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, O @ O O An Integrated Approach to Reference and O Resolution O Robert T. Kasper, Paul C. Davis~ and Craige Roberts O Department of Linguistics @ Ohio State University 222 Oxley Hall O 1712 Neil Avenue O Columbus, OH 43210" O e-mail: (kasper~ pcdavis, croberts}@ling.ohio-state.edu O RecoL,nlzing the structure of the will there- O Abstract fore play a crucial role in narrowing the search O We describe an approach to resolving definite de- for and other presupposed information. scriptious and pronominal as subcases of We will illustrate our approach with four example O a general strategy for presupposition satisfaction. human-computer dialogues, shown below. SYS in- O Generally, a presupposition is satisfied in a dicates the utterances spoken by the computer sys- if the context contains a specific type of information tem. @ and is organized in such a way that this information Example I illustrates a case of pronominal can be retrieved by the interlocutors. The model anaphora resolution (it in (8)), in which recowniT.ing O of discourse context we develop assumes that dis- the hierarchical structure of the discourse is crucial O course structure is organized around a stack of ques- for identifying the antecedent, which was introduced tions under discussion, which plays a crucial role in many utterances earlier. The overall topic of the O narrowing the search for referents and other presup- conversation is the question of where the user @ posed information. The algerithmA for maintaining can find a hotel for June 15th in New York, and the discourse structures and retrieving presupposed th|8 snper-question both facilitates and constrains O information are presented and illustrated by several the intexpretafion of fl in (8). This example is example dialogues in which human users interact similar to the well-known examples of long-distance O with an agent tomake hotel reservatious. anaphora in task-oriented dialogues described by O Grosz (1981). Our approach is consistent with pre- I Introduction vious research that uses the intentional structure of O "Any theory of referring expressions must take into discourse to determine a set of potential antecedents O account the discourse context in which they ot~ur. for pronominal anaphora. The following examples Indeed, previous research has shown that the hier- will illustrate how a broader range of reference O archical organization of discourse is fundamentally and presuppositional constructions may also be O related to the rderence resolution process. In this addressed by using the discourse structure to guide paper, we show how a highly structured discourse the search for relevant information. @ model, in conjunction with a treatment of referring expressions as presuppmitional, enables us to de- Example L O velop a common strategy for z~olving a number of 1) USER: rm lookln~ for a hotel for June lSth in O reference resolution problems, such as pronominal New York. anaphora and definite . We also out- 2) SYS: What part of the city would you prefer? O line how this approach extends to a larger group of 3) USEI~ Manhattan, near Central Park. O phenomena which we take to be presuppositional,. 4) SYS: How many nights? including domain restriction, ellipsis, and lexically 5) USF~ Just 1. O and syntactically triggered . All of 6) SYS: Will anyone be traveling with you? these constructions are presuppositional in a broad 7) USEI~ No. O sense, in that their use assumes that certain infor- 8) USEP~ Oh, I want it to have a swimming pool O marion can be retrieved from the discourse context. too. O

