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Logic, Information & Conversation c1998PaulPiwek P(cid:0)rintedbyPrintPartnersIpskamp,TheNetherlands CoverDesignandLayOutbyPaulPiwekinLATEX Logic, Information and Conversation Ditproefschriftisgoedgekeurddoordepromotoren: prof.dr.D.G.Bouwhuis en prof.dr.H.C.Bunt Copromotor: dr.ir.R.J.Beun PROEFSCHRIFT terverkrijgingvandegraadvandoctoraandeTechnische UniversiteitEindhoven,opgezagvandeRectorMagnificus, prof.dr. M.Rem,vooreencommissieaangewezendoorhet CollegevoorPromotiesinhetopenbaarteverdedigenop dinsdag10november1998om16.00uur door PaulLeoAntoinePiwek geborenteVenlo Tomyparents offworkinthediscosofplacessuchasGeldern,MarmarisandL’Escala. Brighton,September1998 Acknowledgments First,IwouldliketothankmysupervisorsDonBouwhuis,HarryBuntandRobbert- JanBeunforgivingmetheopportunitytowritethisdissertation. Thanks are due to Rene´ Ahn, Tijn Borghuis, Anita Cremers, Emiel Krah- mer,Marie¨tTheuneandKeesvanDeemterforcommentingonthecontentsof oneormorechapters. SpecialthankstoEmielwithwhomIhadthepleasureof co-authoringtwopaperswhichformthebuildingblocksofchapter3. Icannot imaginehowIcouldhavewrittenthisdissertationwithouthavingbeenexposed toEmiel’spositiveandenergeticapproachtodoingresearch.Furthermore,Irecall withpleasurethelongphilosophicaldiscussionswithRene´inthetrainbetween Tilburg and Eindhoven (one should not underestimate the time itcan take the DutchrailwaystogetfromTilburgtoEindhoven). Iconsidermyselfveryfortu- natetohavehadtheopportunitytobenefitfromKees’abilitytospottheweak pointsofatheory.Hiscomments,thoughoftencritical,werealwaysconstructive. Iwouldliketothankthefollowingpeopleforaskingpertinentquestionsand making useful suggestions atsomepoint during the preparation ofthis disser- tation: NicholasAsher,HansKamp,LeenKievit,PeterKrause,SteveBerman, BarbaraPartee,RemkoScha,MarcSwerts,JacquesTerken,JanvanKuppevelt, MargrietVerlinden, HenkZeevat,EdeZimmermannandeverybodyIforgotto mention. Furthermore, thanks are due to all the people at IPOand the Com- putationalLinguisticsGroupatTilburgUniversitywhomadethoseplacessuch pleasantenvironmentstoworkin. Theresearchreportedinthisdissertationwascarriedoutforthelargestpart attheCentreforResearchonUser-SystemInteraction (IPO)oftheEindhoven UniversityofTechnology,andforasmallerpartattheComputationalLinguistics Group of Tilburg University. MyPhD.project was part of the DENK project (DialogueManagementandKnowledgeTransfer). DENKwasfinancedbythe Co-operationCentreofTilburgandEindhovenUniversities(SOBU). Finally,thankstoEric,Erwin,BertandDimitriforhelpingmetogetmymind 4 AnswersandContexts 63 4.1 TheRoleofContext. . . . . . . . . . . . . . . . . . . . . . . . . 64 4.2 RepresentingquestionsandanswersinPTS . . . . . . . . . . . . 65 4.3 Formalizinganswerhood . . . . . . . . . . . . . . . . . . . . . . 68 4.4 FurtherPragmaticsofQuestionsandAnswers . . . . . . . . . . . 77 Table of Contents 4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5 AccentsandAlternatives 83 5.1 PresuppositionandPlurality . . . . . . . . . . . . . . . . . . . . 86 5.2 AlternativeAssertions. . . . . . . . . . . . . . . . . . . . . . . . 88 5.3 FurtherApplications . . . . . . . . . . . . . . . . . . . . . . . . 100 5.4 AlternativeProposals . . . . . . . . . . . . . . . . . . . . . . . . 108 5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Introduction xi III Conversation 115 I Logic xxvii 6 ConversationalGames 117 1 ContextandConsistency 1 6.1 ConversationandDiscourseAnalysis . . . . . . . . . . . . . . . 118 1.1 ContextandInterpretation . . . . . . . . . . . . . . . . . . . . . 2 6.2 StoresandRules . . . . . . . . . . . . . . . . . . . . . . . . . . 123 1.2 ConsistencyandLogic . . . . . . . . . . . . . . . . . . . . . . . 