasetofexpressionsassumedtobegrammaticalbothinformandmeaningandtotra