O " Paul C. Davis is the recipient et~ a Motorola Partnemhipe O in Research Grant. Example II shows a definite , the structure Of discourse and the related background hotel in (7), whose can only be uniquely literature. In section 3, we present algorithms which determined with respect to the indefinite hotel de- we have developed in a partially completed imple- scription ( a hotel close to Madison Square Garden) mentation of a natural language dialogue system in the question under discussion (1): where users interact with an automated hotel reser- vation booking system. In section 4, we discuss the Example II. use of the algorithms and discourse structures to 1) USER: I want to make a reservation at a hotel resolve the reference and presupposition problems close to Madison Square Garden. shown in the above examples. In the final section, @ 2) SYS: What dates will the reservation be for? we highlight the contributions of our approach and 3) USER: March 3rd and 4th. discuss future plans related to this research. 0 4) SYS: Wouldyou like a single room? 0 5) USER: Yes. 2 Background: Discourse Structure 6) USER: Also, I'll need a conference room on We assume the general theoretical framework of 0 the 4th. Roberts (1996), where discourse is formally charac- O 7) USER: I'd prefer it if the hotel had one. terized as a game of intentional inquiry. As in Grosz & Sidner (1986), discourse is organized by the in- 0 Example HI involves a contextually determined terlocutors' goals and intentions and the plans, or O domain restriction, with a quantificationai deter- strategies, which conversational participants develop miner every, innstrating that domain restriction to achieve them. Following Stalnaker (1979), the pri- 0 must be handled in a ~imilar way for a broader mary goal of the language game is communal inquiry, class of expressions than those which are normally i.e., interlocutors attempting to share information 0 regarded as rderring expr_~-_qjons or presupposition about their world, with the repository of that shared 0 triggers. information characterized as the interlocutors' com- Example HI." mon groun~ CG. The set of acceptable moves in the 0 I) USEI~ Does the Holiday Inn have any vacan- game are defined by the (conventional and conver- cies for sational) rules of the game, and are classified on the 0 a) Tuesday, 12/4- Friday 12/7? basis of their relatio_n~blp to the goals. Ignoring im- @ b) Thursday, 12/6 - Saturday 12/87 peratives, there are two main types of moves (see 2) SYS: Yes, several. also Carlson 1983): questions and assertions. If a 0 3) USER: Do they have a breakfast buffet question is accepted by the interlocutors, this com- @ every mor~;=g? mits them to a common dis(x)ur~ goal, l~lding a sat- 4) SYS: isfactory (asserted) answer; like the commitment to 0 a) Yes, Monday through Friday. a goal in Planning Theory, thiA strong commitment @ b) No. There's a breakfast buffet Monday persists until the goal is satJ'~ed or else shown to be through unsatisfi~le. The accepted question becomes the 0 Friday, but none on Saturday. immediate topic of discussion, the quest/on under discussion. An assertion is a move which proposes 0 Finally, in example IV we give a glimpse into an addition of information to the CG. 0 our larger research program, where an elliptical Roberts defines the structure of a discourse at @ question (3) must be resolved with respect to the a given point, its Information Structure, as a tu- question under discussion, in addition to estab- pie which includes (among other things) the ordered 0 lishing the reference of the deflm'te description the set of moves in the discourse (M), CG, and the set Marrio~ where the context might contain more of the questions currently under discussion at that 0 than one hotel with that ~ point (QUD). The QUD is ordered by order of ute • terance and is updated in a stack-!i!~ f~b!on, I with 0 E~-mple IV. questions popped when they are answered (or de- 0 I) USER: Which hotels near the airport have f.-mined to be practically unanswerable). The or- vacancies? dered set of questions under disc~-_~f~on corresponds O 2) SYS: The Holiday Inn and Sheraton have to the hierarchical intentional structure of the dis- 0 vacancies. course. The QUD in this structure constitutes the 3) USER: How about the Marriott7 set of d/sco,rse goa/s of the interlocutors; the dis. 0 4) SYS: No, the airport Marriott doesn't have any course goals are only a subset of the set of common vacancies. .goals of the interlocutors, their domain goals, and 0 1However, all elements of the QUD list are accessibledur. 0 The remainder of the paper is organized as follows. ing the interpretation of an utterance. Only the top element In section 2 we discuss our assumptions about the is wr/table, but any entry is readable. 0 0 2 0 0 0 the discourse goals ar e subordinate to, and subserve (2) Weak Familiarity: A discourse referent i is the domain goals. Hence, the requirement that in- weakly familiar in a context C (i E Domain(C) terlocutors stick to the question under discussion is and C encodes the information that i has prop- just an instance of the more general commitment erties Pi .... , Pk) iff the Common Ground of C to plans; and in turn, in a fully integrated theory entails the existence of an entity with properties we would expect that domain goals and plans would P~, . . . , Pk. influence interpretation as directly as the discourse goals represented by the questions under discussion. Informational uniqueness only requires that the Any move in a discourse game is interpreted with discourse referent which satisfies the defmite's famil- respect to the Information Structure of the discourse iarity presupposition be unique among the discourse at that point. There are two main aspects to the referents in the context in satisfying the definite's interpretation of any given move: its presupposed descriptive content. These two constraints sufllce to content and its proffered content, the latter includ- characterize the presuppositional content of definite ing what is asserted in an assertion and the non- descriptions: presupposed content of questions and commands. When an utterance presupposes a p, (3) Presuppositions of Definite Descriptions then in order for the utterance to be felicitous in the (informal): Given a context C, use of a definite context, p must be entailed by the CG (Staluaker description NPi presupposes that there is a dis- 1979). But in addition, any move in a discourse course referent weakly familiar in C which is the is interpreted by interlocutors under the Gricean unique weakly familiar discourse referent which met,a-presupposition of Relevance, with Relevance satisfies the (possibly contextually restricted) formally defined as follows in Roberts' framework: descriptive content of NP/.

