A computational model of misunderstandings inagent communication?Liliana Ardissono, Guido Boella and Rossana DamianoDipartimento di Informatica - Universit�a di TorinoCorso Svizzera n.185 - 10149 Torino - ItalyE-mail: fliliana, guidog@di.unito.itFax: +39-11-751603; Phone: +39-11-7429111Abstract. In this paper, we describe a plan-based model for the treat-ment of misunderstandings in NL cooperative dialogue: an utterance isconsidered coherent if it is related to some of the interactants' intentionsby a relation of goal adherence, goal adoption or plan continuation. Ifnone of them is fully satis�ed, a misunderstanding is hypothesized andthe goal of realigning the interactants' interpretation of the dialogue isadopted by the agent detecting the problem. This goal makes the agentrestructure his own contextual interpretation, or induce his partner todo that, according to who made the mistake.1 IntroductionWe describe a plan-based model of misunderstandings within an agent architec-ture supporting cooperative NL communication. In a dialogue, a misunderstand-ing occurs when an interactant chooses an interpretation for some turn whichis complete and coherent from his point of view, but it is not the one intendedby the speaker [21]. A wrong interpretation of one or more turns can cause amisalignment of the speakers' dialogue contexts, with the eventual productionof a turn perceived as incoherent by its hearer. At this point, however, eitherthe speaker or the hearer might have constructed separately an erroneous dia-logue context, so it is necessary to exploit the incoherent turn to identify theresponsible for the mistake.We model the treatment of misunderstandings as a goal-directed, rationalbehavior: our notion of coherence in communication is based on the idea that thegoals identi�ed when interpreting a turn have to be related with the previouslyexpressed or inferred goals of the interactants [2, 8]. When an agent receives anincoherent turn (or a turn which only partially matches his expectations), headopts the further goal of realigning the interactants' diverging interpretations.To do so, he reasons to understand which agent misunderstood the other one;then, he can restructure his own interpretation, or make the partner restructure? We are indebted to Prof. Leonardo Lesmo and Prof. Carla Bazzanella for their fruitfuldiscussions and hints to our work. This work has been supported by MURST andCNR, project \Piani�cazione e Riconoscimento di Piani nella Comunicazione".

his accordingly. Repair turns are explained as cooperative subdialogues aimedat restoring the common interpretation ground; in fact, the maintenance of acorrect dialogue context is a mutual goal of the interactants [10].Incoherent turns are not always due to misinterpretations: also topic shiftsand breakdowns in cooperation should be considered. Currently, we don't modeltopic shifts due to the initiation of new dialogues; however, as pointed out bymany researchers [11, 17, 18], focus and topic shifts are usually marked by thepresence of \cue" words. On the contrary, since we model cooperative dialogues,we exclude the hypothesis that a breakdown in communication can occur.2 BackgroundScheglo� [24, 25] has analized misunderstandings with respect to the sequencesof turns of a dialogue, in order to identify the mechanisms used by the interac-tants to defend the \intersubjectivity", i.e. the common set of beliefs necessaryfor an interaction to continue successfully. He points out that speakers moni-tor their partners' reactions and interpret them as displays of understanding /misunderstanding of the previous turns. [25] identi�es di�erent repairs to misun-derstandings, according to their position in the dialogue and whether the agentperforming them is correcting himself, or his partner.In particular, in \third position repair", the misunderstood agent realizes thatthe partner has a wrong interpretation and urges him to restructure it:Example1 (translated from [14]):T0: B: \Hello. I'd like to have an English book [...] for the American school.Is there a 10% discount?"T1: A: \Do you have the enrollment card?"T2: B: \Yes, I have it."T3: A: \No, you should show me your card."T4: B: \Oh I understand."Independently from the actual turn position, this corresponds to a repairaccomplished by the misunderstood speaker in one of his own subsequent turns,i.e. a \self-repair".Instead, in \fourth position repair", a speaker A realizes that he has misunder-stood a turn T1 uttered by his partner only after having replied to it (T2) andhaving received back a turn T3 incoherent with respect to T1 and T2 (T3 iscoherent with the partner's intended interpretation of T1). Typically, after hav-ing corrected his interpretation, A performs another type of repair, telling thepartner that he has understood what he initially meant:Example2 (from [25]):T1: Marty: \Loes, do you have a calendar,"T2: Loes: \Yeah" ((reaches for her desk calendar))T3: Marty: \Do you have one that hangs on the wall?"T4: Loes: \Oh, you want one."

