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<Paper uid="W99-0101">
  <Title>O @ O O O O O @ O O O O O O O O @ O O O @ O O O O O O O @ O O O O O O O O O O An Integrated Approach to Reference and Presupposition Resolution</Title>
  <Section position="2" start_page="0" end_page="0" type="metho">
    <SectionTitle>
I Introduction
</SectionTitle>
    <Paragraph position="0"> &amp;quot;Any theory of referring expressions must take into account the discourse context in which they ot~ur.</Paragraph>
    <Paragraph position="1"> Indeed, previous research has shown that the hierarchical organization of discourse is fundamentally related to the rderence resolution process. In this paper, we show how a highly structured discourse model, in conjunction with a treatment of referring expressions as presuppmitional, enables us to develop a common strategy for z~olving a number of reference resolution problems, such as pronominal anaphora and definite descriptions. We also outline how this approach extends to a larger group of phenomena which we take to be presuppositional,.</Paragraph>
    <Paragraph position="2"> including domain restriction, ellipsis, and lexically and syntactically triggered presuppositions. All of these constructions are presuppositional in a broad sense, in that their use assumes that certain informarion can be retrieved from the discourse context.</Paragraph>
    <Paragraph position="3"> RecoL, nlzing the structure of the discourse will therefore play a crucial role in narrowing the search for referents and other presupposed information.</Paragraph>
    <Paragraph position="4"> We will illustrate our approach with four example human-computer dialogues, shown below. SYS indicates the utterances spoken by the computer system. null Example I illustrates a case of pronominal anaphora resolution (it in (8)), in which recowniT.ing the hierarchical structure of the discourse is crucial for identifying the antecedent, which was introduced many utterances earlier. The overall topic of the conversation is the question of where the user can find a hotel for June 15th in New York, and th|8 snper-question both facilitates and constrains the intexpretafion of fl in (8). This example is similar to the well-known examples of long-distance anaphora in task-oriented dialogues described by Grosz (1981). Our approach is consistent with previous research that uses the intentional structure of discourse to determine a set of potential antecedents for pronominal anaphora. The following examples will illustrate how a broader range of reference and presuppositional constructions may also be addressed by using the discourse structure to guide the search for relevant information.</Paragraph>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
Example L
</SectionTitle>
      <Paragraph position="0"> 1) USER: rm lookln~ for a hotel for June lSth in New York.</Paragraph>
      <Paragraph position="1"> 2) SYS: What part of the city would you prefer? 3) USEI~ Manhattan, near Central Park.</Paragraph>
      <Paragraph position="2"> 4) SYS: How many nights? 5) USF~ Just 1.</Paragraph>
      <Paragraph position="3"> 6) SYS: Will anyone be traveling with you? 7) USEI~ No.</Paragraph>
      <Paragraph position="4"> 8) USEP~ Oh, I want it to have a swimming pool too.</Paragraph>
      <Paragraph position="5"> &amp;quot; Paul C. Davis is the recipient et ~ a Motorola Partnemhipe in Research Grant.  Example II shows a definite description, the hotel in (7), whose referent can only be uniquely determined with respect to the indefinite hotel description ( a hotel close to Madison Square Garden) in the question under discussion (1):  Example II.</Paragraph>
      <Paragraph position="6"> 1) USER: I want to make a reservation at a hotel close to Madison Square Garden.</Paragraph>
      <Paragraph position="7"> 2) SYS: What dates will the reservation be for? 3) USER: March 3rd and 4th.</Paragraph>
      <Paragraph position="8"> 4) SYS: Wouldyou like a single room? 5) USER: Yes.</Paragraph>
      <Paragraph position="9"> 6) USER: Also, I'll need a conference room on the 4th.</Paragraph>
      <Paragraph position="10"> 7) USER: I'd prefer it if the hotel had one.  Example HI involves a contextually determined domain restriction, with a quantificationai determiner every, innstrating that domain restriction must be handled in a ~imilar way for a broader class of expressions than those which are normally regarded as rderring expr_~-_qjons or presupposition triggers.</Paragraph>