8 6.3 AConversationalGame. . . . . . . . . . . . . . . . . . . . . . . 125 6.4 Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 2 PureTypeSystems 11 6.5 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 2.1 InformalExposition . . . . . . . . . . . . . . . . . . . . . . . . . 12 6.6 PresuppositionsinConversation . . . . . . . . . . . . . . . . . . 140 2.2 FormalExposition . . . . . . . . . . . . . . . . . . . . . . . . . 16 6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 2.3 ContextsofInterpretation . . . . . . . . . . . . . . . . . . . . . . 19 2.4 ReasoningandNormality . . . . . . . . . . . . . . . . . . . . . . 20 7 ConveyedMeaning 145 7.1 InDefenseofLiteralMeaning . . . . . . . . . . . . . . . . . . . 146 7.2 SomeObservations . . . . . . . . . . . . . . . . . . . . . . . . . 148 II Information 27 7.3 TheConversationalGame. . . . . . . . . . . . . . . . . . . . . . 150 7.4 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 3 PresuppositionsandProofs 29 7.5 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 3.1 PresuppositionsasGaps . . . . . . . . . . . . . . . . . . . . . . 32 7.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 3.2 ConditionalsandDisjunctions . . . . . . . . . . . . . . . . . . . 34 3.3 Bridging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 SummaryandConclusions 157 3.4 ConstructingDeterminateBridges . . . . . . . . . . . . . . . . . 44 3.5 RelatedWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 SummaryinDutch 161 3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.7 Appendix:TheResolutionAlgorithm . . . . . . . . . . . . . . . 57 Notes 163 3.8 Appendix:TheQuestionnaire. . . . . . . . . . . . . . . . . . . . 60 References 169 Conversationanalysts(e.g.,Sudnow,1972)anddiscourseanalysts(e.g.,Sten- stro¨m,1994)haveexaminednaturallyoccurringconversationsandprovidedde- taileddescriptionsofthepatternsthatoccurinsuchconversations.Thesedescrip- tions aremainlyintermsofanon-technical vocabulary thatisdirectly related totheeverdaywaysofspeaking aboutconversation. Thedescription ofapat- Introduction ternmayuseavocabularyconsistingofthetermssuchas‘question’,‘answer’, ‘request’,etc. Althoughthedescriptionsthatarearrivedatinthiswayarevalid,theyrely heavily on the judgements of the person that analysed the conversation. This informerlabelscertainutterancesasquestions,othersasanswers,etc.Indoingso, Theaimofthisbookistocontributetothedevelopmentofatheoryofconver- heorsheuseshisorherimplicitunderstandingoftheutterancesathand.Amodel sation. Onthesurface, aconversation isasequence of(possibly overlapping) intermsofagameisintended toprovideanexplicit basisforsuchhighlevel utterances. Weareinterestedinthequestionwhatmakessuchasequenceintoa descriptions. Thisisachievedbyrelatingthemove—i.e.,thestatetransition— conversation?Thisquestionisapproachedbylikeningtheutterancesofaconver- thatanutterancegivesrisetodirectlyitssyntacticandprosodicsurfaceform. sationtothemovesinagame.Thus,weask:whatkindofagameisaconversa- Inadditiontotheaforementionednaturallyoccurringconversations,constructed tion? Wittgenstein(1953)wasoneofthemostprominentproponentsoftheidea fragmentsofconversationareusefulasameansfortestingthepredictionsofa thatlanguageuseisagame-likeactivity. theory. Theadequacyofthetheorycanbeputtothetestbycheckingwhether Agamecanbecharacterizedintermsofthestatesofthegameandtherules theanalysisthatthetheoryassignstosomefictitiousstretchofconversationcor- thatregulatethetransitionsbetweenthestatesofthegame. Therefore,inorder responds with the judgements of ahuman informer. Ideally, such judgements tomodelconversationasagame,henceforthaconversationalgame,weneedto shouldbeelicitedthroughquestionswhichdirectlymatchtheeverydayconcepts specifythestatesandstatedynamicsofthisconversationalgame(cf. Hamblin, ofthenaiveinformer(see,inparticular,section3.4). 