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<?xml version="1.0" standalone="yes"?> <Paper uid="W99-0113"> <Title>Discourse Anaphora Resolution*</Title> <Section position="3" start_page="110" end_page="113" type="metho"> <SectionTitle> 2 Centering Theory </SectionTitle> <Paragraph position="0"> CenteringTheory first described in detail in Gro~z, Joshi and Weinstein (1983, 1986 \[1995\]) is designed to provide an assignment of a preference order among discourse entities in a sentence for the purpose of anaphora resolution. Centering Theory, which built upon earlier work by Joshi and Kuhn (1979) and Joshi and Weinstein (1981, 1998), proposed that (1) is perceived to be more coherent than (2) because in (1) (I) (a) JeH helped Dick wash the mr. (b) He.</Paragraph> <Paragraph position="1"> washed the windows as Dick washed the car (c) Heb soaped a pane..</Paragraph> <Paragraph position="3"> washed the windows as Dick wazed the car (c) Heb b..~ed the hood. =.</Paragraph> <Paragraph position="4"> the referent for//~in (c) is D/ck while he, in (b) refers to Je~.</Paragraph> <Paragraph position="5"> We quote here from the concise description of Centering given in (Walker et.al., 1998b): The centering model is very simple. Discourses consist of constituent segments and each segment is represented as part of a discourse model. Centers are semantic entiUes * that ~re part of the discourse model for each utterance in a discourse segment. The set of vO~wxao-LOOKma C/~r~, Cj(vi~v) represeats discourse entities evoked by an utterance Ui in a discourse segment D (Webber 1978; Prince 1981). The \[unique\] BACKWARD-WOKmO c~-rza, C,(Ui.D) is a sp~l member of the C:, which represents the discourse entity that the utt~ance U most omtrally concermL ... The Ct entity links the current utterance to the previous discour~ ...(or not more thaa one) ... The set of I~01~WARDwoxmo cm~m~.s, C:, is ranked according to discom~ s~enm. This ranki~ is a part~ order. The hi~es~ ranking member of the set of forward-looking centers.., represents a prediction about the CGd the following utlterance. W~ker, Joshi, Prince (1998b) in Walker, Jochi, &quot; Prince 1998a henceforth WJP) p. 3.</Paragraph> <Paragraph position="6"> From a linguistic perspective (cL papers and references in Walker, Joshi and Prince 1998; Strube 1998), Centering theor/sts have explained the choice of C6 in a sentence in terms of a'large .number of potential factors. In particular: the grammatical hierarchy with subjects ranking higher than objects (Grosz, Joshi, Weinstein 1983), topic or empathy marking (Kameyama 198,5), surface order position (Rainbow, 1993) or grammatical function (Brennan, Friedman and Pollard 1987) of the encoding of discourse entities in the immediately preceding segment. null Roberts (1998) argues that C0 is an unordered setof backward-looking centers in terms of classical Discourse Representation Theory notions of familiarity, compatibility and logical accessibility (Kamp 1981, Helm 1982, Kamp and Reyle 1993, Asher 1993), with an additional constraint that the set of discourse referents are attentionally accessible, a notion taken from Grosz and Sidner (1986). Under Roberts' treatment, the set of preferred centers, takes the place of the original C6. Walker (1998) also replaces a unique Ct with a set of possible backward looking centers computed from a set of possible forward looking centers using agreement features, selection constraints of the verb and contra-indexing conditions. null The choice of segment also remains contested ground in Centering, with mint linguists choosing for the sentence or clause while Walker (1998), argues for integrating Centering with a more global model of discourse focus. Within computational linguistics, several Centering Algorithms have been proposed, most notably by Brennan, S, M. ~iedman and C. Pollard (1987), Walker, Iida and Cote (1990, 1994) and, more recently, by Strube and Hahn (1996), Strube (1998), and Walker (1998) which reflect these various perspectives.</Paragraph> <Paragraph position="7"> Although the several variants of Centering can be argued to be better suited to one or another task or to account for phenomena in one or another language, they all fail to account for the interpretation of common examples SUch as (3) s.</Paragraph> <Paragraph position="8"> (3) (a) Joan s went to ~ork at e~hZ. (b) B//g art/veal at n/he. (c) Th~+a met in the C/on/erence rOOl~ In (3), no entity in a single target clause or sentence resolves the plural pronoun in (3c). Thqa+a refers to a complex semantic entity created by combining entities in (3a) and (3b).</Paragraph> <Paragraph position="9"> In the reformulation of Centering in terms of Dynamic Quantifier Logic presented in Section 3, below, we show how multiple anaphoric elements can be handled and each assigned its preferred resolu-. tion. DQL allows us to calculate a preference ordering on the discourse referents that can be used to account for multiple anaphors refering to different antecedents. When paired withthe LDM, we also provide a means for one anaphor to refer back to multiple antecedents.