      <Paragraph position="11">  b) Thursday, 12/6 - Saturday 12/87 2) SYS: Yes, several.</Paragraph>
      <Paragraph position="12"> 3) USER: Do they have a breakfast buffet every mor~;=g? 4) SYS: a) Yes, Monday through Friday.</Paragraph>
      <Paragraph position="13"> b) No. There's a breakfast buffet Monday through  Friday, but none on Saturday.</Paragraph>
      <Paragraph position="14"> Finally, in example IV we give a glimpse into our larger research program, where an elliptical question (3) must be resolved with respect to the question under discussion, in addition to establishing the reference of the deflm'te description the Marrio~ where the context might contain more  than one hotel with that name~ E~-mple IV.</Paragraph>
      <Paragraph position="15"> I) USER: Which hotels near the airport have vacancies? 2) SYS: The Holiday Inn and Sheraton have vacancies.</Paragraph>
      <Paragraph position="16"> 3) USER: How about the Marriott7 4) SYS: No, the airport Marriott doesn't have any  vacancies.</Paragraph>
      <Paragraph position="17"> The remainder of the paper is organized as follows. In section 2 we discuss our assumptions about the structure Of discourse and the related background literature. In section 3, we present algorithms which we have developed in a partially completed implementation of a natural language dialogue system where users interact with an automated hotel reservation booking system. In section 4, we discuss the use of the algorithms and discourse structures to resolve the reference and presupposition problems shown in the above examples. In the final section, we highlight the contributions of our approach and discuss future plans related to this research.</Paragraph>
    </Section>
  </Section>
  <Section position="3" start_page="0" end_page="2" type="metho">
    <SectionTitle>
2 Background: Discourse Structure
</SectionTitle>
    <Paragraph position="0"> We assume the general theoretical framework of Roberts (1996), where discourse is formally characterized as a game of intentional inquiry. As in Grosz &amp; Sidner (1986), discourse is organized by the interlocutors' goals and intentions and the plans, or strategies, which conversational participants develop to achieve them. Following Stalnaker (1979), the primary goal of the language game is communal inquiry, i.e., interlocutors attempting to share information about their world, with the repository of that shared information characterized as the interlocutors' common groun~ CG. The set of acceptable moves in the game are defined by the (conventional and conversational) rules of the game, and are classified on the basis of their relatio_n~blp to the goals. Ignoring imperatives, there are two main types of moves (see also Carlson 1983): questions and assertions. If a question is accepted by the interlocutors, this commits them to a common dis(x)ur~ goal, l~lding a satisfactory (asserted) answer; like the commitment to a goal in Planning Theory, thiA strong commitment persists until the goal is satJ'~ed or else shown to be unsatisfi~le. The accepted question becomes the immediate topic of discussion, the quest/on under discussion. An assertion is a move which proposes an addition of information to the CG.</Paragraph>
    <Paragraph position="1"> Roberts defines the structure of a discourse at a given point, its Information Structure, as a tupie which includes (among other things) the ordered set of moves in the discourse (M), CG, and the set of the questions currently under discussion at that point (QUD). The QUD is ordered by order of ute * terance and is updated in a stack-!i!~ f~b!on, I with questions popped when they are answered (or def.-mined to be practically unanswerable). The ordered set of questions under disc~-_~f~on corresponds to the hierarchical intentional structure of the discourse. The QUD in this structure constitutes the set of d/sco,rse goa/s of the interlocutors; the dis.</Paragraph>
    <Paragraph position="2"> course goals are only a subset of the set of common .goals of the interlocutors, their domain goals, and  the discourse goals ar e subordinate to, and subserve the domain goals. Hence, the requirement that interlocutors stick to the question under discussion is just an instance of the more general commitment to plans; and in turn, in a fully integrated theory we would expect that domain goals and plans would influence interpretation as directly as the discourse goals represented by the questions under discussion.</Paragraph>