1971;Stalnaker,1978andLewis,1979). InpartIofthisbook,weintroducethe Thesortofadequacythatwehavediscusseduptillnowisindifferentwith formaltoolstodoso.PartIIdealswiththestatechangesthatindividualutterances respecttotherelationbetweentheconversationalgameandthementalstatesof giveriseto. Finally,inPartIIIwefocusontheinfluenceofconversationalrules thepersonsthatareinvolvedinaconversation.Sincenaturallyoccurringconver- onsequencesofutterances. sationsinvolverealpeople,itislegitimatetoinquireintotherelationbetweena Beforeprovidingasummaryofeachoftheaforementionedparts,wedescribe conversationalgameandthementalstatesoftheinterlocutors. theassumptionsunderlyingourmodelofconversations. Wedealwithissuesof Togetthingsintoperspective,considertherelationbetweenadescriptionof adequacyofaconversationalmodelandintroducelogicasatoolformodelling thegameofchessandthementalstatesofsomeindividual thatisplaying the conversations. Furthermore,weindicatewhatpartofthecontextinwhichcon- game. Thedescription of thegame(the board, the chess pieces and the legal versationsoccuriscoveredbytheconversationalstate.Finally,weprovidesome moves)neednotsayanythingaboutthewayaplayerrepresentsthisgameinter- backgroundaboutthenotionofinformationthatisusedthroughoutthisbook. nally. Humanplayersshould,however,beabletorepresentthegamesomehow. Similarly, itmakesnosensetoprovide adescription ofaconversational game Adequacy whichcannotbeplayedbyhumanbeings. Forpracticalpurposes,adescriptionoftheconversationalgamewhichallows Theadequacyofaconversationalgameasamodelofconversationsdependson a computer programme to play the gameis attractive. It makes it possible to howwellitaccountsforthepatternsthatoccurinnaturallyoccurringconversa- explorethepatternsthatareaccountedforbytheconversationalgame. Theex- tions.Thesepatternsarethedatathatthegameistoexplain.Thepatternsthatwe plorationcanbecarriedoutbyhavingthecomputerprogrammeplaywithacopy takeasabasiswillbederivedfrombothnaturallyoccurringandconstructedcon- ofitself(see,e.g.,Power,1979)orwithahumanbeing. Themodeldescribedin versations,wherethelatterareintendedasconversationsthatcouldhaveoccurred thisbookhasbeendevelopedpartlyonthebasisofourexperienceswithanim- naturally. xi xii plementationofaconversationalgame. Thisimplementationwascarriedoutas compatible withtheinformational content oftheconversational state. Wedis- partoftheDENKproject(seeAhnetal.,1995;Buntetal.,1998). cussthisroleofconversationalstatesindetailinpartIII.There,wedistinguish betweenthecompabilityofphysicalactionsversuscommunicativeactionswith LogicasaTool theconversationalstate. Forinstance,weproposethatiftheconversationalstate containstheinformationthatoneoftheinterlocutorsisgoingtoperformsomeac- Inordertoprovideanadequatemodelofconversations,weneedthetoolstocon- tion,thentheconversationalgameprescribesthatheshouldindeedperformthat structsuchamodel. Whatrequirementsdoesthenatureofconversationsimpose action(e.g.,afteraninterlocutorhassaidthatheisgoingtothecinema,thisac- uponsuchatool? Primarily,conversationsinvolvetheexchangeofinformation. tionisrecordedontheconversationalstateasacommitmentoftheinterlocutor). Theconversationalstatekeepstrackoftheinformationthathasbeenexchanged Thecompatabilityofcommunicativeactionswiththeconversationalstateisex- inthecourseofaconversationandtheinformationthatwasalreadypublicbefore plicatedprimarilyintermsofconsistency. Forinstance, thepresuppositions of theconversationstarted. acommunicativeactionshouldbeconsistentwiththeinformationthatisalready Inthecourseofthisbook,wewillshowthatmuchoflanguagebehaviourcan