T5: Marty: \Yeah"Since these repairs are typically accomplished by the interlocutor who hasmisunderstood in one of his turns, these turns are called \other-repairs", referringto the agent they belong to.3 Our agent modelThe work presented in this paper extends our agent model to enable it to copewith misunderstandings in NL communication. Our agent architecture has atwo-level plan-based representation of the knowledge about acting [4, 5]. At themetalevel, the Agent Modeling (AM) plan library describes the (precompiled)problem-solving recipes used by an agent to choose the actions for reaching hisgoals, and to execute them; at the object level, the Domain library describesrecipes for obtaining domain goals (such as buying a book, see Example1), andthe Speech Act Library describes the direct and indirect speech-acts [3]. Thethree libraries are composed of a Generalization Hierarchy and a DecompositionHierarchy [16] and share the same representation formalism.The AM actions take domain actions and speech-acts as objects: an agentperforming a problem-solving activity can plan to perform domain and linguisticactions. In the AM actions, one parameter (source) denotes the bene�ciary ofthe action that the modeled agent is performing: usually, source is bound tothe agent of the AM action itself; however, it can be used to model cooperationbetween agents. There are two major actions in the AM library:{ \Satisfy(agt, source, g)" describes the behavior of an agent agt, who wantsto satisfy a goal g; its body consists of looking for a feasible plan for gand executing it. If no feasible plan is found, the decomposition of \Satisfy"includes the noti�cation to the source agent that the goal cannot be reached(see the notion of Joint Intention in agent cooperation [10]).{ \Try-execute(agt, source, action)" describes the execution of actions; it in-cludes checking the preconditions of action and performing it (possibly ex-panding its decomposition, if it is complex). The decomposition of \Try-execute" also describes acknowledgements in agent cooperation: after a suc-cessful execution of action, if agt is collaborating with another source agent,he has to inform him that the action has succeeded; on the contrary, if theaction could not be executed, he has to inform him of the problem.The agent's behavior is ruled by an interpreter which loops on three phases,each one performed by means of a call to a \Satisfy" action: interpretation ofthe input (P1), decision of which goal to commit to (P2), and reaction (P3,where the agent acts to reach the chosen goal). The plan-based representationof knowledge supports a declarative representation style, that can be used bothfor interpreting and generating the agent behavior. A basic assumption of therecognition task is that all agents have equal plan libraries (on the contrary, wedon't assume that agents have equal beliefs about the world state).

The agent interprets a dialogue incrementally: for each turn, he builds thesemantic representation of the input sentence [6], �nds the goal which the sen-tence is aiming at, and relates it with the dialogue context. The interpretation ofeach turn consists of a Context Model (CM), which contains the problem-solvingactions (AM) referring to the linguistic (SAM) and domain-level (DM) actionsobserved (or performed) by the agent: the AM actions explain the reasons forperforming the object-level actions. The local CM built during the interpretationof each turn is embedded into the dialogue context by identifying how the sen-tence contributes to the previous interaction: the context contains the sequenceof interpretations (CMs) of the turns (properly interleaved), together with therelations existing among them, as explained in the following section.4 Coherence and misunderstandingsWe consider a new contribution coherent if a relation exists among the intentionsunderlying it and the previous pending intentions of the interactants, eitherexpressed explicitly, or inferred by reasoning on their plans [9]. An utterance iscoherent with the previous context if its receiver A can interpret it as a meansof the speaker B to achieve a goal g such that:1. Goal adherence: g is one of the goals previously expressed by A.2. Goal adoption: g is one of the goals that B has inferred A is going to aimat; e.g. in:T1: A: \I need a book. Where is the library?"T2: B: \It is over there, but it is closed."B provides A with an extra-helpful information which satis�es his next goalof checking whether the library is open [2].3. Plan continuation: g contributes to a plan that B is carrying on.2 E.g:T1 B: \Where is the library?"T2 A: \It's over there."T3 B: \Is it open today?"Goal adherence and adoption refer to a complete satisfaction of the hearer'spending intentions. So, when the partner satis�es only some of the goals thatthe hearer expects him to obtain, although a partial match exists, the analyzedturn is not considered coherent with the previous part of the interaction.32 We assume that an agent continues the execution of his plans only when there aren'tother goals of the partner to be achieved.3 Actually, it is not necessary to satisfy all the pending goals separately. In a CM, somegoals strictly depend upon other ones, at a higher level. In that case, the satisfactionof the latter makes the former irrelevant, so that they can be considered as \closed".For example, if somebody asks a question, he expects that his partner acknowledgesin some way the fact that he has understood the utterance. However, if the partneranswers the question directly, this satis�es all the pending expectations and no otheracknowledgement is required in order to be coherent.