    <Paragraph position="3"> Any move in a discourse game is interpreted with respect to the Information Structure of the discourse at that point. There are two main aspects to the interpretation of any given move: its presupposed content and its proffered content, the latter including what is asserted in an assertion and the nonpresupposed content of questions and commands.</Paragraph>
    <Paragraph position="4"> When an utterance presupposes a proposition p, then in order for the utterance to be felicitous in the context, p must be entailed by the CG (Staluaker 1979). But in addition, any move in a discourse is interpreted by interlocutors under the Gricean met, a-presupposition of Relevance, with Relevance formally defined as follows in Roberts' framework:  (1) A move m is Relevant to the question under discussion q iff (i) m is an assertion such that CGU{m} entails a partial answer to q, or (ii) m is a question whose complete answer contextually entails a partial answex to q.</Paragraph>
    <Paragraph position="5"> (10)) tells us that the interpretation of an as- null sertion will be constrained so as to yield a partial answer (possibly via contextual entailment) to the question under discussion. (l(ii)) tells us that the Q UD in a felicitous Information Structure is constrained by Relevance so that each question on the QUD must address the (prior) question below it on the stack. Of course, (1) correctly predicts a variety of classical Gricean conversational implicatures, now characterizable as contextual entailments. But Roberts argues that Relevance is also crucial in presupposition resolution, broadly construed to include anaphora resolution, the interpretation of ellipsis, and domain restriction (Roberts 1995), as well as lexically and syntactically triggered presuppositions.</Paragraph>
    <Paragraph position="6"> We will also assume the general approach to anaphora resolution argued for in Roberts (1999).</Paragraph>
    <Paragraph position="7"> The CG is augmented with.a set of discourse referents familiar to the interlocutors, the Domain of the discourse context. All definite NPs, including pronouns and demonstratives as well as definite descriptions using the, presuppose both weak \[amiliariQI and informational uniqueness. Weak famifiarity (cf.</Paragraph>
    <Paragraph position="8"> the slightly different notion of familiarity in H_m'~ 1982) is the theoretical realization of anaphoricity, and is licensed by existential entailments of the common ground, not requiring an explicit NP antecedent or even perceptual salience of the intended referent: (2) Weak Familiarity: A discourse referent i is weakly familiar in a context C (i E Domain(C) and C encodes the information that i has properties Pi .... , Pk) iff the Common Ground of C entails the existence of an entity with properties P~, . . . , Pk.</Paragraph>
    <Paragraph position="9"> Informational uniqueness only requires that the discourse referent which satisfies the defmite's familiarity presupposition be unique among the discourse referents in the context in satisfying the definite's descriptive content. These two constraints sufllce to characterize the presuppositional content of definite descriptions:  (3) Presuppositions of Definite Descriptions  (informal): Given a context C, use of a definite description NPi presupposes that there is a discourse referent weakly familiar in C which is the unique weakly familiar discourse referent which satisfies the (possibly contextually restricted) descriptive content of NP/.</Paragraph>
    <Paragraph position="10"> Unlike Russell's (1905) theory, this does not generady entail semantic uniqueness, although in certain special contexts it will yield the same effect via pragmatic means. Definite descriptions may have their descriptive content contextually enriched in the same way that domain restriction works for operators generally, i.e., via Relevance to the question under discussion. This will be illustrated in our discussion of example 4 below. Many apparent counter-examples to the presupposition of uniqueness for definite descriptions are solved by appeal to this principled contextual enric\]~ment, as discussed at length in Roberts (1999). Pronouns carry an additional presuppomtion of maxima\] salience:  (4) Presuppositions of Pronmmm (informal):  Given a context C, use of a pronoun Pros presuplz3ses that there is a discourse referent i in C which is the unique weakly familiar discourse referent that is both maximally salient and satisfies the descriptive content suggested by the person, number and gender of Proi.</Paragraph>