</Paragraph> <Paragraph position="10"> with Dynamic Semantics. DQL was designed to handle phenomena such as plurals and complex relations between discourse referents often left unaddressed by other formal semantic frameworks (see van de Berg 1992,1996a,b).</Paragraph> <Paragraph position="11"> Dynamic Quantifier Logic is based on the observation that NPs are generally anaphoric, quantiflcationa\] and can be the antecedent of further anaphora, as illustrated by (4): (4) (a) The children I arrived at the natural history museum early in the morning. (b) Threes boys 2 disappeared in the girl shop. (c) The~ had a great time touching almost evert~ing.</Paragraph> <Paragraph position="12"> In (4b), thr~ boys is anaphoric: its domain of quantification is given by The chi/dre~ ,Within this domain, it is quantificatiunal:, there are exactly three boys that disappeared in the gi~ shop. Finally, it is an antecedent: it introduces a referent picked up by Theyl in (4c) to refer back to the three/w~.</Paragraph> <Paragraph position="13"> DQL, designed to explaia examples like (4), was d~ned to preserve as far as possible the prediction of its precursors while inheriting most of the/r results. Under DQL well known, solid results and established procedures remain tmehanL, ed. As. an illustration of a DQL representation of a sentence, take the simplified representation of (5b) below (5) (a) Some childrerf were playing in the backyar~ (b) Every= g/rP ~ wear/ng a hat,.</Paragraph> <Paragraph position="14"> (c) ~ had put ~ on belore ~ le# the house..</Paragraph> <Paragraph position="15"> (5'b) Vg C z (girl(y), ~ C_ * (hat(z), wear(y, z))) Formula (50o) states that/or ever g eat/ry that is a g/d, taken from the doma/n Siren by the d/scourse ngereat z', it is the case that there is a hat such tha~ she wmws iL This expremion is vew similar to clamcal umslatious into logic of Co). The only diffe~mco in the form of the expression is the explicit mention d the context set that sets the domain of . qumstiflcation. These context sets are given by dis-Course referents. The universal quantification Eve~ girl takes its range from the discourse referent =, and introduces a subset y, the indefinite a haPS takes its domain from an as yet unspecified domain (-).</Paragraph> <Section position="1" start_page="111" end_page="112" type="sub_section"> <SectionTitle> 3.1 Quantification and Reference Resolution </SectionTitle> <Paragraph position="0"> In DQL, all di~ourse anaphoric effects take place through discourse referents functioning as context sets to quantifiers. Variables that are quantified over 2 are introduced as discourse referents to function as :context sets in subsequent sentences.</Paragraph> <Paragraph position="1"> Although (Sb) introduces both referents y for the girls and z for the hats, the referents do not have equivalent status. This is caused by the quantificationaI structure. The set of girls is given as a simple subset of the set of children, and as such is readily available. The set of hats, on the other hand, is only introduced relative to the set of girls. The hats are not introduced independently, but rather are introduced indirectly as belonging to the girls. Referring back to the set of hats is much more computationally expensive than referring back to the set of girls; to refer to the hats we must implicitly refer to the girls relative to which the set of hats is defined.</Paragraph> <Paragraph position="2"> A consequence of the fact that the hats are introduced relative to the g/r/s, is that there is an implied ordering of the discourse referents that we use in reletting back to these sets. The discourse referent corresponding to the ~ is much easier to pick up from the conti~ than the discourse referent referring back to the hats s. Everything else being equal, the discourse referent referring to 'the g/r/a will be preferred over the discourse referent referring to the hats because accessing it requires less computation.</Paragraph> <Paragraph position="3"> * This preference order corresponds closely to the forward-lcoking centers C 1. However, there is nothing in the construction of the preference ordering based on complexity of retrieval sketched above that would lead us to believe that there is at most one backward-looking center. In fact, our treatment gives the same predictions as Centering for the first pronoun resolved, but results in different predictions for embedded auaphors. The foliowing diagram representing the scopes of (b) and (c) illustrates th!~: ==~vts/mts</Paragraph> <Paragraph position="5"/> </Section> <Section position="2" start_page="112" end_page="113" type="sub_section"> <SectionTitle> 3.2 Anaphera Resolution Preference Order </SectionTitle> <Paragraph position="0"> It follows from the argument we have laid out above, * that the referent I/in (e), is preferred for anapherie However, once the girk are available as a set :in(c) via u, the hats are ako available, via discourse referent z, to ser~ as an antecedent. The set of girls, being already available no longer adds to the computational burden of calculating the set of hats.