Abduction** Conversational*Implicature* and*misleading

Abduction** Conversational*Implicature* and*misleading Chiaki&Sakama&(WakayamaUniversity) Katsumi&Inoue&(Na2onalIns2tuteofInforma2cs) MBR2015

Abduction*in*Dialogue*(1) Mary:You relatethismorning,aren tyou? John:Thetrainsarenotrunningonschedule. FromtheresponsebyJohn,Marythinksthattherewassome accident. Inthisreasoning,Maryusestheimplica2on someaccidenthappens" trainsarenotrunning". MarybelievesJohnsuReranceandshehasnoreasonto believethenega2onof someaccidenthappens. ThenMaryabduces someaccidenthappens for anexplana2onof trainsarenotrunning".

Objective*Abduction Letabeahearerandbaspeaker.WhenbuRers a(proposi2onal)sentenceφ,a(proposi2onal)sentenceψis inferredbyobjec4ve&abduc4on&(o8abduc4on)fromφbyaif B a φ B a (ψ φ) B a ψ whereb a φmeansabelievesφ. ψiscalledano8explana4onofφ. WewriteOWabd a (φ,ψ)ifψisanowexplana2onofφbya. Itiscalled``objec2ve"abduc2onbecauseabduc2onis performedbasedontheobjec2vefactofanurerance.

Abduction*in*Dialogue*(2) Mother:Whatareyoudoing? Daughter:Imwri2ngaleRertoSantaClaus. Fromtheresponsebyherdaughter,motherthinksthather daughterbelievestheexistenceofsantaclaus. Motherbelievesthatherdaughterbelievestheimplica2on SantaClausexists" ShecanwritealeRertohim". Motherbelievesthatherdaughterbelievesthatshecanwrite alerertosantaclaus. Motherhasnoreasontobelievethatherdaughterdisbelieves theexistenceofsantaclaus. Thenmotherabduces herdaughterbelievestheexistenceof SantaClaus.

Subjective*Abduction Letabeahearerandbaspeaker.WhenbuRers a(proposi2onal)sentenceφ,a(proposi2onal)sentenceb b ψ isinferredbysubjec4ve&abduc4on&(s8abduc4on)fromφbya if B a B b φ B a B b (ψ φ) B a B b ψ B b ψiscalledans8explana4onofφ. WewriteSWabd ab (φ,ψ)ifb b ψisanswexplana2onofφbya. Itiscalled``subjec2ve"abduc2onbecauseabduc2onis performedbasedonthehearerssubjec2veviewonthe speakersbeliefstate.

O8abduction*vs.*S8abduction a:ahearer,b:speaker,φ:urerance OWabduc2oninfersψifB a φ B a (ψ φ) B a ψ SWabduc2oninfersB b ψifb a B b φ B a B b (ψ φ) B a B b ψ InOWabduc2on,aheareramaybelieveanOWexplana2onψ whichaccountsforanureranceφbyaspeaker. InSWabduc2on,aheareramaybelievean SWexplana2onB b ψbutdoesnotnecessarilybelieveψby himself/herself.

O8abduction*vs.*S8abduction SupposeaspeakerbuRershis/herbeliefB b φ. ThenahearerainfersB b ψbyowabd a (B b φ,b b ψ) B a B b φ B a (B b ψ B b φ) B a B b ψ Itshouldbedis2nguishedfromSWabd ab (φ,ψ)whichinferb b ψby B a B b φ B a B b (ψ φ) B a B b ψ SinceB b (ψ φ)implies(b b ψ B b φ), SWabd ab (φ,ψ)impliesowabd a (B b φ,b b ψ) Wecanalsoconsideranotherabduc2onOWabd a (φ,b b ψ)as B a φ B a (B b ψ φ) B a B b ψ

Different*Types*of** Abduction*in*Dialogue O8abduc4onS8abduc4on& a:&hearer& φ ψ φφb b:&speaker b (ψ φ) ψb b ψ φ:ureranceφ:urerance ψ φ:hearera sbeliefb b (ψ φ):hearera sbelief ψ:hearera sexplana2onb b ψ:hearera sexplana2on imply O8abduc4on&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&O8abduc4on& B b φb b ψ B b φφb b ψ φ B b ψb b ψ B b φ:ureranceφ:urerance B b ψ B b φ:hearera sbeliefb b ψ φ:hearera sbelief B b ψ:hearera sexplana2onb b ψ:hearera sexplana2on

Conversational*Implicature*(CI) Apragma2cinferencetoanimplicitmeaningofasentence thatisnotactuallyureredbyaspeaker(grice1975). Twoprinciplesfromthespeaker sviewpoints: WQ8principle:Sayasmuchasyoucan. WI8principle:Saynomorethanyoumust. Twoprinciplesfromthehearer sviewpoints: WQ8implicature:Implythenega2onofaseman2callystronger sentencethanwhatisactuallyurered. WI8implicature:Implyaseman2callystronger(ormorespecific) sentencethanwhatisactuallyurered. Twoimplicaturesconflictintheirinterpreta2ons.