    <Paragraph position="11"> This amounts to an additional, conventional restriction on the search space for pronominal antecedents, implemented along the general lines suggested by Grosz &amp; Sidner, and explains the differential distribution of pronouns and definite descriptions. We will discuss how m~-~dmal salience is implemented in terms of the QUD stack in SS4. These presuppositional constraints result in a straightforward theory of anaphoric reference which explains a broad range of data and can be extended to a treatment of demonstrative NTs as definites, as well.</Paragraph>
    <Paragraph position="13"> &amp;quot;/:1:1. 1. Determine contextually interpreted meaning.</Paragraph>
    <Paragraph position="14"> ULF = parse(U) (CULF, CDRS) = determine.L'ULF(ULF, Level) 7.Y.~ 2. Update discourse structures.</Paragraph>
    <Paragraph position="15"> If presuppositions remain, attempt to accommodate them by adding information from system database to CG. If accommodation fails (sysC/em has no information or system information is inconsistent gith CG), indicate non-acceptance of move.</Paragraph>
    <Paragraph position="16"> If U is an assertion: assert CULF to CG, update QDL of C~D\[top\] (i.e., merge CDRS into CDRS of QDL) If U is a question: push new QDL entry &lt;ULF, CULF, CDRS&gt; onto QUD ~7, 3. Call back-end applicat$on.</Paragraph>
    <Paragraph position="17"> Perform SYSTEM action (e.g., query or update database) Perform SYSTEM dialogue move if necessary (e. g., generate a response)</Paragraph>
    <Paragraph position="19"> if atomic_formula(U) 7, contains no presuppositional operators re~urn (U, {}) else (U must contain an operator) return resolve_term(U, Level / 1)</Paragraph>
  </Section>
  <Section position="4" start_page="2" end_page="2" type="metho">
    <SectionTitle>
3 Resolution Algorithms
</SectionTitle>
    <Paragraph position="0"> In Figures I, 2, and 3 (shown later in SS4.4), we show simp/ified, pseudo-coded versions of the algorithm~ which drive the presupposition resolution process. Of central importance in this process is the maintenance of the QUD stack. Each entry on the stack is represented by a Question Data Log (QDL), an ordered triple which contains the utterance's logical form (ULF), its Contextually Understood LF (CULF), and a set of current discourse referents (CDRS). QDL entries represent i~ormation about units of discourse structure which roughly correspond to the discourse segments developed by Grosz and Siduer.</Paragraph>
    <Paragraph position="1"> Process.utterance is the top-level function inyoked for each discourse utterance. The utterance is parsed to yield a logical form representing its context-independent meaning (ULF). This ULF is further processed by det~e-CULF, the. goal of which is to produce a refined logical form (CULF) and a set of discourse referents (CDRS) by.resolving presuppositions with respect to the current con~ text. Presuppositions are represented in the logical form by certain operators~ including def, pronoun, (for wh-questions), and WH.EllJ.peis. The terms introduced by these operators, as., well as other generali~ quantifier terms, are processed by the resolve_~erm function (see Figure 2). The set of presuppesitional operators listed in this algorithm covers the exmnples tlmt we will discuss, but is not intended to be exhaustive. After resolve_term has processed a presuppositional term, the variable that it binds will appear on the CDRS list, and will either be identified with a set of referents from the common ground or be tmanchored (indicated by the empty set or '?'). Once the CULF and CDRS are determined, the discourse structures, including the CG and QUD, are updated, depending.on the type of conversational move (i.e., assertion or question). After the dialogue model has been updated, the CULF is sent to the back-end application (e.g., to query or update its database), and the system may generate utterances as need~L The algorith _,~ presented here have been hnplemented in Common Lisp, using the Loom knowledge representation framework (MacGregor (1991)) to maintain the common ground and background knowledge of the hotel application domain. Several components, e.g., the emtchtsubstitute and add_domain.resCriction functions, have not yet been implemented in a fully general way, and currently handle only simplified cases. The e~amp\]es discussed in the next section demonstrate how the r~olution procedure works.</Paragraph>
