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    On Coordination and the Common Ground

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    OnCoordinationandthe
    CommonGround
    AntonBenz

    1Introduction
    Inthistalkweconsidertheroleofcommongroundforsomecoordinationproblemsindialogue.There,weconcentrateespeciallyonthedifferencebetweenexplicitandimplicitrepresentations.Aprototypicalexampleforacoordinationproblemistheso-calledcoordinatedattackproblem1:(1Twodivisionsofanarmyarecampedontwohilltops.Inthevalleyawaitstheenemy.Itis
    clearthatifbothdivisionsattacktheenemysimultaneouslytheywillwinthebattle,whileifonlyonedivisionattacksitwillbedefeated.Asaresult,neithergeneralwillattackunlessheisabsolutelysurethattheotherwillattackwithhim.Inparticular,ageneralwillnotattackifhereceivesnomassage.Thecommandinggeneralofthefirstdivisionwishestocoordinateasimultaneousattack.Thetwoarmieshavetocoordinateajoinedproject—simultaneousattack—withacommongoal—defeatingtheenemy.Thereisaviewonlanguageuse2whichemphasisesespeciallytheroleofjoinedprojectsandtheirrelationtocommongroundandpublicgoals.Inthistalkwewanttoconsidertheroleofcommongroundmoreclosely,especiallyitstwoaspectsascommoninformationwhichisprovidedbygeneralrulesoflanguageinterpretation,andasexplicitlyrepresentedcommonknowledge.
    Ifweconsideronlymonologue,thenwecanidentifythecommongroundatacertainpointwiththeinformationwhichhasbeenintroducedintheprevioustext.Thereareprincipallytwowaystorepresentthecommonground:Asasetofpossibleworldsorinamoresyntacticway,e.g.asaDiscourseRepresentationStructure(DRS3.Itiscommongroundthatasentenceψholdsiffψistrueinallworlds,oriffitisaDRS–condition.ThemeaningofaDRSisasetofworlds,orworld–assignmentpairs.Thisallowstocomparethetworepresentations.Themaindifferenceiswithrespecttofine–grainednessandlogicalomniscience4.Wecallthepossibleworldsrepresentationthecommoninformation,andtheDRS-likerepresentationacommonDRS.
    Ifwelookatdialogue,thenthedistinctionbetweentheserepresentationshasmoreinterestingaspects.Asanexample,welookattheuseofspecificindefiniteNPsandreferencetothembyuseofpronounsordefinitedescriptions5.
    (2A:Yesterday,amanranintomyoffice,whoinquiredafterthesecretary’soffice.
    B:Wasthemanwearingapurplejoggingsuit?
    A:IfitwasArnoldhewas,andifitwassomebodyelsehewasnot.
    DekkerobservesthatA’sanswersoundsstrange,evenifweassumethattherewasmorethanonepersoncomingintotheoffice,oneofthemArnold.Weassumethatadefinitedescriptiondefϕpicksoutanobject(1whichmustbegiveninthecommonground,and(2whichistheonlyoneinthecommongroundwhichhasthepropertyϕ.Fordialoguethereareagainthetwowaystorepresentthecommonground:Asasetofpossibleworldsorinasyntacticway.Accordingtothefirstview,thecommongroundcanbeidentifiedwiththesetofallworldswhichareepistemicallypossibleforoneofthedialogueparticipants,orwhicharepossibleforoneoftheparticipantsaccordingtothebeliefsoftheotherparticipantsabouthisbeliefs,etc.Intuitively,B’suseofthemanintheexamplerefersbacktoaspecificpersonintroducedbyA.Butifwerepresentthecommongroundasasetofpossibleworlds,thenthereisnouniquerealobjectsuchthatadefinitedescriptioncanpickitoutastheonlyobjectwhichisaman.Thereisonlyauniquediscoursereferent,butdiscoursereferentsarenotpartofthecommoninformation.Hence,wecantryaDRS–likerepresentationforthecommonground,butthenwehavetoexplaininwhichsensesuch
    [4,pp.176–183].Theexampleistakenfromp.176.course,itisH.H.Clark’sviewwehaveinmind[2].3[6],ore.g.asasentenceinDynamicPredicateLogic[5].
    4See[4,Ch.7]and[7,Ch.2]foradiscussionofvariousnotionsofknowledgeandbeliefinmodalapproachesandtheproblemoflogicalomniscience.
    5TheexampleisduetoP.Dekker[3].InDekker’soriginalversionB’sutterancecontainsapronounbutourpointbecomesclearerifwereplaceitbyadefinitedescription.
    2Of1See
    1

    aDRSiscommon,andhowinterlocutorsmanagetorefertothesameobject.Thelastpointiscriticalespeciallyifweassumethatreferentsintroducedbyspecificindefinitesarefreevariables.Wewillarguethat:
    •Bothrepresentationshavetobekeptdistinct.
    •Successofcoordinationisdefinedrelativetocommoninformation.•TherearefixedrulesinacommunityforhowtoupdatethecommonDRS.
    Ourmainexamplewhichshowsthatwehavetomakeadistinctionbetweencommoninforma-tionandcommonDRSesistheuseofspecificindefinitesandanaphoricreferencetotheobjectsintroducedbythem.Here,weassumethatallparticipantsuseDRS-likerepresentationsforthecommongroundandthattheinterpretationofdefinitedescriptionsdependonthem.Thatthedescriptionthenreferstothesameobjectisacoordinationproblem.WediscussthisexampleinSection3.Wemodelitbyuseofmulti–agentsystems.Thissystemsconsistofasetofsituations,joinedacts,atransitionoperation,andafunctionPwhichspecifieswhichjoinedactscanpossiblybeperformedinwhichsituation.SemanticandpragmaticconditionsenterasrestrictionsonthefunctionP.Weintroducemulti–agentsystemsinmoredetailinSection2.Successhastobedefinedwithrespecttocommoninformation.ThisismotivatedbyExample(1.Wheresuccessmeansthatinterlocutorsmanagetosolveacoordinationproblem.Inordertoshowthatfixedupdaterulesplayacrucialroleforcoordinationwediscussthetimeimprecisionproblem6,andtheMuddyChildrenPuzzle7inSection4.
    2DialogueandMulti–AgentSystems
    WedescribedialoguefragmentsasMulti–AgentSystems.Here,wefollowthetheorydevelopedin[4].Withinthisframeworkwecandescribedialogueandtheupdateoftheknowledgebasesoftheparticipantsasagame.Thishastheadvantagethatwecanexploitstandardtechniquestodefinetheinformationofagentsinapossibleworldsframework,andwegettheusualdefinitionofmutualknowledge.Amulti–agentsystemconsistsofthefollowingcomponents:1.AsetSofglobalstates.
    2.AsetACTofpossibledialogueacts.
    3.AfunctionP8whichtellsuswhichdialogueactscanbeperformedinwhichdialoguesitua-tions.4.Atransitionoperationτ:ACT×S−→Swhichmodelstheeffectofperformingadialogueact.5.AsetofinitialdialoguesituationsS0.
    WeidentifydialogueswiththesetDofallsequences

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