Uncooperative replies (e.g. refusals) and subdialogues for solving interpreta-tion problems are other types of coherent contributions. Although in this paperwe do not take these phenomena into account, they have to be explained asrelated with some speaker's goal as well: respectively, the goal to know whetherthe hearer intends to cooperate, and that the hearer interprets the utterance.The interpretation phase (P1) is performed by means of an elementary \Build-interpretation" action. Consider the basic interpretation of an input turn by itshearer A: \Do(B, Utterance-act(B, A, \input-utterance"))".4 As the result of asuccessful execution of \Build-interpretation", the agent A has a new dialoguecontext where the last turn is related with the previous context by one of thethree relations described above. In principle, the previous context can be:- void (e.g. at the beginning of a dialogue);- composed of an elementary uninterpreted CM, simply containing the executionof an utterance act (\Do(agt, Utterance-act(...))");- a complex context, composed of the interpretations of the previous turns, prop-erly linked by coherence relations.The process of executing \Build-interpretation" is composed of a local and aglobal interpretation phase. In the description of these phases, we will representthe uninterpreted turns of the form \Do(agt, Utterance-act(...))" with the no-tation ti. On the contrary, we will use the notation Ti to represent in a genericway either an uninterpreted turn or its local interpretation.1. The local turn interpretation phase is called \upward-expansion", becauseit consists of an expansion of a CM along a path up in the plan libraries.In this phase, the possible (metalevel and object level) plan leading B tothe execution of the turn is looked for, and the agent's current goals areidenti�ed.2. In the global interpretation phase, the newly identi�ed goals and their high-level plans are related with the participants' goals pending from the previousdialogue context. This is done by means of the \matching" and \focusing"functions, which model two di�erent relations among turns:{ The \matching procedure" succeeds when the top-level goal, recognizedin the local interpretation phase as the reason for B's last turn Tn,corresponds to one of the (unsatis�ed) goals ascribable to A. This goalhas been expressed by A (see the notion of goal adherence above), or Bcan have inferred it during the interpretation of A's previous turns (goaladoption).{ The \focusing procedure" succeeds when B's turn Ti is the continuationof an AM plan performed by B (and previously identi�ed by A).5In practice, these two phases are carried on together by a number of heuristicrules we have de�ned. The rules exploit the speaker and hearer's contextual4 In the CM, \input-utterance" is a string of characters.5 The continuation of an AM plan can correspond to the continuation of a domain ora communicative action [19].