  </Section>
  <Section position="5" start_page="2" end_page="8" type="metho">
    <SectionTitle>
4 Discussion of Examples
</SectionTitle>
    <Paragraph position="0"> In this section, we discuss the examples given in the introducti6h, and highlight how the presupposition resolution algorithms can be used to resolve pronouns, definites, and quantifiers in general (i.e., reference related presuppositions, under our view) as well as other presuppositional phenomena, such as elliptical questions. 2 We illustrate the crucial changes which take place to the QUD data structures, allowing effective resolution of referents and presuppositions.</Paragraph>
    <Paragraph position="1"> While the Utterance LF (ULF) describes only the literal content of an utterance, the CULF, along with the CDRS, can be thought of as a record of what the utterance really means, in the context in which it is said. For example, the following (ULF, CULF, CDRS) triple illustrates the QDL structure that resuits from question (2) of Example II (What dates will the resereation be for.~: (A\[z, date(z), d~/\[I/, reserv,ztion(y),/or.time(y, z)\]\],</Paragraph>
    <Paragraph position="3"> Each discdegurse referent in the set of CDRS is shown in the form (variable:type insCance).</Paragraph>
    <Paragraph position="4"> One fact to keep in mind when viewing the examples is that questions always produce a new QDL entry * on top of the QUD stack, and therefore a new CULF and CDRS, while answers may update the CDRS of the current entry on top of the QUD stack, but never produce a new one.</Paragraph>
    <Section position="1" start_page="2" end_page="6" type="sub_section">
      <SectionTitle>
4.1 Pronomhm! Anaphora: Example I
</SectionTitle>
      <Paragraph position="0"> We will focus on the resolution of the pronoun it in the final utterance (8). We claim that at any time there is a set of accessible entities in the discourse, and when a pronoun is used in a discourse felicitously (i.e., as constrained by Relevance), there needs to be a unique maximally salient discourse referent for the pronoun belonging to this set of accessible entities. Under our approach; the set of accessibh entities is represented by the union of the CDRS sets of all entries on the QUD stack. Salience is a partial ordering on this set determined primarily by two factors. First, the members of the CDRS of &amp;quot; each entry on the QUD stack are more salient than those for all entries below it on the stacL Second, the relative salience of discourse referents within the CDRS of a single QDL entry is determined by local constraints, such as those given by centering theory (cf. Grosz, et.al. (1995)), or the theory of focusing ~The careful reader will note that these dialogues contaln additional reference resolution problems, such as one- anaphora (example II) and a nonplural antecedent for the~/ (example III), etc., not discussed here for brevity.</Paragraph>
      <Paragraph position="1"> developed by Suri and McCoy (1994). Our overall approach could be adapted to use any theory of local coherence to determine a partial ordering over the CDRS within a discourse segment corresponding to a single QUD, but it is similar to Suri and McCoy's approach in allowing the CDRS of prior questions to be stacked. Further explanation of how centering constraints can be integrated with our approach is given by Roberts (1998). In our implementation of pronoun resolution (see Figure 2), the function r=-lr.accessible_referents gives the partial ordering of the accessible entities from the QUD, filtering out all entities that are incompatible with the agreement features of the pronoun, which are represented in the restriction component of a pronoun term.</Paragraph>
      <Paragraph position="2"> In processing this dialogue, the system treats (I) as a question (requests and statements of need and desire should be coerced to questions), and produces (CDRS I), which is the set of discourse referents mentioned in sentence (1).</Paragraph>
      <Paragraph position="4"> As the system attempts to find out more specific information (imagine that it is filling out a template), it asks subquestions, such as (2), (4), and (6). After each subquestion, a new entry is added on top of the QUD stack, and therefore a new CDRS as well, e.g., the set of discourse referents in the top QUD entry</Paragraph>