</Paragraph> <Paragraph position="1"> Within the scope of they, the referent z is much more accessible than outside that scope.</Paragraph> <Paragraph position="2"> We can push this line of reasoning further. Consider example (Ta). In this example, the subject, 2Like y and z in (5'b).</Paragraph> <Paragraph position="3"> SThk is related to the discussion in Jmhi and Weinstein 1998, whiC/.h motivates Centering from the perspective of complexity of inference in discourse.</Paragraph> <Paragraph position="4"> Every amman, has scope over the object, a car. As (7-8) shows, the preferred center of the C! corresponding to this is the set of women because the cars are introduced as a function of the women. To refer correctly to the set of cars, we must also refer indirectly to the set of women since we are interested in retrieving only the cars owned by the women, not cars owned by men. On the other hand, to refer to the women, we need no information about their cars.</Paragraph> <Paragraph position="5"> This does not mean that we cannot refer to the cara in a subsequent sentence, as (gb) shows...</Paragraph> <Paragraph position="6"> (7) (a) Every waman in this town has a car.</Paragraph> <Paragraph position="7"> (b) They park them in their garages.</Paragraph> <Paragraph position="8"> Where the set of women is referred to with Theg, the cars can be.referred to directly. There is then no longer a hidden cost of retrieving the set of women in addition to the cars, since cars are already given in the sentence.</Paragraph> <Paragraph position="9"> But now consider (8) and (9): (8) (a) Every woman in this town has a car..</Paragraph> <Paragraph position="10"> (b) They use it to drive to work.</Paragraph> <Paragraph position="11"> (9) (a) Every t~oman in this town has a car.</Paragraph> <Paragraph position="12"> ~o) They are l~u'ked in their garages.</Paragraph> <Paragraph position="13"> Note that (7-9) are decreasin&quot; g in acceptability. (8) is more problematic than (7), because in (7) only the set of cars need be retaieved, while in (8) also the actual dependence of the carsonthe women that own them is invoked by the use of the singular ~. (9) is much less acceptable than either (7) or (8), because in (9) They refers to the cars without the help of an explicitly given set of women.</Paragraph> <Paragraph position="14"> The fact that once we have used a discourse referent, we can use other discourse referents that depend on it has important consequences as soon as we consider anaphora more complex than pronouns. Consider exmnple (I0)..</Paragraph> <Paragraph position="15"> (10) (a) Seventeen people 1 in our lab have their own cmnputer~. (b) Three o~f themt are silly and them~ oD ~ n~L h (10a), a discourse referent d~ to aset of seventeen people is introduced, and as well as a discourse referent d~ to a the set of computers they own, which depends on ds. In (10b), Three o! them quantifies over the domain given by all, and states that within dh there are exactly three people who switch their demand a plural here as in (7), seemingly preferring semantic number agreement over syntactic number agreement. However, syntactic agreement does occur, as the following example illustrates: ~ sotd/er/, neqmu/bte lot ~ own gun. He haJ to dean it and will be reln'imandd i\] anll dirt is found on it. :!deg&quot; own computers off every night. If the discourse referent introduced by their own computers would simply refer to the set of computers owned by people in the company, and not be dependent on the people, them2 would refer to this set, rather than only to the set of computers owned by the three people. The meaning of (10b) would then be that these three people switch off all computers in the company, not just their own. This, of course, in not the correct reading.</Paragraph> </Section> </Section> <Section position="4" start_page="113" end_page="113" type="metho"> <SectionTitle> 4 Quantifier Scope and Anaphora </SectionTitle> <Paragraph position="0"/> <Section position="1" start_page="113" end_page="113" type="sub_section"> <SectionTitle> R~-solution </SectionTitle> <Paragraph position="0"> Under our analysis, the preferred antecedent for a pronoun is based on computational complexity arising from universal facts of scope ordering in the logical representation of the antecedent utterance. Different approaches to centering will be better or worse at predicting ordering relations depending on the match between the ordering scheme decided upon and the underlying scopal ordering.</Paragraph> <Paragraph position="1"> We argue as follows.</Paragraph> <Paragraph position="2"> If the discourse referent A is introduced by a term that has scope over a term introducing discourse refe~.nt B, and discourse zefe~ent B is introduced by a term that has scope over discourse referent C, A will be preferred over B and B will be preferred.