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1、PropositionalLogicUSEM40aSpring2006JamesPustejovskyEvaluationofDeductiveArgumentsargumentAisadeductiveargument=df.Aisanargumentinwhichtheconclusionissupposedtofollowfromthepremiseswithnecessity/withcertaintydeductiveargumentAisvalid=df.itisnotpossibleforallofA’
2、spremisestobetrueanditsconclusionfalsedeductiveargumentAissound=df.(i)Aisvalid,and(ii)allofA’spremisesaretrue(P1)IfGroverisdead,thenGroverdoesnotvote.(P2)Groverisdead.(C)Therefore,Groverdoesnotvote.FormalLogicwithmanydeductivearguments,validityisamattersimplyof
3、form,ofstructureformallogicstudiesthesecasesinwhichvaliditydependssolelyonformnotallvalidargumentsareformallyvalid:(P)Groverisabachelor.(C)Therefore,Groverdoesnothaveawife.argumentAisformallyvalidif,invirtueofA’slogicalformalone,itisimpossibleforallofA’spremise
4、stobetrueanditsconclusionfalse(P1)All19thCent.Americanpresidentsaredeadpeople.(P2)Alldeadpeoplearepeoplewhodonotvote.(C)Therefore,all19thCent.Americanpresidentsarepeoplewhodonotvote.Whystudyformallogic?ItgivesusamorerobustunderstandingofvalidityingeneralItforms
5、thebuildingblockforourmodelofmeaninginlanguageandforreasoningingeneralIntroductiontoPropositional(or“Sentential”or“Truth-Functional”)Logicdealswithpropositions–wholestatements;meaningfuldeclarativesentencesSisasimpleproposition=df.Sdoesnotcontainanyotherproposi
6、tionasacomponentGroverisdead.Sisacompoundproposition=df.ScontainsatleastonesimplepropositionasacomponentGroverisdeadandStevensonisdead.ItisnotthecasethatGroverisbeautiful.ThewomanwhomarriedGroverisbeautiful.PropositionalForms,Variables,Constants,andSubstitutio
7、nInstancesapropositionalformisapatternforawholeclassofpropositions(p&q)v~p~&)pq)apropositionalvariableisalowercaseletter(e.g.,‘p’,‘q’,‘r’,‘s’)forwhichapropositionmaybesubstitutedapropositionalconstantisacapitalletterthatstandsforaparticular,definitepropositionG
8、=Groverisdead.S=Stevensonisdead.asubstitutioninstanceofapropositionalformistheresultofuniformlyreplacingthepropositionalvariablesinthatformwithpropositionsthesameproposition