(1) A move m is Relevant to the question under Unlike Russell's (1905) theory, this does not gen- discussion q iff (i) m is an assertion such that erady entail semantic uniqueness, although in cer- CGU{m} entails a partial answer to q, or (ii) m tain special contexts it will yield the same effect via is a question whose complete answer contextu- pragmatic means. Definite descriptions may have ally entails a partial answex to q. their descriptive content contextually enriched in the same way that domain restriction works for oper- (10)) tells us that the interpretation of an as- ators generally, i.e., via Relevance to the question sertion will be constrained so as to yield a partial under discussion. This will be illustrated in our dis- answer (possibly via contextual entailment) to the cussion of example 4 below. Many apparent counter- question under discussion. (l(ii)) tells us that the examples to the presupposition of uniqueness for def- Q UD in a felicitous Information Structure is con- inite descriptions are solved by appeal to this prin- strained by Relevance so that each question on the cipled contextual enric]~ment, as discussed at length QUD must address the (prior) question below it on in Roberts (1999). carry an additional the stack. Of course, (1) correctly predicts a vari- presuppomtion of maxima] salience: ety of classical Gricean conversational implicatures, now characterizable as contextual entailments. But Roberts argues that Relevance is also crucial in pre- (4) Presuppositions of Pronmmm (informal): supposition resolution, broadly construed to include Given a context C, use of a Pros pre- anaphora resolution, the interpretation of ellipsis, suplz3ses that there is a discourse referent i in and domain restriction (Roberts 1995), as well as C which is the unique weakly familiar discourse lexically and syntactically triggered presuppositions. referent that is both maximally salient and sat- We will also assume the general approach to isfies the descriptive content suggested by the anaphora resolution argued for in Roberts (1999). person, number and gender of Proi. The CG is augmented with.a set of discourse refer- ents familiar to the interlocutors, the Domain of the This amounts to an additional, conventional re- discourse context. All definite NPs, including pro- striction on the search space for pronominal an- and demonstratives as well as definite descrip- tecedents, implemented along the general lines sug- tions using the, presuppose both weak [amiliariQI gested by Grosz & Sidner, and explains the differ- and informational uniqueness. Weak famifiarity (cf. ential distribution of pronouns and definite descrip- the slightly different notion of familiarity in H_m'~ tions. We will discuss how m~-~dmal salience is im- 1982) is the theoretical realization of anaphoricity, plemented in terms of the QUD stack in §4. These and is licensed by existential entailments of the com- presuppositional constraints result in a straightfor- mon ground, not requiring an explicit NP antecedent ward theory of anaphoric reference which explains a or even perceptual salience of the intended referent: broad range of data and can be extended to a treat- ment of demonstrative NTs as definites, as well.

- 3 O O O O process_utterance (U) O "/:1:1. 1. Determine contextually interpreted . ULF = parse(U) O (CULF, CDRS) = determine.L'ULF(ULF, Level) O 7.Y.~ 2. Update discourse structures. O If presuppositions remain, attempt to accommodate them by adding information from system database to CG. O If accommodation fails (sys¢em has no information or system information is O inconsistent gith CG), indicate non-acceptance of move. If U is an assertion: O assert CULF to CG, O update QDL of C~D[top] (i.e., merge CDRS into CDRS of QDL) @ If U is a question: push new QDL entry onto QUD O ~7, 3. Call back-end applicat$on. O Perform SYSTEM action (e.g., query or update database) Perform SYSTEM dialogue move if necessary (e. g., generate a response) O O determine~lLF (U, Level) if atomic_formula(U) 7, contains no presuppositional operators re~urn (U, {}) else (U must contain an operator) return resolve_term(U, Level ÷ 1) Figure 1: Presupposition resolution algorithm