Restructure �name: Restructureroles: ((agent x)(partner y)(turns [t1, . . . ,tn]) (old-inter ctx)(intended-inter ctxj))var-types: ((person x y)(turn t1 . . . tn)(context ctx ctx0 ctxj))e�: inter(x, [t1, . . . ,tj ], ctxj)constr: inter(x, [t1, . . . ,tn], ctx) ^ inter(y, [t1, . . . ,tn], ctx0) ^correct-subcontext(ctxj,ctx,ctx0) ^ agent(y,ctxj[j])Fig. 1. The \Restructure" action.pending goals to guide the interpretation of the new contribution toward thesegoals, by pruning the non promising directions. The rules look for the paths inthe plan library relating an object-level action (underlying the input utterance)with the object-level plan built in the interpretation of the previous turns. Sincea rule searches for the shortest path linking the last turn to the previous context,\Build-interpretation" provides at each call a di�erent result, with a progressivedegree of complexity.The hypothesis that a misunderstanding among the agents has occurredarises in the following situation: if, during the interpretation of an utterance,the \matching" and \focusing" procedures fail,6 no relation is established be-tween the turn and the dialogue context. In this case, the interpretation phasereturns a context where the last turn remains unrelated. In principle, two hy-potheses are possible: a focus shift has occurred or the cooperation between thespeakers has broken down. If neither hypothesis is feasible, the lack of coherencecan be interpreted as a display that a misunderstanding has occurred.In this case, the agent (A) commits to the goal of realigning the interactants'subjective views of the dialogue; this is done by the execution of a \Satisfy"action on the goal that A's interpretation of the dialogue is the same as B's:(i) Satisfy(A, B, (inter(A, [t1, . . . , tj ], ctxj) ^ inter(B, [t1, . . . , tj ], ctxj)))The variables j and ctxj occurring in the third argument of the \Satisfy" actionare intended to be existentially quanti�ed. The meaning of the complex formulacontaining them is that agents A and B have two equivalent interpretation con-texts (ctxj) for the part of the dialogue from turn t1 to tj . Although j and ctxjare unbound when the \Satisfy" action is started by the agent, at the end of itsexecution they are bound respectively to the �rst turn which was misunderstoodand to the correct interpretation context of subdialogue [t1, ..., tj ].The execution of (i) starts with a planning activity, where A identi�es the actionwhich has a change of dialogue interpretation in its e�ects: \Restructure" (shownin Figure 1).76 I.e. although the utterance is interpretable, at least, as a speech act, there is nointerpretation of it such that the procedures above can �nd a contextual pendinggoal to which the turn can be related.7 The \Satisfy" action does not manage complex goals in a general way. It can howeversatisfy separately the subgoals of a conjunctive goal. In this particular formula, thisis enough, because after the instantiation of \Restructure", variable ctxj is bound

Reinterpret(agt, [T1, . . . , Tn], ctx) �begin i := n - 1; LC := ;; RestC := ;;while ( i > 0 ^ empty(LC)) dobegin LC := Build-interpretation(agt, Ti, Tn, ctx);if empty(LC) then i := i - 1else begin RestC := Reinterpret(agt, [T1, . . . , LC[1]], ctx);if RestC thenbegin j := i + 1;while ( j < n ) dobeginRestC := Build-interpretation(agt, RestC, Tj , ctx);j = j + 1;end;if empty(RestC) then LC := ; /*Try another local ctx*/endelse LC := ; /*Try another local context*/endend;return(RestC) /* Return the reinterpreted context */end. Fig. 2. The \Reinterpret" algorithm.In order to perform the \Restructure" action, its constraint must be true. Theconstraint of \Restructure" requires that:- The agent x (who has to perform the action to correct his wrong interpreta-tion) has an interpretation ctx of the whole dialogue, up to the last turn tn.- An alternative interpretation ctx0 of the dialogue can be attributed to x's part-ner y.- ctxj is the coherent interpretation of the misunderstood speaker, up to themisinterpreted turn tj (j < n).- The agent y corresponds to the speaker of the �rst turn that has been inter-preted di�erently in ctx and ctx0 (i.e. the last turn of ctxj , denoted as ctxj [j] inFigure 1).In order to evaluate this constraints, the agent A must determine B's inter-pretation context ctx0, alternative to A's one (ctx). He does this by executing a\Satisfy(A, B, Knowref(A, ctx0, inter(B, [t1, . . . , tn], ctx0))".The \Knowref(...)" goal is obtained by executing an action corresponding to the\Reinterpret" algorithm described below.If, after the execution of \Reinterpret", the �rst turn for which ctx and ctx0di�er has been uttered by A, then he has to persuade B to restructure his dia-logue context, by means of a linguistic repair. Otherwise, A executes \Restruc-to the interpretation subcontext of one of the two speakers; so, it is not necessary tosatisfy both the subgoals.

