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1、ANewApproachtoBaseRevisionPaoloDiGiusto1GuidoGovernatori21RegioneEmilia-Romagna,v.leA.Moro52,40122Bologna,Italy,e-mailcoc0788@iperbole.bologna.it2CIT,GrithUniversity,NathanQLD4111,Australiae-mailG.Governatori@cit.gu.edu.auAbstract.Wepresentthreeapproachestorevisionofbeliefbases,whicharealsoex
2、aminedinthecaseinwhichthesentencesinthebasearepartitionedbetweenthosewhichcanandthosewhichcannotbechanged;theapproachesareshowntobesemanticallyequivalent.Anewapproachisthenpresented,basedonthemodi cationofindividualrules,insteadofdeletion.Theresultingbaseissemanticallyequivalenttothatgenerated
3、bytheotherapproaches,inthesensethatithasthesamemodels,buttherulepartalonehasfewermodels,thatis,issubjectedtoasmallerchange.IntroductionBeliefrevisionfacestheproblemofmaintainingtheconsistencyofasystemofbeliefswhennewpiecesofinformationareadded,and,atthesametime,itshouldpreserveasmanybeliefscom
4、patiblewiththenewdataaspossible.Inotherwords,givenasetofbeliefsandanewbelief,wewantto ndanewsetofbeliefswhichincludesthenewbeliefanddi ersaslittleaspossiblefromtheoldset.Classicallogichastheexabsurdosequiturquodlibetprinciple,i.e.,fromacontradictionanythingfollows;so, ndingacontradictioninasys
5、temshouldrenderitcompletelyuseless.Weknowthatthingsgodi erently.Contradictionsaretackledtryingtorepairsystemslocally,andkeepingmodi cationsassmallaspossible.Systems(notonlylogicalones,butalsonormativesystems)areveryconservative{or,atleast,thisishowwebehaveaboutthem.Beliefrevisiontheoriesarethe
6、logictoolsforkeepingchangesmall.Di erentspeci cationsoftheproblemresultindi erentformaltreatments.The rstwatershedisbetweentheoriesdealingwithsetsclosedw.r.t.log-icalconsequence(beliefsets)andtheoriesdealingwith( nite)non-closedsets(beliefbases).Beliefsetsaresimpler;theprincipleofirrelevanceof
7、syntax,forinstance,istriviallysatis ed:itdoesnotmatterhowIdescribeaset,becausewhatisimportantistheset(closedw.r.t.logicalconsequence){theprincipleofextensionality.Beliefbases,onthecontrary,aremuchmorerealistic.Ourknowl-edgeisdescribedby