      <Paragraph position="6"> When a subquestion is answered, as in (3), the CDRS of the current QUD is updated, e.g., the referent (x:area ?) becomes (x:area Manhattan), and a new referent introduced in the answer is added: (z:area CentralPark). However, once a question is completely answered it is popped off the stack.</Paragraph>
      <Paragraph position="7"> Thus, after (3) is completely processed as an answer to (2), the stack is popped, and subquestious are also popped after processing (5) and (7). Therefore, when we arrive at (8), the QUD stack is just as it was aRer (I), since all of the intervening subquestions have been popped. This approach accounts for the observation ~ more recently mentioned entities, such as Manhattan or Centre/Park, are less likely as antecedents for/t than those from (CDRS 1), which are closer in terms of hierarchical discourse structure. null In order to determine the antecedent for it, r~-k~ccessible.referents only has to consider (CDRS I), returning a subset from which (x:person user) is removed, because a person, being animate, does not match the restrictions of /L Thus, the search for possible antecedents has been significantiy</Paragraph>
      <Paragraph position="9"> constrained by using the CDRS associated with the QUD. Among the remaining .elements, the most likely antecedent is (y:hotel ?), which we call an unanchored discourse referent, since it is not yet bound to an actual instance of a hotel. This might be ranked highest by some versions of centering theory, because it is a direct complement of the verb, while the other referents were introduced by adjunct phrases (for June 15th and in New York). In general, however, pragmatic plausibility must be considered as an additional filter when determining whether a candidate is a potential antecedent. For example, (z:date D1) can be ruled out because it is not plausible for dates to have swirpmlng pOOlS.</Paragraph>
    </Section>
    <Section position="2" start_page="6" end_page="7" type="sub_section">
      <SectionTitle>
4.2 Definite Descriptions: Examples II-IV
</SectionTitle>
      <Paragraph position="0"> Although definite descriptions can often be identified with antecedents from the CDRS in essentially the same way as pronouns (since the set of CDRS is a subset of the CG Domain), they are not required to corder with a maximally salient discourse referent. Therefore, our algOrithm specifies three ways for a definite reference to be resolved. First, we check whether the CDRS accessible on the QUD stack conrains a unique element that matches the restriction of thedefinite operator. Second, if there is no salient antecedent of the appropriate type, then we attempt to find a unique entity in the CG which satisfies the restriction. Third, if this fails, we use acco_m_modation where possible to introduce an entity from the application's databs-qe into the CG.</Paragraph>
      <Paragraph position="1"> In example II, we focus on the resolution of the hotel in sentence (7). We first look for an appropriate antecedent in the CDRS ac _ce_~J'___'ble on the QUD stack, as in our treatment of pronominal anaphora, so we need to trace the stack for this dialogue. A request is made by the user in (1), followed by a series of specific questions generated by the system. The QUD after (1) has the following CDRS:</Paragraph>
      <Paragraph position="3"> Subquestious are asked in (2) and (4) and answered in (3) and (5), respectively, so the QUD stack is pushed and popped, but at (6), it is at the same state as it was after (1}. (6) is interpreted as a request, so a new entry with (CDP~ 6) is pushed onto the QUD on top of the QDL for (1).</Paragraph>
      <Paragraph position="4"> (cvRs e} ' {(x:pe~son user) (v:conf-room ?) (u:date D4)} In order to interpret the d~finlte description anaphorically, we search for discourse referents whose type satisfiesthe explicit hotel restriction within the set of all accessible CDRS, viz., the union of CDRS 6 and CDRS 1. Since this set contains exactly one referent (z) which matches the hotel type, the uniqueness presupposition is satisfied&amp;quot; and z is selected from CDRS 1 as the antecedent.</Paragraph>
      <Paragraph position="5"> It is also possible for a definite description to have no explicit antecedent, as in the Marriott in sentence (3) of example IV. In such cases, an empty set of referents will be retttrned by all_accessible-referents, and our algorithm will attempt to retrieve a referent from the common ground. Before resolution, the content of this description is DEF 3, in which the variable ?NS is a placeholder for the unspecified nuclear scope of the def operator.</Paragraph>
