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1、IntroductiontoIntensionalLogicLing406/802ReadMeaningandGrammar,Ch.5.1-5.21TowardsIntensionalSemantics•Extensionalsemanticsthatmodelsthemeaningofsentencesbasedontheextensionsoflinguisticexpressionsislimitedandcannothandletheseintensionalconstructions.•Whatiscommonin
2、theseintensionalconstructionsisthattheycallforaconsiderationofextensionsthatanexpressionmayhaveincircumstancesotherthantheoneinwhichitisevaluated.ThisiscalledanINTENSIONofalinguisticexpression.•Inordertogetattheintensions,weneedtoconsideralternativewaysinwhichthewo
3、rldmighthavebeen,alternativesetsofcircumstances,orPOSSIBLEWORLDS.•TheframeworkthatmodelsthemeaningofsentencesbasedontheintensionsoflinguisticexpressionsiscalledINTENSIONALSEMANTICSorPOSSIBLE-WORLDSSEMANTICS.2PossibleWorldsandIntensions•Possibleworldsarepossiblecirc
4、umstancesinwhichsome(orall)eventsorstatesaredifferentfromwhattheyinfactareintheactualcircumstance.wwwMatandSuearefunnySue,PeteandJohnarefunnyMatandPetearefunnySueistallSueistallSueisnottallStevensonisthepres.ofSFUAndersonisthepres.ofSFUAndersonisthepres.ofSFU•Wi
5、sasetofallpossibleworlds.W={w,w,w,...}•TheintensionofasentenceS:proposition(e.g.,Matisfunny)Thesetofpossibleworldsinwhichitistrue.Functionfrompossibleworldstotruthvalues.w→w→w→p=w→...3PossibleWorldsandIntensions(cont.)•TheintensionofaVP
6、:property(e.g.,isfunny)Functionfrompossibleworldstosetsofindividualsw→{Mat,Sue}w→{Sue,Pete,John}w→{Mat,Pete}[[isfunny]]=w→{Sue,John,Pete}...•TheintensionofanNP:individualconcept(e.g.,thepresidentofSFU)Functionfrompossibleworldstoindividu
7、alsw→Stevensonw→Andersonw→Anderson[[thepresidentofSFU]]=w→Pete...4PossibleWorlds,TenseandIntensions•Toincorporatetense,weneedtoconsiderpossibleworldsatdifferenttimes.Thatis,wewillwanttoconsidernotjustpossibleworlds,butpossibleworld-timep
8、airs(circumstances).W={,,...,,...,,...}•Proposition:asetofpossibleworld-timepairs,orafunctionfrompossibleworld-timepa