partoftheconversationalstate(cf.Stalnaker,1978;chapter3,thisbook). beexplainedintermsofthequestforconsistentinformationbyconversational Inlinewiththeaforementionedviewontheconversationalstate,andfollow- partners.Inordertostriveforconsistency,itisnecessarytodisinguishconsistent ingHamblin(1970),weusethetermcommitmentsfortheinformationalitemsthat frominconsistentinformation. Sinceaninconsistencymightbeimplicitinsome makeuptheconversationalstate.InpartIII,weproposethatifaninterlocutorA bodyofinformation,atoolisneededforbringinginconsistenciesintotheopen. assertssomesentenceSwhichexpressestheproposition ,thenitwillbecome Atthispoint,logicentersthepicture.Logic—thestudyofcorrectreasoning— apubliccommitmentthatAiscommittedto . Let beth(cid:0)econversationalstate providesthemeanstobringtolighttheinconsistenciesthatmightbehiddenina aftertheassertion,and meansAiscom(cid:0)mitted(cid:3)to . Inthatcase,wecan bodyofinformation,suchasaconversationalstate.Givenabodyofinformation, write tostateCtAh(cid:0)at holdsintheconvers(cid:0)ational state . Wecall ittellsushowtosetupachainofinferenceswhichleadsuptosomepieceof t(cid:3)he(cid:2)utCteAra(cid:0)ncemeaningaCnAd(cid:0) thesentencemeaningoftheafore(cid:3)mentioned informationthatwasimplicitinthebodyofinformation.Forinstance,themodus CutAte(cid:0)ranceofthesentenceS. (cid:0) ponensruleoflogicsaysthatonthebasisof and implies ,wemayinfer Atthispoint,letusaddresstherelationbetweentheterm‘commitment’and that .Thefollowingargument,whichreveals(cid:0)theimp(cid:0)licitinform(cid:2)ationthat‘One sucheverydaywordsas‘belief’and‘intention’. Shouldweequatecommitment cann(cid:2)otdriveinMike’scar’,islicensedbythemodusponensrule: withwhatwenormallycallbelief?Inotherwords,shouldtheutterancemeaning beequivalentto (i.e.,Abelievesthat )? Moore’sParadoxappears (1) Ifthemotorofacarisbroken,thenonecannotdriveinit. Themotorof CtoAp(cid:0)rovidesomeevidenBcAe(cid:0)forthatposition. Thep(cid:0)aradoxinvolvesthefollowing Mike’scarisbroken. sentence: THEREFOREOnecannotdriveinMike’scar. Now,iftherulesoflogicallowustoinfersomepieceofinformationandits (2) Itrains,butIdonotbelievethatitrains. negationfromabodyofinformation,thenthatbodyofinformationisinconsistent. Thatis,asentenceoftheform ,butIdonotbelievethat . Moorepoints outthatalthoughthesentencemean(cid:0)ingisnotself-contradictory(cid:0),theutteranceas ConversationalStatesandContext awholedoesseemtobeself-contradictory.Wecanexplainthisbyassumingthat Inthechapterstocome,thenotionsofacontextandaconversational stateare istheutterancemeaningofadeclarativesentencewithasentencemeaning usedinterchangeably. Thetermcontextis,however,oftenusedinamuchwider BAa(cid:0)ndaspeakerA.Theutterancemeaning of(2)(where isthe sensethantheonethatweemploy.Inthissection,wepointoutinwhichrespects (cid:0)propositionitrains)isindeedself-contradicBtoAr(cid:4)yp,g(cid:3)iv(cid:4)eBnAsopm(cid:5)eplausibleaxipomsfor ournotionofcontextismorerestrictedthantheusualone. belief(seeThijsse,1994;1998). Thijsse(1994;1998), however,pointsoutthattheformalisationofutterance Commitment Inourview,theconversationalstateorcontextdirectlyconstrains meaning in terms of is deficient. In particular, it cannot account for the thebehaviouroftheinterlocutors: theyaresupposedtostriveforactionsthatare anomalyof‘Itrains,bBuAtIdonotknowthatitrains’. Aftercarefulanalysisof xiii xiv exampleslikesthelatter,Thijsseproposesthattheutterancemeaningofadeclar- ground,cf. Clark,1996),ifsomepieceofinformationiscommonground,then ativesentencewithcontent andspeakerAis (where standsfor itisalsocommongroundthatitiscommonground. Furthermore,itwillalsobe Abelievestoknow.Itmayb(cid:0)eparaphrasedas‘ABAisKcAo(cid:0)nvincedthBaAt’K).AThisfinding