Examples ``Ihavetwochildren"QWimplicates ``Idonothavemorethantwochildren. ``Someofmyfriendslikeclassicalmusic"QWimplicates ``Notallofmyfriendslikeclassicalmusic. ``IwillstudyFrenchorGermanyintheclass"QWimplicates ``IwillnotstudybothFrenchandGermanyintheclass. ``Ihavetwodollarstopaythebill"IWimplicates ``Ihaveatleast&twodollarstopaythebill. ``Wellgoonapicnicifitisfinetomorrow"IWimplicates ``Wellgoonapicnicifandonlyif&itisfinetomorrow. ``JohncametotheofficeandheturnsonthePC"IWimplicates ``Johncametotheofficeandhe,John,turnsonthePC."

ConElicts*between*Abduction,** Q8implicature*and*I8implicature O8abduc4onS8abduc4on& a:&hearer& φ ψ φφb b:&speaker b (ψ φ) ψb b ψ φ:ureranceφ:urerance ψ φ:hearera sbeliefb b (ψ φ):hearera sbelief ψ:hearera sexplana2onb b ψ:hearera sexplana2on Q8implicatureI8implicature& φ B b (ψ φ)φb b (ψ φ) B b ψb b ψ φ:ureranceφ:urerance B b (ψ φ):hearera sbeliefb b (ψ φ):hearera sbelief B b ψ:hearera sinterpreta2onb b ψ:hearera sinterpreta2on

Q8*and*I8implicatures Letabeahearerandbaspeaker.WhenbuRers a(proposi2onal)sentenceφ,a(proposi2onal)sentence B b ψisinferredbyq8implicaturefromφbyaif B a B b φ C(ψ φ) B a B b ψ Ontheotherhand,a(proposi2onal)sentence B b ψisinferredbyi8implicaturefromφbyaif B a B b φ C(ψ φ) B a B b ψ C(ψ φ)meansthatψ φiscommon&knowledgethatis sharedbythespeakerandthehearer. WewriteQWimp ab (φ,ψ)(resp.iwimp ab (φ,ψ))ifb b ψ(resp. B b ψ)isinferredbyqw(resp.iw)implicaturefromφbya.

Why*common*knowledge*in*CI? Conversa2onalimplicatureisbasedoncommon&knowledge, i.e.,bothaspeakerandahearerknowthetruthofthe implica2onψ φandeachonealsoknowsthattheother partyknowsthetruthofthesentence. Ifthehearerdoesnotknowwhetherornotthespeaker knowstheimplica2on,thenthehearercannotinferthe intendedmeaningofthespeakersurerance. Ifthespeakerdoesnotknowwhetherornotthehearer knowstheimplica2on,thenthespeakercannotexpectthe hearersreasoningbyq/iwimplicature. Thusconversa2onalimplicatureisineffectifandonlyifa speakerandahearersharethesameknowledgeandeachone knowsthattheotherpartyalsosharesthesameknowledge.

Abduction**vs.*CI*(1) Bothabduc2onandCIuseanimplica2onψ φtoinfer informa2onbehindanurerance.inabduc2on,theimplica2on isahearersprivate&belief,whileinciitiscommon&knowledge. Abduc2onisaprocessofprivatereasoning,andonecanreason abduc2velywithoutknowingthebeliefstateoftheotherparty. Bycontrast,conversa2onaimsatcommunica2nginforma2on. Since Cφ B a φ and Cφ B a B b φ,onemayusecommon knowledgeforthepurposeofabduc2on,butnotviceversa.

Abduction**vs.*CI*(2)* a:ahearer,b:speaker,φ:urerance IWimp ab (φ,ψ):inferb b ψfromb a B b φ C(ψ φ) B a B b ψ SWabd ab (φ,ψ):inferb b ψfromb a B b φ B a B b (ψ φ) B a B b ψ SinceC(ψ φ)impliesb a B b (ψ φ), IWimp ab (φ,ψ)impliesswabd ab (φ,ψ). QWimp ab (φ,ψ):inferb b ψfromb a B b φ C(ψ φ) B a B b ψ SWabd ab (φ,ψ):inferb b ψfromb a B b φ B a B b (ψ φ) B a B b ψ WhenB a B b φ C(ψ φ), ahearermayconcludeb b ψbyswabduc2onif B a B b ψ;while ahearermayconcludeb b ψbyqwimplicatureif B a B b ψ.

