ACut-monKnowledge PietroAbateandRajeevGor′e AustralianNationalUniversity,Canberra,Australia, [,]***@ December1,2006 Abstract Inthispaperwefocusonthedevelopmentofacut-free?nitarytableau calculuswithhistoriesforn-monknowledge (LCK).Thus,wegetaproofsystemwhereproof-esfeasible andwelaythebasisfordevelopingauniformframeworkforthetreatment -passdecision methodslikethosefortemporallogics,ourcalculusgivesasingle-pass decisionprocedurewhichisspace-optimal. 1 Introduction Reasoningaboutknowledge,inparticularabouttheknowledgeofagentswho reasonabouttheworldandeachother’sknowledge,playsanimportantrole puterscience,philosophy,gametheoryandmanyother ?(CK),whereeverybodyknows,every- oneknowsthateveryoneknows,etchasalsobeenprovedfundamentalin?elds whichdealwiththeanalysisofinteractinggroupsofagents:see[FHMV95]for anextensiveoverview. Inthispaperwefocusonthedevelopmentofacut-free?nitarytableau calculuswithhistoriesforn-monknowledge(LCK). Thus,wegetaproofsystemwhereproof-esfeasibleandwelaythe basisfordevelopingauniformframeworkforthetreatmentofthefamilyof -passproofcalculibasedontemporal logics,orthetheexistingsolutionsin[AJ02],[vD02],wegiveasingle-pass, ?nitaryandcut-freedecisionprocedureforLCK 2 SyntaxandSemantics WeconsidercountablymanyatomicpropositionsAP,a?nitenon-emptysetof agentsAwithAP∩A=?,theconnec
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