commongroundthatitiscommongroundthatitiscommonground,andsoon. canbeincorporatedintoourframeworkbyaddinganaxiomto whichsaysthat This property of the common ground is appropriate for the conversational foranyproposition , isequivalentto . (cid:3) state. Theconversationalstateisupdatedinthecourseofaconversation. After Interestingly,the(cid:0)reCaAre(cid:0)alsoutterancesinBvAolKviAn(cid:0)gtheverb‘intend’whichap- thefollowingexchange:‘A:TheearthisflatB:Yes,sheis’,wemightaskthein- peartobepragmaticallyanomalous.Consider,forinstance: terlocutorswhichinformationhasbeenexchangedasaresultoftheconversation. Wecontendthattheanswerwouldbethatithasbecomepublic(amongstAand (3) Iwillopenthedoor,butIdonotintendtodoit. B)thattheearthisflat. Whatismore,ithasalsobecomepublicthatitispublic thattheearthisflat(andsoon). Onthebasisofexample(3)wemightbetemptedtoconcludethataperson Thereisanotherpropertyofthecommongroundwhichturnsouttobecrucial intendstodosomethingifheorshebelievesthatheorshewilldoit.Thiswould forthemodellingofconversationalstructures(seechapter6).Thepropertyisthat giveusahandletoexplaintheanomalyof(3).Compare,however: ifitiscommongroundthatAiscommittedto andthatBiscommittedto , thenitiscommongroundamongstAandBthat (cid:0).Inotherwords,ifitiscommo(cid:0)n (4) Iwillloosethematch,but/althoughIdonotintendtolooseit. groundthatAandBsharetheinformation ,th(cid:0)en iscommonground. Formodellingthestructureofconvers(cid:0)ations,t(cid:0)hefirstmentionedpropertyof Ifintentionandbeliefinafutureactionwereindeedthesame,then(4)would thecommongroundplaysonlyaminorrole. Onthebasisofthefirstandthe havetobeanomalous. Theutterancemeaningwouldthenfitthepattern secondpropertywecan,forinstance,predictthatafterAhassaidthattheearthis fromwhichacontradictioncanbederived. ItseemsthatforanaBgAe(cid:4)npt(cid:3)to flat,itisuninformativewithrespecttotheconversationalstateforBtosaythatA (cid:4)inBteAndp(cid:5)todosomething,itisnotsufficientthattheagentbelievesthathewilldo iscommittedtotheearth’sflatness. it.Weproposethefollowinganalysis: foranagenttointendanaction,heorshe Clark(1996)distinguishesbetweenthecommunalandthepersonalcommon shouldnotonlybelieveinperformingtheaction,butalsohavecontroloverthe ground. Whereasthelatterisdirectlybasedonjointperceptualexperiences,the action. communalcommongroundconsistsofinformationthatpeoplesharebyvirtueof Theanomalyof(3)nowfollowsfromthefactthatpeoplearenormallyas- beingpartofaculturalcommunity.Communitiescanbebasedon,amongstother sumedtobeincontrolofwhethertheywillorwillnotopenadoor.Therefore,the things,language,nationality,profession,religionandhobbies. negationof‘Iintendtoopenthedoor’—whichweanalyseasIbelieveIwillopen Althoughconversationsalwaystakeplaceagainstthebackgroundofacom- thedoorandIhavecontrolovermyselfopeningthedoor’—canonlymeanthat munalcommonground,itisthepersonalcommongroundwhichisdirectlyacted ‘IdonotbelievethatIwillopenthedoor’,whichgivesusanutterancemeaning (cid:0) uponinaconversation. Whereasthepersonal commonground changes inthe of(3)whichisequivalenttotheutterancemeaningofMoore’sexample. courseofaconversation,thecommunalcommongroundisnormallystaticwithin For(4),thedenialoftheintentioncomesdowntothedenialofbeingincon- theboundsofaconversation. Thedistinctionbetweenthedynamicandthestatic trol,nottothedenialofthebeliefthatonewillloose. Thusweget: Iamcon- (cid:2) partofthecontextcanalsobefoundinBunt(1994),whospeaksofthelocaland vincedofthefollowing:Iwillloosethematch,andIbelievethatIwilllooseitand theglobalcontext,respectively. thatIhavenocontroloverwhetherIlooseit. Inthiscase,noinconsistencycan Wedonottakethecommongroundtobeanentitythatexistsindependently bederivedonthebasisoftheutterancemeaning.Thisisinlinewiththeintuition oftheindividual language users. Thismeansthat