ConElicts*between*Abduction,** Q8implicature*and*I8implicature O8abduc4onS8abduc4on& a:&hearer& φ ψ φφb b:&speaker b (ψ φ) ψb b ψ φ:ureranceφ:urerance ψ φ:hearera sbeliefb b (ψ φ):hearera sbelief ψ:hearera sexplana2onb b ψ:hearera sexplana2on imply Q8implicatureI8implicature& φ C(ψ φ)φc(ψ φ) B b ψb b ψ φ:ureranceφ:urerance C(ψ φ):commonknowledgec(ψ φ):commonknowledge B b ψ:hearera sinterpreta2onb b ψ:hearera sinterpreta2on

What*happens*if*a*hearer*does*not* believe*an*utterance? SupposetheTuringsimita2ongameinwhichahumanjudge asksques2onstoaninterlocutorinordertodetermine whetherheorsheisinterac2ngwithahumanoramachine. Judge(a):Areyouamachine? Interlocutor(b):I mahuman. Supposethatthejudgebelievestheimplica2on: machine human (Theinterlocutorishumanifhe/sheisnotamachine.) Giventheresponse``human"bytheinterlocutor,willthe judgebelievethattheinterlocutorisnotamachine(by OWabduc2on)?

What*happens*if*a*hearer*does*not* believe*an*utterance? IntheTuringimita2ongame,amachineaRemptstoconvincea judgethatitishumanthroughappropriate,andojen decep4veresponses. Intheabovedialogue,ifthejudgedisbelievestheuReranceφ bytheinterlocutor,then B a φholdstherebyowabd a (φ,ψ) B a φ B a (ψ φ) B a ψ whereφ=human,ψ= machine isnotappliedandthejudgedoesnotabduceψ= machine.

What*happens*if*a*hearer*believes* the*falsity*of*an*utterance? Supposethesamedialogue Judge(a):Areyouamachine? Interlocutor(b):I mahuman. andthejudgebelieves machine humanasbefore. TheinterlocutoruRersφ=human,butthejudgebelievesthe contrary φ. Inthiscase,itholdsthatB a φ B a (ψ φ) B a ψ andthejudgebelieves ψ=machine.

What*happens*if*a*hearer*believes* that*a*speaker*is*lying? Dialogue: Judge(a):Areyouamachine? Interlocutor(b):I mahuman. Thejudgebelievesthattheinterlocutorbelievesthe implica2onψ φ=( machine human)andthejudgealso believesthattheinterlocutorislying,i.e.,thejudgebelieves thattheinterlocutorbelievesthefalsityofhis/herurerance φ=human. Inthiscase,itholdsthat B a B b φ B a B b (ψ φ) B a B b ψ thenthejudgeabelievesthattheinterlocutorbelieves ψ=machine.

Misleading Aspeakermaybelievethatahearerwouldabduceψasa resultofthespeakersureranceφ. Considerthedialogue. Judge(a):Areyouamachine? Interlocutor(b):ShallIsingasong? Theinterlocutor(whoisinfactahuman)expectsthathis/her responsewouldmakethejudgeabducethefact``human" basedonhis/herbeliefthatthejudgebelievestheimplica2on ``human sing". Thusaspeakerwilldecidewhattosaybyconsideringthe effectofhis/herureranceonthehearersside. Aspeakermayusethistomisleadahearertoreachawrong assump2on.

Misleading*by*O8abduction WhenaspeakerbuRersasentenceφtoahearera, bmisleadsaby&o8abduc4onif B b (B a φ B a (ψ φ) B a ψ) B b ψ WewriteOWmislead ba (φ,ψ)ifb sureranceφmisleadsato abduceanowexplana2onψ. Theaboveformulasaysthataspeakerbbelievesthathis/her urerancewouldleadaheareratoanassump2onψby OWabduc2on,however,bbelieves ψ. Aspeakermayuseaweakerversionofmisleadingby replacingb b ψwith B b ψ.

Misleading*by*O8abduction Dialogue: Judge(a):Areyouamachine? Interlocutor(b):I mahuman. Theinterlocutor(whoisinfactamachine)believesthatthe judgeabelievestheresponseφ=humanbyb. Theinterlocutoralsobelievesthat: thejudgebelievestheimplica2on machine human whiledisbelieves ψ=machine. Iftheinterlocutorbelievesthatitisamachine ψ=machine, theinterlocutormisleadsthejudgebytheresponse φ=human.