3 Resolution Algorithms presuppesitional operators listed in this algorithm covers the exmnples tlmt we will discuss, but is not In Figures I, 2, and 3 (shown later in §4.4), we intended to be exhaustive. After resolve_term has show simp/ified, pseudo-coded versions of the al- processed a presuppositional term, the variable that gorithm~ which drive the presupposition resolution it binds will appear on the CDRS list, and will ei- process. Of central importance in this process is ther be identified with a set of referents from the the maintenance of the QUD stack. Each entry on common ground or be tmanchored (indicated by the the stack is represented by a Question Data Log empty set or '?'). Once the CULF and CDRS are (QDL), an ordered triple which contains the utter- determined, the discourse structures, including the ance's (ULF), its Contextually Under- CG and QUD, are updated, depending.on the type of stood LF (CULF), and a set of current discourse conversational move (i.e., assertion or question). Af- referents (CDRS). QDL entries represent i~orma- ter the dialogue model has been updated, the CULF tion about units of discourse structure which roughly is sent to the back-end application (e.g., to query or correspond to the discourse segments developed by update its database), and the system may generate Grosz and Siduer. utterances as need~L Process.utterance is the top-level function in- yoked for each discourse utterance. The utterance is parsed to yield a logical form representing its context-independent meaning (ULF). This ULF is The algorith _,~ presented here have been hnple- further processed by det~e-CULF, the. goal of mented in Common Lisp, using the Loom knowl- which is to produce a refined logical form (CULF) edge representation framework (MacGregor (1991)) and a set of discourse referents (CDRS) by.resolv- to maintain the common ground and background ing presuppositions with respect to the current con~ knowledge of the hotel application domain. Sev- text. Presuppositions are represented in the logical eral components, e.g., the emtchtsubstitute and form by certain operators~ including def, pronoun, add_domain.resCriction functions, have not yet (for wh-questions), and WH.EllJ.peis. The terms been implemented in a fully general way, and cur- introduced by these operators, as., well as other rently handle only simplified cases. The e~amp]es generali~ terms, are processed by the discussed in the next section demonstrate how the resolve_~erm function (see Figure 2). The set of r~olution procedure works.

4 resolve_term(Term, Level). Let OP = top-level operator of Term VAR = top-level variable of Term RESTR = top-level restriction of Term O NS = top-level nuclear of Term

O ~ Process embedded formulas inside-out O (RESTR1, CDRS.R) = determine_CULF(RESTR, Level) O (NS1, CDRSJS) = determine_CULF(NS, Level) O if OP is a non-presupposttional operator: -.- DomainRestr = add_domain_restriction(VAR, RESTR1, QUD) e return (OP[VAR,DomainRestr,NS1], CDRS.R U CDRS.NS)

O else (handle according to OP type) O case OP=pronoun: ~ must be anaphoric reference RANKEDJIEFERENTS = r~-k~ccessible.referents(QUO, RESTR1) O REFERENT3ET=mmx4mAI.elements(RANKEDJIEFERENTS) O If sinKleton(REFERENT.SEr), ~assume REFERENT.SET= {INST}, substitute INSTfor VAR in NS1 O reEurn(NSI[VAR->INST], {(VARREFERENT.SET)} U CDRS.NS) O • else report no salient referents or failure of Uniqueness presupposition O case OP=def: Z possible anaphoric reference REFERF2tT~'ET = all_accesstble~eferents(QUD, RESTRI) O If singleton(REPEBENT.qET), O return(NSI[VAR->INST], {(VAR~.SL~r)}U CDRS_NS) else if I~_SL~[ > 1, O repor¢ failure of uniqueness presupposition else Z no salient antecedent, retrieve referent from common ground O DomatnRestr : add.domaiu.restrictton(VAR, P~..~I'R1, QUD) O REPERENT.qET : retrieve_referents(VAR, DomainRestr, CG) If singleton(REFERENT.SET), return (0P[VL~,DomaLuRestr,NS1], {(VAR REFE:RFJ~_qL~I')} U CDRS£ U CDRSJ~S) else if laUEaE~r.S~I > I, report failure of uniqueness presupposition else ~ attempt ¢o acco,-,odate later return (OP[VAR,DomainRestr,NS1], {(VAR {})} U CDRS.RU CDRSJ/S)

case ~: DomLinRestr - add.domatn_restriction(VAR, RESTR1, QUD) case non-top-levelORnon-question: X non-prasupposRional return (OP[VAR,DomdnRestr,NS1], CDRS.RU CDRS_NS) case eh-question: ~presupposes some object satisfies DomatnRestr ~-qET = retrieve_referents(VAR, DomatnRestr, CG) return (OP[VAR,DomainRestr,NS1], {(Vat REFEREMT-qET)} U CDRS.R U CDRS_NS) case polar-question: return (OP[VAR,DoBainRestr,NS1], CDRS_NS)