whenwedescribe therules thatthesentencecanbeutteredfelicitously. andstatesofaconversational game,weshouldbearinmindthataplayerina conversationalgamewillalwaysactonthebasisofhisorherrepresentationof CommonGround InlinewiththepioneeringworkofStalnaker(1974;1978) theconversationalstate. Thisallowsforsituationswheredifferentplayershave andLewis(1979),wetaketheconversationalstateorcontexttoconsistofthein- differentrepresentationsoftheconversationalstate. formationthatispublictotheconversationalpartners,i.e.,theircommonground. Intuitively(andaccordingtothebestknownformalizationsofthetermcommon xv xvi ContextinDENK Wetaketheconversationalstateorcontexttoconsistofpub- cupboard, thenBsaysso. TheDENK prototype employsprecisely thattactic. licinformation,whereeachinformationalitemrepresentsapubliccommitment. However,othertacticsareconceivable. IfBknowsthatthereisonlyonecookie Thisnotionofcontextissufficientfordefiningaconversationalgame,butfalls leftandwantstoeatit,Bmightanswer‘no’althoughBknowsthattherestillisa short when it comes to specifying how an agent could play such a game. A cookie. fullsystemforplayingconversationalgameshasbeenimplementedintheDENK Notethatinthelattersituation,Bisstilladheringtotheconversationalrules. project (Buntetal.,1998). ThisbookwaswrittenaspartoftheDENKproject. However,Bviolatesarulethatmightbesaidtobepresupposedbytheconver- (cid:3) Letusexplainhowthenotionofcontextthatwedescribeherefitsintothebroader sationalgame,i.e.,trytomakeyourcontributiononethatistrue. Grice(1975) notionofcontextthatisemployedintheDENKproject. termedthisthemaximofQuality. (cid:4) TheDENKarchitectureisbasedonasimpleconversationalsituationinvolv- Ournotionofaconversationalstateexcludestheinformationthatisprivately ingtwointerlocutorsandadomainofconversation.Thedomainoftheconversa- availabletotheinterlocutors. Furthermore,wedonotdistinguishbetweenpublic tionconsistsof(1)thatpartoftheworldthattheconversationoftheinterlocutors information obtained through conversation and public information obtained by isaboutand(2)thatpartoftheworldwhichtheycandirectlymanipulateand means of joint perceptual observations on the domain of conversation. In the observe. Ideally,thepartoftheworldthatcanbetalkedaboutandthepartthat DENKsystem,observationsonthedomainareexplicitlydealtwith. canbemanipulatedandobservedarethesame. Thisdoesnotmeanthatevery Thesetupwhichwehavedescribed—i.e.,twointerlocutorsandadomainof aspectofthedomainthatcanbetalkedaboutcanalsobeobserveddirectly. For conversation—maybecalledthegeneralizedDENKsituation.TheDENKarchi- instance,regularitiesintheworld(e.g.,everytimeevent occurs,event oc- tectureitselfwasconceivedofasanewparadigmforhuman-computerinteraction. cursaswell),canbetalkedabout,butarenotaccessiblevei(cid:0)adirectobservaeti(cid:2)on:a Takeasituationinwhichausercandirectlyinteractwithsomeapplication.Now, singleobservationcannotverifyastatementthatquantifiesuniversallyovertimes theDENKarchitectureisobtainedbyaddingacooperativeassistanttothissitu- (thoughitmayfalsifyit). ation. Thisassistant,whichisasoftwareagent,isabletoconversewiththeuser InDENK,thecontextisequatedwiththeconversationaldomain,therepre- abouttheapplicationanddirectlyinteractwiththeapplication. sentationsthattheinterlocutorsmaintainofthedomainandthestateofthecon- Theconnection withthegeneralized DENK situation isobvious: theinter- versation. Inadditiontowhatwecalltheconversationalstate,thiswidernotion locutorsaretheuserandthecooperativeassistantandthedomainofconversation ofcontextinvolvesthedomainofconversationandtherepresentationthateach correspondstotheapplication. FortheDENKprototype,theapplicationconsists interlocutorprivatelymaintainsofthisdomain.Whereastheconversationalstate