</Paragraph> <Paragraph position="3"> over C. Since this explanation is not dependent on conventions that might be different in different languages our treatment is universal. This is not the case for explanations based on linear ordexing of syntactic constituents or arguments based on gemnmatical function, for example. Because in .Engli~ the subject has scope over the objects, and the objects have scope over more deeply embedded terms, the ordering of discourse rderents familiar to us from the literature will result in the well known C! predictions. null Rejecting a preferred ordering for a less preferred ordering is a computationally complex operation.</Paragraph> <Paragraph position="4"> First the preferred order is computed, then this analis rejected ---perha~ on pragmatic grounds.</Paragraph> <Paragraph position="5"> The calculations must then be re-done and the resulting less preferred ordering checked to see if it fits * the pragmatic facts of the situation described in the target utterance. Differences ha computational complexity arising from rejecting more prderred interpretations for less preferred thus result in the judgments of relative coherence which have been noted in the literature. Our account thns explains how Centering effects originate and why some anaphoric choices may involve more attention to the referent retrieval process than others s.</Paragraph> <Paragraph position="6"> SThe DQL formalism has been explicitly designed to look as similar as peasible to weIl-lmown, standard logiel. &quot;1&quot;o argue about issum of acceesibility of the referents, a logical system that is le88 natural, but externalizes the dependencies between</Paragraph> </Section> <Section position="2" start_page="113" end_page="113" type="sub_section"> <SectionTitle> 4.1 Acceptability Predictions </SectionTitle> <Paragraph position="0"> To return then to examples (1) and (2), reproduced here as (11) and (12) (11) (a) Jeff helped Dick wash the car. (b) Hea washed the windows as Dick washed the car (c) He6 soaped a pane.</Paragraph> <Paragraph position="1"> (12) (a) 3e~ helped Dick wash the car. (b) Hee washed the windows as Dick waxed the car (c) Heb bused the hood Since the d iscom-se referent Jell is introduced bY a term that has scope over a term introducing discourse referent D/ck, Je~ will be preferred over D/ok The difference in perceived coherence between (1/11) and (2/12) falls out of the more general fact that wide scope quantifiers are preferred over narrow scope quaatifiers.</Paragraph> <Paragraph position="2"> We will now turn to discussing how discourse structure and Anaphora Resolution interact to produce different acceptability predictions for different structures of discourse.</Paragraph> </Section> </Section> <Section position="5" start_page="113" end_page="115" type="metho"> <SectionTitle> 5 Discourse Structure and Anaphora </SectionTitle> <Paragraph position="0"/> <Section position="1" start_page="113" end_page="113" type="sub_section"> <SectionTitle> Resolution </SectionTitle> <Paragraph position="0"> Although Centering Theory is associated with the Discourse Structurm Theory of Gr~z and Sidner (1986) which considers speaker intention and hearer attention as the critical dimensions to be modeled in discourse understanding, there are alternative models for understanding the relations among utterances in a discourse which are based on other principles. In particular, Dynamic Quantifier Logic, the anaphora resolution mechanism based on quantifier scope we are working with here, has been designed to provide the semantic machinery for the Linguistic Discourse Model (LDM). The LDM provides an account for discourse interpretation in terms of structural and semantic relations among the linguistic constituents making up a discourse e.</Paragraph> </Section> <Section position="2" start_page="113" end_page="114" type="sub_section"> <SectionTitle> 5.1 The Linguistic Discourse Model </SectionTitle> <Paragraph position="0"> The LDM is designed as a discourse ~ designed to construct a meaning representation of the input discourse icrementally. The LDM treats a discourse as a sequence of basic discourse units (evue) ranges of values for ~ might be more suitable, such as liar to DO~ we thank eae mmaymous revumer mr pomung out the work of Ranta (1991), who's use of Marthz-16Ps type theory, m~ atso be suttsble ts a~ anal3~t8 tool ela Prfmt, Scha and van den Berg 1991, * resolution mechanJmn for unification based discourse grammar for verb phrase anaphom is defined, in terms of the Linguistic Discourse Model (LDM; PolanyJ and Scha 1984;. Polanyi 1987, i988.</Paragraph> <Paragraph position="1"> 1996), which takes semantic representations as input. This treatment was later extended to a unification based discourse grammar actinf~ on dynamic quantifier logic in Polanyi 1996, van den Berg and Polanyl 1996. The current paper extends that work.