case WHllltpsis: resolveJ~H_Ellipsis(Term, Level) shown in Figure 3

Figure 2: resolve_term a/gorithm 4 Discussion of Examples developed by Suri and McCoy (1994). Our overall In this section, we discuss the examples given in approach could be adapted to use any theory of local the introducti6h, and highlight how the presuppo- coherence to determine a partial ordering over the sition resolution algorithms can be used to resolve CDRS within a discourse segment corresponding to pronouns, definites, and quantifiers in general (i.e., a single QUD, but it is similar to Suri and McCoy's reference related presuppositions, under our view) approach in allowing the CDRS of prior questions as well as other presuppositional phenomena, such to be stacked. Further explanation of how center- as elliptical questions. 2 We illustrate the crucial ing constraints can be integrated with our approach changes which take place to the QUD data struc- is given by Roberts (1998). In our implementa- 0 tures, allowing effective resolution of referents and tion of pronoun resolution (see Figure 2), the func- 0 presuppositions. tion r=-lr.accessible_referents gives the partial While the Utterance LF (ULF) describes only the ordering of the accessible entities from the QUD, fil- 0 literal content of an utterance, the CULF, along with tering out all entities that are incompatible with the O the CDRS, can be thought of as a record of what agreement features of the pronoun, which are rep- the utterance really means, in the context in which resented in the restriction component of a pronoun O it is said. For example, the following (ULF, CULF, term. CDRS) triple illustrates the QDL structure that re- In processing this dialogue, the system treats (I) 0 suits from question (2) of Example II (What dates as a question (requests and statements of need and 0 will the resereation be for.~: desire should be coerced to questions), and produces (CDRS I), which is the set of discourse referents @ (A[z, date(z), z)]], d~/[I/,reserv,ztion(y),/or.time(y, mentioned in sentence (1). Air,date(z),def[y, re,ervat/on(y) A @ 3[z, hotd(z) ^ r~.ar(z, ~SG), atJoc(zl, z)], (CDRS 1) @ fo~+me(m =)]], {(x:person user)(y:hotel?)(z:date D1)(w~.city NYC)} {(x:,hte ?)(y.'mm-mtion ?)}) 0 As the system attempts to find out more specific in- Each disc°urse referent in the set of CDRS is formation (imagine that it is filling out a template), 0 shown in the form (variable:type insCance). it asks subquestions, such as (2), (4), and (6). After O One fact to keep in mind when viewing the examples each subquestion, a new entry is added on top of the is that questions always produce a new QDL entry QUD stack, and therefore a new CDRS as well, e.g., O • on top of the QUD stack, and therefore a new CULF the set of discourse referents in the top QUD entry @ and CDRS, while answers may update the CDRS of aRer (2) is (CDRS 2). the current entry on top of the QUD stack, but never (CDRS 2) ((w:city NYC)(x:area ?)(y.-perso n nser)} 0 produce a new one. O 4.1 Pronomhm! Anaphora: Example I When a subquestion is answered, as in (3), the We will on the resolution of the pronoun it CDRS of the current QUD is updated, e.g., the ref- 0 in the final utterance (8). We claim that at any erent (x:area ?) becomes (x:area Manhattan), and 0 time there is a set of accessible entities in the dis- a new referent introduced in the answer is added: course, and when a pronoun is used in a discourse (z:area CentralPark). However, once a question 0 felicitously (i.e., as constrained by Relevance), there is completely answered it is popped off the stack. O needs to be a unique maximally salient discourse ref- Thus, after (3) is completely processed as an answer erent for the pronoun belonging to this set of acces- to (2), the stack is popped, and subquestious are sible entities. Under our approach; the set of ac- also popped after processing (5) and (7). Therefore, cessibh entities is represented by the union of the when we arrive at (8), the QUD stack is just as it was CDRS sets of all entries on the QUD stack. Salience aRer (I), since all of the intervening subquestions is a partial ordering on this set determined primarily have been popped. This approach accounts for the .,L by two factors. First, the members of the CDRS of observation ~ more recently mentioned entities, " each entry on the QUD stack are more salient than such as Manhattan or Centre/Park, are less likely as those for all entries below it on the stacL Second, antecedents for/t than those from (CDRS 1), which the relative salience of discourse referents within the are closer in terms of hierarchical discourse struc- CDRS of a single QDL entry is determined by local ture. constraints, such as those given by centering theory In order to determine the antecedent for it, (cf. Grosz, et.al. (1995)), or the theory of focusing r~-k~ccessible.referents only has to consider (CDRS I), returning a subset from which (x:person ~The careful reader will note that these dialogues con- user) is removed, because a person, being animate, taln additional referenceresolution problems, such as one- anaphora (example II) and a nonplural antecedent for the~/ does not match the restrictions of /L Thus, the (example III), etc., not discussed here for brevity. search for possible antecedents has been significantiy