      <Paragraph position="6"> (DEF 3) de/\[y, Hotel(y) ^ Na..ed(~, M a,','iotO, ?.s\] The restriction of this term is obtained from the lexical entry for Marriott, which contains the information that it refers to a hotel, in addition to specifying its name. Although we rely on domain-specific knowledge in assuming that it refers to a hotel, we believe this assumption is reasonable, because the proper names for hotels can be automatically acquired from the hotel database used by the application. null Now suppose that there are a number of Marriotts in the area. In an empty discourse context, this reference would have an unsatisfied uniqueness presupposition, so the system would need to ask the user which Marriott was intended. However, in this case, uniqueness can be established by searching the QUD for an appropriate domain restriction, which can be conjoined with the explicit restriction given in (DEF 3). Since doma/n restrictions can be contextually supplied for most restricted operators, we interpret (DEF 3) as if there were an additional conjunct, which is schematically represented</Paragraph>
      <Paragraph position="8"> As in our treatment of anaphora, the key to constraining the search for an appropriate domain restriction is the QUD structure of the discourse. The entry on top of the QUD corresponds to question (I) of example IV, whose CULF is (simpli~ed):</Paragraph>
      <Paragraph position="10"> To determine whether any implicit domain restriction can be added to the Marriott, our algorithm Calls add.domain_resl:r$ction to search the QUD for predicates that match the same basic type as the SWe do not actually include an explicit conjunct for the domain restriction in our implemented logical forms, because an implicit domain restriction may be added to virtually any restricted operator, as motivated by Roberts (1995), and it is of course possible for no new information to be added by domain restriction.</Paragraph>
      <Paragraph position="11">  explicit restriction, HOteL In (CULF 1) it finds the restriction Hotd(z) A Near(z, Airport), which can be added in place of the virtual QUD_RESTR(X) conjunct in (DEF 3') to further restrict the domain for the Marriott. This restriction (DEF 3&amp;quot;) is then used by retrieve.referents to find a matching referent in the CG.</Paragraph>
      <Paragraph position="13"> It is important to note that the familiarity presupposition for a definite description does not require its referent to be previously mentioned in the discourse. In sentence (1) of Example HI, the referent for the Holiday Inn does not yet exist in our representation of the common ground, because the system initially has no knowledge that the user is aware of any particular Holiday Inns. In such cases, no objects are returned from the CG by retrieve_referents, and the definite presuppositional term will remain with an unknown referent in the Output of determine.CULF. Our approach to accommodation for such unsatisfied presuppositions (in step 2 of process_ul;terance) is to look for a referent in the application'S private database of facts about the domain of hotels, since this database represents all of the world knowledge that the system has available. If it finds a unique hotel named Holiday Inn, we can assume this hotel satisfies the user's presupposition. On the other hand, if it turns out that there are either no hotels named Holiday Inn in the database, or multiple Holiday Inns, the system could report the failure of these presuppositions, rather than giving an uninformative simple negative answer to the user's question (1).</Paragraph>
    </Section>
    <Section position="3" start_page="7" end_page="7" type="sub_section">
      <SectionTitle>
4.3 Generalized Dom~|n Restriction:
Example HI
</SectionTitle>
      <Paragraph position="0"> Consider next the quantificational definer ever// in sentence (3) of example HI. It should be clear that the user is not ~.qld~ about every morning for all time, hut only about all mornings during the planned trip. As with definite descriptions, our algorithm allows the restriction of most operators with semantically contentfifl restrictions i to be further specified by information from the QUD, so the interpretation of every morn/rig will differ depending on whether the dialogue began with question (la) or (Ib). Now, if it is the case that the Holiday Inn has a breakfast buffet on weekdays only, it is imp0rrant for the system to answer (3) appropriately, asin (4s) and (4b), depending upon the context created by (h) and (Ib).</Paragraph>