ture", changing his own interpretation to ctxj (see the e�ect of \Restructure");after that, they can continue the interaction from the reestablished interpreta-tion context. In both cases, the recovery goal is shared among the speakers; wheneverything ends up well, the agent informs the partner about the success of theiraims (see turns T4 in Example 1 and 2); otherwise, if no reconstruction is feasi-ble, the agent warns his partner that the intersubjectivity cannot be recovered(as the last step of \Satisfy" prescribes).We now describe the reinterpretation algorithm \Reinterpret", shown in Fig-ure 2. The algorithm traces back the dialogue, turn after turn, and looks for arelation between the problematic turn Tn and some previous (misinterpreted)turn. \Reinterpret" has the following arguments: the agent (agt), a sequence ofturns ([T1, . . . , Tn]) and the old context ctx (the agent's wrong interpretationof the dialogue). It tries to relate Tn to the alternative interpretations of a pre-vious turn, in order to constrain the search for the correct interpretation of thedialogue and improve this search, with respect to a blind form of backtracking.It is worth noting that the agent executing the algorithm must consider thealternative interpretations of his own turns, beside those of the partner's turns.When \Reinterpret" is called on a list of uninterpreted turns [t1, ..., tn],it goes backward from the problematic last turn tn, towards the beginning ofthe dialogue. It stops when it �nds the most recent turn ti for which \Build-interpretation" has found a new interpretation, coherent with tn.8 Then, \Rein-terpret" propagates the new interpretation LC (Local Context) to the wholecontext, using the interpretation Ti of ti in LC (which corresponds to the �rstcomponent of this context, denoted by LC[1]) as a \pivot", backward by callingitself recursively, and forward by means of a loop of \Build-interpretation" onthe remaining turns.5 ExampleWe now sketch how our model works on Example1; Figure 3 shows the intendedinterpretation of the clerk's (A) turns.9In order to sell a book with a discount as requested by B, A must checkwhetherB has the enrollment card (action \Satisfy(A, B, Knowif(have(B, Card)))"in AM1). Cautiously, he decides to obtain that goal by making B show him thiscard. He has to request B to show him the card, but he adopts an indirect strat-egy to suggest B that he wants to see her card: in T1, he asks her whether \shehas" the card (a precondition of action \Show").108 Although \Build-interpretation" takes in input a context and a turn, there is nocontradiction here, because a single turn is by itself an elementary context.9 The �gure represents the Agent Modeling plans and the object level actions, linkedby means of arcs.10 Although AM1 contains two equal occurrences of the \Satisfy" action, they do notlead to any loop. In fact, we constrain the search strategy in the AM library not toselect any object-level action that the agent is already carrying on. In our example,

Get-to-do(A,B, )

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Fig. 3. Intended interpretation of the clerk's (A) turns in Example1.In T2, B answers positively to the question; this is interpreted by A as a\Satisfy(B, A, done(B, Inform-if(B, A, have(B, Card))))", not shown in the�gure.However, T2 alone is not a coherent reply to T1, because it leaves unsat-is�ed A's implicit expectation that B shows him the card. This expectationcorresponds to the formula \SH(A, B, Cint(A,B, Goal(A, done(B, Show(B, A,Card)))))11 which is the e�ect of A's request (in SAM1). So, A hypothesizesthat a misunderstanding has occurred and commits to realigning the two in-terpretations, by performing action \Satisfy(A, B, inter(A, [t1,. . . ,tj ], ctxj) ^inter(B,[t1,. . . ,tj ],ctxj))".12 A selects the \Restructure" action for obtaining histhe lower-level \Satisfy" for discovering the value of the constraint cannot be solvedby another \Show" action.11 In the formula, the SH modal operator represents mutual beliefs; the Cint modaloperator, instead, represents communicative intentions, as de�ned in [1]. Finally,Done maps an action on the (world) state where the action has been successfullyexecuted.12 In this case, the dialogue [t1,. . . ,tj ] reduces to T1, since j < n and n = 2: see AM2