6 O O constrained by using the CDRS associated with the the uniqueness presupposition is satisfied" and z is QUD. Among the remaining .elements, the most selected from CDRS 1 as the antecedent. O likely antecedent is (y:hotel ?), which we call an It is also possible for a to O unanchored discourse referent, since it is not yet have no explicit antecedent, as in the Marriott @ bound to an actual instance of a hotel. This might in sentence (3) of example IV. In such cases, be ranked highest by some versions of centering the- an empty set of referents will be retttrned by O ory, because it is a direct complement of the verb, all_accessible-referents, and our algorithm will while the other referents were introduced by adjunct attempt to retrieve a referent from the common O phrases (for June 15th and in New York). In general, ground. Before resolution, the content of this de- however, pragmatic plausibility must be considered scription is DEF 3, in which the variable ?NS is a O as an additional filter when determining whether a placeholder for the unspecified nuclear scope of the @ candidate is a potential antecedent. For example, def operator. O (z:date D1) can be ruled out because it is not plau- (DEF 3) sible for dates to have swirpmlng pOOlS. de/[y,Hotel(y) ^ Na..ed(~, M a,','iotO,?.s] O 4.2 Definite Descriptions: Examples II-IV The restriction of this term is obtained from the @ Although definite descriptions can often be identi- lexical entry for Marriott, which contains the infor- fied with antecedents from the CDRS in essentially mation that it refers to a hotel, in addition to speci- O the same way as pronouns (since the set of CDRS is fying its name. Although we rely on domain-specific O a subset of the CG Domain), they are not required knowledge in assuming that it refers to a hotel, we to corder with a maximally salient discourse refer- believe this assumption is reasonable, because the O ent. Therefore, our algOrithm specifies three ways proper for hotels can be automatically ac- @ for a definite reference to be resolved. First, we check quired from the hotel database used by the applica- whether the CDRS accessible on the QUD stack con- tion. O rains a unique element that matches the restriction Now suppose that there are a number of Mar- of thedefinite operator. Second, if there is no salient riotts in the area. In an empty discourse context, O antecedent of the appropriate type, then we attempt this reference would have an unsatisfied uniqueness @ to find a unique entity in the CG which satisfies the presupposition, so the system would need to ask restriction. Third, if this fails, we use acco_m_moda- the user which Marriott was intended. However, in O tion where possible to introduce an entity from the this case, uniqueness can be established by search- application's databs-qe into the CG. ing the QUD for an appropriate domain restriction, O In example II, we focus on the resolution of the which can be conjoined with the explicit restriction O hotel in sentence (7). We first look for an appropri- given in (DEF 3). Since doma/n restrictions can ate antecedent in the CDRS ac _ce_~J'___'bleon the QUD be contextually supplied for most restricted oper- O stack, as in our treatment of pronominal anaphora, ators, we interpret (DEF 3) as if there were an addi- O so we need to trace the stack for this dialogue. A re- tional conjunct, which is schematically represented quest is made by the user in (1), followed by a series by Qvn.arara(z) in (DF.~" 3')3 O of specific questions generated by the system. The (DEF 8') O QUD after (1) has the following CDRS: cle/~,(Hotel(y)ANamed(y, Ma~/at"t)AQUD.REST.(Z)), @ (CDRS 1) ((x.person user) ~on ?) ?Ns] (,:hotel ?) (w~.placeMSG)} As in our treatment of anaphora, the key to con- 0 straining the search for an appropriate domain re- Subquestious are asked in (2) and (4) and an- striction is the QUD structure of the discourse. The swered in (3) and (5), respectively, so the QUD stack entry on top of the QUD corresponds to question (I) is pushed and popped, but at (6), it is at the same of example IV, whose CULF is (simpli~ed): state as it was after (1}. (6) is interpreted as a re- (CD~F 1) A[z,Hotd(z)^Ne~r(z, Airport), quest, so a new entry with (CDP~ 6) is pushed onto 3Iv, De~(y), So~V~=~uO-(-, y)]] the QUD on top of the QDL for (1). To determine whether any implicit domain restric- (cvRs e} ' tion can be added to the Marriott, our algorithm {(x:pe~son user) (v:conf-room ?) (u:dateD4)} Calls add.domain_resl:r$ction to search the QUD for predicates that match the same basic type as the In order to interpret the d~finlte description anaphorically, we search for discourse referents SWe do not actually include an explicit conjunct for the domain restriction in our implemented logical forms, because whose type satisfiesthe explicit hotel restriction an implicit domain restriction may be added to virtually any within the set of all accessible CDRS, viz., the union restricted operator, as motivated by Roberts (1995), and it of CDRS 6 and CDRS 1. Since this set contains ex- is of course possible for no new information to be added by actly one referent (z) which matches the hotel type, domain restriction.