      <Paragraph position="1"> 4Domain restriction isnot usually applicable to pronouns and other expressions that have little explicit content, because these expressions depend on recovering a salient antecodent in order to determine the type of the refenmt, rather than searching for a l~icular type of object in the common ground.</Paragraph>
      <Paragraph position="2"> To determine the domain restriction for every morning, add_domain.xestrict ion searches the QUD for predicates that match the same basic type as the explicit restriction, morning. In this case, we take the basic type to be a temporal entity, so it will search for temporal descriptions in the QUD. s By using the QUD stack to constrain the search, every Will quantify over any temporal entities that are found at a level of discourse structure closest to the current segment, but crucially not over every tern* poral entity in the entire common ground. Thus, to determine the response in:(4a), only the date range mentioned in (la) is relevant, and a positive response can be given, since the question relates to weekdays.</Paragraph>
      <Paragraph position="3"> In (4b) however, the date range includes a Saturday, so the system should generate a negative response.</Paragraph>
    </Section>
    <Section position="4" start_page="7" end_page="8" type="sub_section">
      <SectionTitle>
4.4 Elliptical Questions: Example IV
</SectionTitle>
      <Paragraph position="0"> Example IV is a somewhat more complex dialogue, including an elliptical question as well as several definite descriptions. It illustrates how our approach generalizes ~ the larger class of presuppositional constructions which we identified in the in. troduction. Let. us focus on the interpretation of sentence (3), How about the Marriottg., which is assigned the following ULF: (ULF 8) Wa_~Up,i,\[~,~(~), ~\[x -, (de/\[y, Uotd(y) ^ Na~(y, ~a~), ?.s\])\]\] is a variable referring to some contextually salient question, and the de6nlte description correspondlnE to the Marriott is to be substituted for some term (X) within ~b. Recall that the variable ?NS is a placeholder for the ,,n~ecified nuclear scope of the def operator.</Paragraph>
      <Paragraph position="1"> our algorithm processes the logical form of an utterance ins/de-out, i.e., the embedded context resolution problems are handled first, so it first resolves the de/term corresponding to the Mar,'/o~ as we discussed in SS4.2 on definite descriptions, and add_domain.restriction produces the refined description (DEF 3&amp;quot;):</Paragraph>
      <Paragraph position="3"> Next, the top.level Wh.dlip~ris term in (ULF. 3) is resolved, according to the resolve.Y~ ~llipsis algorithm of Figure 3. ~ must be a question, sowe retrieve the question on top of the QUD stack, and attempt to identify ~ with its CULF (CULF 1).</Paragraph>
      <Paragraph position="4"> (C'Ur_,F '9 A\[=, H~d(z) ^ JV~,-(z, Airport), 3~1, Date(y), Has V acancyOn( z, y ) ~ SA complete explanation of this situation might require the system to infer the domain goals of the user. However, when the QUD contains some descriptions of the appropriate * type, we can use them as an approximate domain restriction, thereby avoiding the computational expense of full plan inference. null  We must now find a term within (CULF 1) for which the term corresponding to the Marriott can be substituted. Our matchksubscitute algorithm looks for terms whose restrictions specialize a common basic type, so it again findsthe restriction on the</Paragraph>
      <Paragraph position="6"> The operator and restriction of this term are replaced by those from (DEF 3&amp;quot;) and the variables are -nlSed, but the nuclear scope of (DEF 3&amp;quot;) is unspecified, so the nuclear scope of (CULF 1) rem~ unchanged in the result: (3&amp;quot;) clef\[z, Hotd(z ) A Named(y, M,rr/ott) A Near(z, AiT7x~t), 3\[y, D.ze(~), S.aVo~.q~.(z, y)\]\] (3&amp;quot;) is (almost) the CULF for How about the Marr/ottf, but it must be noted that it should be interdeg preted as a polar question, since the A-term characteristiC/ of a wh-question has been replaced by a definite descriptione Thus, both the elliptical question and the domain restriction of the definite description are processed by the same overall strategy. They are interpreted by incorporating information contained in the question under discussion.</Paragraph>
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