goal, because the e�ect \inter(x, [. . . ], ctx)" matches the goal to be obtained (itcan be used to change interpretation context).As described in the AM library, before executing an action, its constraintsmust be evaluated.13 So, A performs a \Satisfy" action (not reported in the�gure) to know if the constraints of \Restructure" are true. This leads A to �ndan alternative interpretation context (CTX1') to be ascribed to B, by means ofthe \Reinterpret" algorithm: in fact, T1 is ambiguous since A's question could beinterpreted as a direct way of learning from B's answer whether she is enrolled.In this case, the ambiguity that misleads B is due to alternative reconstructionsof the speaker's problem solving activity (in the �gure, B's wrong interpretationof T1 can be derived from AM1 by ignoring the contents of its inner dashedrectangle). In this second interpretation, T2 would be a coherent reply to T1,since it does not leave any unsatis�ed goal.At this point, the misunderstood turn has been detected by A. Given thatA is the misunderstood speaker, B should perform a \Restructure" action tocorrect her interpretation (to CTX1). So, A performs a \Get-to-do" action14 toinduce her to do that: this leads A to plan a \Request" for \Restructure". Therequest would be expressed by making explicit his real intentions, which wereimplicit in T1.6 ConclusionsWe have described a plan-based agent model for a computational treatment ofmisunderstandings in dialogue. In this model, the coherence of a turn is evaluatedby relating its underlying goals with the interactants' contextual pending goals.If a satisfactory relation cannot be found, a misunderstanding is hypothesizedand the goal of reestablishing the intersubjectivity among the interactants isadopted. This goal leads the agent who has received the incoherent turn toreason on the previous context, to understand which agent has misunderstoodthe other one. The whole processes of interpretation and recovery are basedon goal acquisition and the occurrences of self and other repairs are reducedto the same goal-based process. Moreover, by modeling linguistic and domainactions uniformly, we provide a general model of misunderstandings, not limitedto linguistic interaction.Our model takes into account the di�erent types of ambiguity which maycause a misunderstanding: since the interpretation process is performed in alayered model of dialogue processing, at each level a misinterpretation is possible.So, we can analyze misunderstandings related with the syntactic or semanticinterpretation of utterances (including references), with their illocutionary forceand with the domain-level and AM plans underlying the speech-acts.in Figure 3.13 See the description of \Try-execute" in section 3.14 The \Get-to-do" action has been introduced in the AM library to model the strategiesadopted by an agent to induce another agent to perform an action for his own sake.

Other researchers have used abductive frameworks for managing the inter-pretation of utterances [22, 21] but they cover only a subset of the levels at whicha misunderstanding can be identi�ed in our approach (typically only the illocu-tionary one). Moreover, some of these works exploit contextual expectations toguide the interpretation process, but they are principally focused on linguisticexpectations (e.g. [21]), so that they strictly depend on the occurrence of inco-herent turns immediately after the misunderstood turn. For instance, in [21] and[12] only third and fourth turn repairs are analyzed, while our plan-based ap-proach supports a more complex dialogue context, where both object level andproblem-solving level expectations are considered; this allows us to analyze selfand other-repairs, without imposing strict constraints on the distance betweenthe �rst misunderstood turn and the repair turn. Our work also di�ers with re-spect to the others in that most of them do not consider collaboration aspects ofdialogue to explain misunderstandings; so, they are resolved by means of strictrecovery strategies, like metarules for restructuring the dialogue context [21, 13].Currently, we don't generate agent behavior,15 so we have not de�ned spe-ci�c repair strategies; however, we can explain a linguistic repair as a behavioradopted by an agent after he instantiates a \Restructure" action (to realign theparticipants' dialogue contexts) and he realizes that his partner has misunder-stood him. On the other hand, we can explain an uptake by an agent in a fourthturn repair (\Oh, you meant ... ") as a noti�cation to his partner that he hascorrected his own dialogue interpretation.In a model for the treatment of communication problems, also speaker andhearer misconceptions should be dealt with, since they can cause breakdowns inthe communication [20, 15, 23, 7, 13]. Note however that plan misconceptionshave been implicitly reduced to the presence of di�erent interpretation contextsin all the approaches based on the presence of buggy plan libraries. This suggeststhat a basic model of misunderstandings can be extended to the treatment ofmisconceptions, by considering also the buggy plans as alternatives.The interpretation of dialogue by means of our plan-based agent model isimplemented in Common Lisp and runs on SUN workstations.References1. G. Airenti, B. Bara, and M. Colombetti. Conversational and behavior games inthe pragmatics of discourse. Cognitive Science, 17:197{256, 1993.2. J.F. Allen. Recognizing intentions from natural language utterances. In M. Bradyand R.C. Berwick, editors, Computational models of discourse, pages 107{166. MITPress, 1983.3. L. Ardissono, G. Boella, and L. Lesmo. A computational approach to speech actsrecognition. In Proc. 17th Cognitive Science Conference, pages 316{321, 1995.4. L. Ardissono, G. Boella, and L. Lesmo. Recognition of problem-solving plans indialogue interpretation. In Proc. 5th Int. Conf. on User Modeling, pages 195{197,Kailua-Kona, Hawaii, 1996.15 In order to process dialogues, we type the input sentences to the system in the formof separate turns; so, the system plays alternatively the role of the two hearers.

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