7 explicit restriction, HOteL In (CULF 1) it finds the To determine the domain restriction for ev- restriction Hotd(z) A Near(z, Airport), which can ery morning, add_domain.xestrict ion searches the be added in place of the virtual QUD_RESTR(X) con- QUD for predicates that match the same basic type junct in (DEF 3') to further restrict the domain for as the explicit restriction, morning. In this case, we O the Marriott. This restriction (DEF 3") is then used take the basic type to be a temporal entity, so it 0 by retrieve.referents to find a matching referent will search for temporal descriptions in the QUD. s in the CG. By using the QUD stack to constrain the search, ev- O ery Will quantify over any temporal entities that are (DEF 3") clef[y, Hotel(y) A Named(y, Marriott) found at a level of discourse structure closest to the 0 ^ Near(y, Airport),?NS] current segment, but crucially not over every tern- It is important to note that the familiarity pre- • poral entity in the entire common ground. Thus, to 0 supposition for a definite description does not re- determine the response in:(4a), only the date range 0 quire its referent to be previously mentioned in the mentioned in (la) is relevant, and a positive response @ discourse. In sentence (1) of Example HI, the ref- can be given, since the question relates to weekdays. erent for the Holiday Inn does not yet exist in our In (4b) however, the date range includes a Saturday, O representation of the common ground, because the so the system should generate a negative response. system initially has no knowledge that the user 0 is aware of any particular Holiday Inns. In such 4.4 Elliptical Questions: Example IV cases, no objects are returned from the CG by Example IV is a somewhat more complex dia- 0 retrieve_referents, and the definite presupposi- logue, including an elliptical question as well as sev- @ tional term will remain with an unknown referent eral definite descriptions. It illustrates how our ap- in the Output of determine.CULF. Our approach to proach generalizes ~ the larger class of presuppo- 0 accommodation for such unsatisfied presuppositions sitional constructions which we identified in the in- @ (in step 2 of process_ul;terance) is to look for a . troduction. Let. us focus on the interpretation of referent in the application'S private database of facts sentence (3), How about the Marriottg., which is as- 0 about the domain of hotels, since this database rep- signed the following ULF: resents all of the world knowledge that the system 0 has available. If it finds a unique hotel named Holi- (ULF 8) Wa_~Up,i,[~,~(~), day Inn, we can assume this hotel satisfies the user's ~[x -, (de/[y, Uotd(y) ^ Na~(y, ~a~), ?.s])]] 0 presupposition. On the other hand, if it turns out is a variable referring to some contextually 0 that there are either no hotels named Holiday Inn salient question, and the de6nlte description cor- in the database, or multiple Holiday Inns, the sys- respondlnE to the Marriott is to be substituted for 0 tem could report the failure of these presuppositions, some term (X) within ~b. Recall that the variable 0 rather than giving an uninformative simple negative ?NS is a placeholder for the ,,n~ecified nuclear scope answer to the user's question (1). of the def operator. 0 our algorithm processes the logical form of an ut- 4.3 Generalized Dom~|n Restriction: terance ins/de-out, i.e., the embedded context res- 0 Example HI olution problems are handled first, so it first re- O Consider next the quantificational definer ever// solves the de/term corresponding to the Mar,'/o~ in sentence (3) of example HI. It should be clear as we discussed in §4.2 on definite descriptions, and 0 that the user is not ~.qld~ about every morning for add_domain.restriction produces the refined de- Q all time, hut only about all mornings during the scription (DEF 3"): planned trip. As with definite descriptions, our algo- 0 rithm allows the restriction of most operators with (DP.F 3") de/Iv, Hoed(y) ^ Na,~d(y, Ma.~) semantically contentfifl restrictions i to be further ^ Near(y, Airport),TNS] 0 specified by information from the QUD, so the in- Next, the top.level Wh.dlip~ris term in (ULF. 3) 0 terpretation of every morn/rig will differ depending is resolved, according to the resolve.Y~ ~llipsis on whether the dialogue began with question (la) algorithm of Figure 3. ~ must be a question, sowe @ or (Ib). Now, if it is the case that the Holiday Inn retrieve the question on top of the QUD stack, and @ has a breakfast buffet on weekdays only, it is imp0r- attempt to identify ~ with its CULF (CULF 1). rant for the system to answer (3) appropriately, asin (C'Ur_,F '9 A[=,H~d(z) ^ JV~,-(z, Airport), (4s) and (4b), depending upon the context created 3~1, Date(y), Has V acancyOn(z, y )~ by (h) and (Ib). 4Domain restriction isnot usually applicable to pronouns SA complete explanation of this situation might require and other expressions that have little explicit content, be- the system to infer the domain goals of the user. However, cause these expressions depend on recovering a salient an- when the QUD contains some descriptions of the appropriate tecodent in order to determine the type of the refenmt, rather • type, we can use them as an approximate domain restriction, than searching for a l~icular type of object in the common thereby avoiding the computational expense of full plan in- ground. ference.