ofthesimulationofanelectronmicroscope. Across-sectionofthemicroscope determinesthelegalmovesthatareavailabletoaninterlocutor,theremainingcon- anditscontrolpanelaregraphicallydisplayedtotheuser. Theusercandirectly textprovidestheinformationforchoosingaparticularmovefromtheavailableset manipulatethismicroscopeorengageinaconversationwiththecooperativeas- oflegalones. sistantabouttheapplication. ThelanguageoftheuserisafragmentofEnglish. Consider,forinstance,asituationinwhichinterlocutorAhasaskedBaques- Theassistanthandlesquestions,(indirect)requestsandassertions. Furthermore, tion. Inthatcase,theconversationalstatewillrequirethatBreactsinanappro- theassistantisabletodirectlymanipulatetheapplication(inresponsetorequests priatewaytothequestion,forinstance,byprovidingananswer.Furthermore,the fromtheuser)andobservethestateoftheapplication(inordertoanswerques- answershouldbecompatiblewiththeinformationthatisalreadypartofthecon- tionsfromtheuser). versationalstate(seechapters4and6fordetails). Inotherwords,alegalmove ThecooperativeassistantisimplementedinPROLOG.Itconsistsoffourmain byBmightconsistofananswerthatiscompatiblewiththeconversationalstate. modules: asyntacticanalyserwhichusesagrammarwhichiswritteninanex- WithintheseboundariesBstillhasalotoffreedomwithregardstodetermin- tensionofHPSG (Verlinden,forthcoming),asemanticinterpreter,whichbuilds (cid:5) ingtheactualanswer. SupposethatAasked‘Aretherestillanycookiesinthe upanunderspecifiedrepresentationofanutteranceandusescontextualinforma- cupboard’.‘Yes’,‘no’and‘Idonotknow’wouldbelegalresponsesbyB.Which tiontofillintheunderspecifiedparts(Kievit,forthcoming),adialoguemanager, ofthethreeistheactualanswermightbebasedonB’sprivateinformationabout whichcontrolstheinteractionprocess,anddeterminesthereactiononthebasis thedomainofconversation.Bmightchoosetoprovideananswerthatislicensed ofarepresentationofthecontext(seethereferencesattheendofthischapter), byB’sprivateinformation. Forinstance,ifBthinksthattherearecookiesinthe andfinallyamoduleforreasoningaboutthedomainandobservingit(seeAhn, xvii xviii forthcoming). mationalitemsareintroductionsoftheform .Now,whatinformationdoes anintroduction representtoanagent?VIn(cid:6)otTherwords,whatisthemeaning InformationandContext of totheVag(cid:6)enTt? Theanswerisstraightforward: theagenttakes to meVan(cid:6)(sTtandfortheinformation)thatthereissomeobjectofthetype .V (cid:6)T ThecooperativeassistantoftheDENKprojectmaintainsformalrepresentations Thisanswercanbedevelopedindifferentdirections. TheagentcTan(cid:6)consider ofthecontext. Theserepresentationsbelongtoaclassofformalsystemsknown the type to be part of a scheme ofclassication of reality, i.e., ‘the external asPureTypeSystems(PTS;Barendregt,1992). PTSisageneralizationoftyped world’. ITnthat case, means to the agent that there exists an object in lambdacalculus(Curry,1943;Church,1940). Inparticular,inDENKtheinfor- theexternalworldwhiVch(cid:6)fitTsthetype . Alternatively, theagentmightuse mationalcontentoftheconversationalstate,whichisdealtwithinthisbook,is toclassifyitsexperiences. Inthatcase,T wouldmeantotheagentthataTn modelledinPTS. experienceoftype occurred. V (cid:6) T Incidentally,theformalobjectsthatPTSprovidesformodellingconversational ThelatterapproTachhas,however,seriouslimitationswhenitcomestomod- statesarecalledcontexts. SuchaformalcontextinaPTSisasequenceofintro- ellingcommunicationbetweenagents. Whatwoulditmeanfortheinformation ductionsofobjects.Eachoftheseintroductionsisoftheform ,where is of tobetransferredfromoneagenttotheother? Sinceexperiencesare avariableand isthetypeofthevariable.Thevariable stanVds(cid:6)foTranarbitVrary privVate(cid:6)tTotheagents, willnevermeanthesamethingfortwodifferentagents. objectoftypeT.Therefore,wewilloftenspeakofthe(aVrbitrary)object . Inparticular,ifanageTntisconvincedthatthemeaningof residesstrictly APTSconTtextcontainsinformationinthefollowingsense: itrecordVswhich withitsownexperiences,thenitwillfinditimpossibletoVsha(cid:6)reTtheinformation typesareinhabited,i.e.,forwhichtypesthereareobjectsbelongingtothosetypes. associatedwith withothers,sincetheseexperiencesarealientotheothers. WecandologicinaPTSbecausepropositionscanbeseenastypes.Thisinsightis WeconcludeVth(cid:6)aTttheinformationthatisconveyedbyanintroduction knownasthepropositionastypesinterpretationoftypedlambdacalculus(Curry toanagent(i.e.,accordingtotheagent’ssubjectivepointofview)andthVatc(cid:6)aTn andFeys,1958). Propositionaltypesareinhabitedbyproofs. Inotherwords,if becommunicatedisobjectiveinnature;theinformationisaboutarealitythatis thecontextintroducesanobjectasbelongingtoaparticularproposition,thenthis externaltotheagent. Paradoxically,ifwelookatthemeaningofanintroduction objectshouldbeseenasstandingforaproofoftheproposition. fromaperspec(cid:7)tivethatisexternaltotheagent(i.e.,fromanobjectivepoint PTSencompassesruleswhichdescribehowtheobjectsandthetypesthatare Vof(cid:6)viTew),thentheinformationassociatedwith becomessubjective. Letus availableinacontextcanbeusedtoconstructnewobjectsandtypes. Consider explain. V (cid:6)T acontext containingtheintroductions and . Inwords,accord- Wemustaskthequestion,‘Howdoesanagentobtaininformationaboutthe ingtothe(cid:3)context thereisaproof forath(cid:6)eppropofsit(cid:6)iopn(cid:5)aqndaproof forthe world?’ormorespecifically‘Howdoesanagentacquiretheinformationthatthere proposition (cid:3). InlinewithHeyating’sconstructivistepxplanationoffimplica- existsanobjectofsometype ?Asobjectiveobserversoftheagent,wemaysee tion(Heytinpg,(cid:5)195q6),aprooffor correspondstoamethodforobtaining theagentinteractwiththeoutsTideworldandrecognizecertainobjectsasinstances proofsof fromproofsof . Intper(cid:5)msqofaPTS,thisistranslatedinto: aproof of . Thisabilitytorecognize inhabitants ofatypeisentirelypersonaltothe for qisafunctionfropmproofsof intoproofsof . Thus, canbeused ageTnt. Thus,fromanexternalpointofviewthemeaningof issubjective. tocpon(cid:5)struqctaproofof fromtheproofpof byapplyinqg to ;fweobtainthe Theagentitself,however,cannottakethisstandwithoutbecomVin(cid:6)gTasolipsist,i.e., proof (‘’standsfqorfunctionapplicaationp)of . Thenoftatioanfor‘ isa withoutdenyingthepossibilityofcommunicationwithotheragents. proofoff(cid:6)agiv(cid:6)encontext ’is: . q f(cid:6)a Wehaveused‘themeaningof ’and‘theinformationthat stands WehqaveseenthatPT(cid:3)Sallo(cid:3)w(cid:2)usft(cid:6)oad(cid:6)oqcalculationswithintroductions: infor- for’interchangeably. Inourview,Vm(cid:6)eaTningandinformation areonVe(cid:6)oTfakind. mationthatisimplicitinabodyofinformationcanbemadeexplicit.Letusnow Thereisnodirectrelationbetweenthisapproachtoinformationandthenotionof addressthequestion‘Inwhatsensedoesanintroduction representapiece informationthatisusedininformationtheory(Shannon,1948). ofinformation?’ Forthatpurpose,wehavetogobeyondVth(cid:6)eTboundariesofthe Informationtheoryisconcernedwiththetransmissionofmessagesfroman formalsystemofPTS. informationsourcetoadestination. Informationisthoughtofasachoiceofone Ourmainpremissisthatinformationdoesnotexistindependentlyofanagent messagefromasetofpossiblemessages, eachofwhichisassociatedwiththe towhomtheinformationismeaningful.Theformalobjectsforrepresentinginfor- xix xx

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Logic,. Information. &. Conversation c 1998 Paul Piwek. Printed by Print Partners Ipskamp, The Netherlands. Cover Design and Lay Out by Paul Piwek in LATEX
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