AspeakersuRerancewillchangedependingonhis/herbeliefthat whetherahearerbelievesthespeakersureranceornot. Supposethattheinterlocutorisamachineanditconsidersthatthe judgewilldoubtitsresponse.inthissitua2on,considerthedialogue Judge(a):Areyouamachine Interlocutor(b):Yes,I mamachine. IfthejudgebelievesthefalsityoftheuRerance,he/sheinterpretsthe contraryoftheresponseandconcludestheinterlocutorisahuman. B a machine B a ( machine human) B a human However,thisiswhattheinterlocutorhasintended.Inthiscase,the interlocutorreasonsbytheformula: B b B a machine B b B a ( human machine) B b B a human. Theinterlocutorbbelievesthatthejudgeabelievesthecontraryof theurerancemachine,expec2ngthatthejudgereachesthewrong conclusionhumanusingtheimplica2on human machine.

Misleading*by*S8abduction WhenaspeakerbuRersasentenceφtoahearera, bmisleadsaby&s8abduc4onif B b (B a B b φ B a B b (ψ φ) B a B b ψ) B b B b ψ WewriteSWmislead ba (φ,ψ)ifb sureranceφmisleadsato abduceanswexplana2onb b ψ. Theaboveformulasaysthataspeakerbbelievesthathis/her urerancewouldleadaheareratoanassump2onb b ψby SWabduc2on,however,bbelieves B b ψ. SWmislead ba (φ,ψ)impliesowmislead ba (B b φ,b b ψ).

Misleading*by*telling*the*truth AspeakermayuRerwhathe/shebelievestruewhile expec2ngahearerwillmakeanincorrectabduc2on. Whenaninterlocutorisamachine,supposethedialogue Judge(a):Areyouamachine? Interlocutor(b):Iojenmakeerrors. Theinterlocutorexpectsthatthejudgewillconsiderita humanbytheimplica2onhuman error. However,theinterlocutor(machine)infactojenmakes calcula2onerrorsbyprogrammingbugs,soittellsthetruth. Suchaspeechactisojensaid``indirect&lies"or``lying&while& saying&the&truth.

Misleading*by*Q8implicature Dialogue: Mother(a):Howwasyourmathexam? Son(b):Icouldnotsolveoneques2on. UsingQWimplicature,motherbelievesthathersonworkedout otherques2ons,excepttheonethatcouldnotbesolved. However,thisiswhatthesonhasintended.Infact,hebelieves thathecouldnotsolvemorethanoneques2on. Sincehebelievesthathecouldnotsolvemorethanone ques2on,healsobelievesthathecouldnotsolveoneques2on. HethenuReredhisweakerbeliefinresponsetoherques2on. Ontheotherhand,motherbelievesthathisuRerancemust meanthathedoesnothavefailedmorethanoneques2on.

Misleading*by*CI WhenaspeakerbuRersasentenceφtoahearera, bmisleadsaby&q8implicatureif B b (B a B b φ C(ψ φ) B a B b ψ) B b ψ AspeakerbbelievesthattheuReranceφleadsahearerato concludethenega2onofastrongersentence ψby QWimplicature,whilebbelievesψ. Likewise,bmisleadsaby&I8implicatureif B b (B a B b φ C(ψ φ) B a B b ψ) B b ψ AspeakerbbelievesthattheuReranceφleadsahearerato concludeaweakersentenceψbyiwimplicature,while bdisbelievesψ.

Abduction*vs.*CI*in*Misleading Misleadingbyconversa2onalimplicaturemayfailifaspeaker believesthatahearerusesqwimplicature(resp.iwimplicature) butinfactthehearerusesiwimplicature(resp.qwimplicature). Whenaspeakerbdisbelievesasentenceψ,he/shewould havetwoop2onsformisleadingaheareratobelieveb b ψ. OneisuReringφunderthecondi2onthatthereiscommon knowledgec(ψ φ)andthespeakerbelievesthatthehearer usesiwimplicature(i.e.,misleadingbyiwimplicature). TheotherisuReringφunderthecondi2onthatthespeaker believesb b (ψ φ)andthatthespeakerbelievesthatthe hearerusesswabduc2on.(i.e.,misleadingbyswabduc2on).

Final*Remark Twodifferenttypesofabduc2onandtwodifferent conversa2onalimplicatures(cis)areformulatedusing proposi2onalmodallogic. Abduc2onusesprivatebeliefofareasoner,whileCIrelieson commonknowledgebetweenpar2cipantsinaconversa2on. Wealsoarguedhowaspeakerwouldmisleadahearerin conversa2on. Theframeworkissimplebutcapableofcapturingdifferent aspectsofabduc2onandciinhumandialogues,thathavenot beenthoroughlyinves2gatedintheliterature.