8

m I $ O O

O r esoive_WH_Ellipsis (Term, Level) O 7,7,7, Assume nuclear scope of Ter~n is of the form: ~[01dExpr->NevExpr] vhile QUD stack is not empty { O QUD-CULF = CULF of QUD[top] @ QUD-CDRS = CDRS of GUD[Cop] (NewExpr, CDRS1) = determlne.CULF(NewExpr, Level) O if NewExpr is a generalized quanClfier, let SubsCLF = march, substitute (QUD-CULF, resCricCion(NevExpr), NewExpr) O else (NewExpr iS a ) O let SubstLF ffi matchksubstiCute(QUD-CULF, NevExpr, NevExpr) if null(SubstLF) O or SubstLF is not Snterpretable as a subquestion of ~ID-CULF, O pop(QUV) else rectum (SubsCLF, priorizy_union(CDRSl, QUD-CDRS)) O 7,7,7, priority-union(X,Y) is like set un$on, but vhen some members of X 7,7,Y, and Y have the same type, only the member of X is included Sn the result. O } O 0 Figure 3: resolve_WH_Ellipsis algorithm O We must now find a term within (CULF 1) for which ing the presuppositions associated with each kind of @ the term corresponding to the Marriott can be sub- construction, and recovering presupposed informa- stituted. Our matchksubscitute algorithm looks tion from a unified discourse information structure, O for terms whose restrictions specialize a common the search space for relevant contextual information O basic type, so it again findsthe restriction on the is restricted in a general way. (top-level) A-term containing the Hote/predicate in Re~li~i-g the full potential of this approach to (CULF 1): O discourse structure requires recoL,,i~.in~ the question ~[z, sots(z) ^ Nes,(~,Ai~po~), ...] under discussion even when it is not stated explic- O The operator and restriction of this term are re- itly as a question. We have found that requests and O placed by those from (DEF 3") and the variables statements of need and desire should be coerced to are -nlSed, but the nuclear scope of (DEF 3") is un- questions, but a general implementation of this coer- O specified, so the nuclear scope of (CULF 1) rem~ cion process remains to be completed. An even more O unchanged in the result: challenging problem involves inferring the domain (3") clef[z, Hotd(z ) A Named(y,M,rr/ott) goals of the user that are related to the question un- O A Near(z, AiT7x~t), der discussion. As will be readily apparent to most 3[y, D.ze(~), S.aVo~.q~.(z, y)]] researchers in NLP, these problems are intertwined O with larger AI problems, such as plan recognition, O (3") is (almost) the CULF for How about the Mar- which are beyond the scope of this paper, but must r/ottf, but it must be noted that it should be inter° ultimately be solved or approximated in any realis- O preted as a polar question, since the A-term char- tic application. As noted in our discussion of domain acteristi¢ of a wh-question has been replaced by a restriction (§4.3), it is sometimes possible to extract O definite descriptione some explicitly mentioned content from the QUD O Thus, both the elliptical question and the domain which is relat~ to the user's domain goals, but we restriction of the definite description are processed recoL,-i~e that this is only an apprarlmate solution. O by the same overall strategy. They are interpreted by incorporating information contained in the ques- Although we have shown several examples where O tion under discussion. this approach to discourse structure is successful, O a comprehensive empirical evaluation still needs to 5 Conclusions be performed to dete_rm_in_e how frequently partic- ular presupposition problems occur in actual cor- O We have described an integrated approach to re- pora, and to assess what proportion of the actual oc- solving presuppositions, which includes pronominal O currences are resolved effectively by our algorithms. and definite reference resolution Central to our ap- The first part of this evaluation could be addressed O proach is the maintenance of discourse structures, by searc~inf a corpus for expressions that trigger especially the QUD stack, which captures the hier- O presuppositions, but assessing the actual perfor- archical organization of the discourse. By identify- mance of the algorithms on existing corpora would O 8When all top-level ),-terms in a Wh-question have been be more diMcult, because it would require the ac- replaced, it is interpreted as a polar question. quisition of background knowledge about other do-

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