</Paragraph> <Paragraph position="2"> ,qp each of which encodes formal semantic, syntactic and phonological properties of either an elementary predication or a discourse function. Using rules of discourse wellformedness whiCh specify how to compute the relationship between a BDO and the previous discourse, the LDM constructs a parse tree by successively attaching the SVUs to a node at the fight of edge of the emerging tree. The nodes of the tree are called Discourse Constituent Umts (VCUS) 7.</Paragraph> <Paragraph position="3"> DCUs encode formal semantic, syntactic and phonological properties that are calculated by following construction rules corresponding to the relationship computed as a result of the attachment process.</Paragraph> <Paragraph position="4"> The discourse parse tree represents the structural relations obtaining ~Lmong the DCUs. There are three basic types of relations among DCUs: Coordination, Subordination and Binary Re!A_tion. Corresponding to these relations, a DCU can be attached at a node on the right edge of a tree in one of three waysS: 1. The input DCU will be Coordinated with a node present o n the fight-edge of the tree if it contin* ues a discourse activity (such as topic Chaining or narrating) underway at that node.</Paragraph> <Paragraph position="5"> 2. The input DCU win be Subordl,a~ted to a node on the right-edge of the tree if it elaborates on material expressed at that node or if it interrupts the flow of the discourse completely.</Paragraph> <Paragraph position="6"> 3. The input DCU will be Binary-attached to a node if it is related to that node in a logical, rhetorical or interactional pattern specified explicitly by the grammar.</Paragraph> <Paragraph position="7"> The LDM is a compesitional framework. Simnltaneoas with the incremental construction of the struco tural representation ofthe discourse by attaching incoming DCUS, a semantic representation of the meanink of the discourse is constructed by incorporating the interpretation of an incomi-~ ~ in the ~mantie representation on the discourse.</Paragraph> <Paragraph position="8"> The LDM a~m~ts for both structural and semantic aspects of discounse parsing using logical and structural notions analogous to units and p~ constituting lower levels of the linguistic hierarchy. It is an ideal framework for tmdenmmding the relatioas between sentential syntax and semantics, on the one hand, and on the other hand, the texts and ~teractious that are constructed using sentential linguistic structures.</Paragraph> <Paragraph position="9"> ?BDU8 once attached to the tree are DCU8.</Paragraph> <Paragraph position="10"> -8Baside8 these three basic composition relations between ncus, a complex ncu can also he constructed by an operator having a ncu as an argdment and within mmtences, a ncu can occur embedded in another DcU. These two cases wiU not be d~umed here.</Paragraph> </Section> <Section position="3" start_page="114" end_page="115" type="sub_section"> <SectionTitle> 5.2 Reference Resolution in the Linguistic Discourse Model </SectionTitle> <Paragraph position="0"> Let us now look at several short example of the interaction of anaphora resolution with discourse structure using the Dynamic Quantifier Logic framework above.</Paragraph> <Paragraph position="1"> (13) (a) Susan came home late yesterday. (b) Doris hod held her up at work. (c) She needed help with the copier.</Paragraph> <Paragraph position="2"> In (13) the relationship between vco (13a) and Dco (13b) is a Subordination relation because (13b) supplies more detailed information about why Susan came home late. As is shown in (13a), the S node inherits all information about the dominating VCO. In this case (a). A representation of Susan is therefore available at this constructed node. (13e) gives more explanation about what went on when Doris held Susan up at work and is therefore Subordinated to (b). Susan and Doris available for reference at that node. In (14) the situation is different.</Paragraph> <Paragraph position="3"> (14) (a) Susan came home late yesterda3l. (b) Doris had held her up at worl~ (e) She didn't ~oen have time \]or dinner. (13') ~-~ (14')~.~., Although the relationship between DCU (14a) and DCU (14b) is a Subordination relation, as shown in (14a), as the di~ourse continues with (14c), the state of the discourse POPS from the embedded explanation to continue describing the state of affairs of Sasan's evening. (14c) is therefor~ in a Coordination relation with (14a) as shown. Only Susan is now available as a potential referent in the current context.</Paragraph> <Paragraph position="4"> In fact, the antecedent of an anaphora need not be one specific earlier utterance, but may be a constructed higher node in the parse tree as in (15): In this case, the antecedent of (15c) is not (15a) or (15b), but the discourse node that constitutes the list (15a+b). In this higher node, there is a constructed schematicrepresentation of what (lSa) and (15b) share, and They is resolved to this. Very schematically, it amounts to resolving the anaphor X to the outer quantifier of its antecedent, Ql+2.</Paragraph> </Section> </Section> class="xml-element"></Paper>