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<Paper uid="C92-2109">
  <Title>A CONSTRAINT-BASED APPROACH TO TRANSLATING ANAPHORIC DEPENDENCIES</Title>
  <Section position="3" start_page="0" end_page="0" type="metho">
    <SectionTitle>
1. Introduction
</SectionTitle>
    <Paragraph position="0"> The normal method for representing anapboric dependencies in Unification Based (UB) grammar formalisms is that of re-entrance (often indicated graphically by means of subscripts, as in (lb)). The interpretation is that two or more attributes share (are pointers to) a single value. In the case of (1), the SUBJ of try is identical to that of employ. This means that changes to the value of the SUBJ of try (e.g. the addition of another feature) are necessarily changes to the value of the SUBJ of employ.</Paragraph>
    <Paragraph position="1"> This token identity should be distinguished from the type identity between these values, and the value of the OBJ attribute in (lb), which just happens to have the same attributes and values.</Paragraph>
    <Paragraph position="2"> (la) Linguists try to employ linguists.</Paragraph>
    <Paragraph position="3"> This device can be thought of as the attribute-value equivalent of a bound variable of logic, and though it is not appropriate for all kinds of anaphoric dependence, it is ubiquitous.</Paragraph>
    <Paragraph position="4"> This paper proposes a novel approach to the treatment of re-entrances in translation, which overcomes the problems of existing approaches using UB formalisms. These prob-</Paragraph>
  </Section>
  <Section position="4" start_page="0" end_page="0" type="metho">
    <SectionTitle>
KCOMP ISUBJ fl\[\]
</SectionTitle>
    <Paragraph position="0"/>
    <Paragraph position="2"> lems are considerable, but have been generally ignored in the literature. Section 2 will review existing approaches, pointing out the problems.</Paragraph>
    <Paragraph position="3"> Section 3 describes the approach, which provides a straightforward treatment of cases where filler-gap dependencies are subject to different constraints in source and target languages (e.g.</Paragraph>
    <Paragraph position="4"> where one language allows, and the other forbids, Preposition Stranding). In exemplifying this, we will focus on the treatment of relative clauses. 1</Paragraph>
  </Section>
  <Section position="5" start_page="0" end_page="0" type="metho">
    <SectionTitle>
2. Existing Approaches
</SectionTitle>
    <Paragraph position="0"> 2.1. Transfer Bused (Structural) Approaches.</Paragraph>
    <Paragraph position="1"> Perhaps the most obvious way to use a LIB formalism for translation is to use a standard UB grammar formalism in analysis to produce a feature structure (FS), which is a collection of attribute-value (A:V) pairs. This is then mapped to a target FS by means of a bilingual grammar of transfer rules whose left-hand-sides (lhs) are matched against the source structure, I ~h(c)rC/, we dL~ctma ca~,es where filler-gap ~ntkndm in one language oorreapond to antecedent-pco~oun dependencies in another.</Paragraph>
    <Paragraph position="2"> ACrEs DE COLING~92, NANTES, 23-28 ao~r 1992 7 2 8 Pgoc. OF COLING-92, NANTES, AUG. 23-28, 1992 and whose fight-hand-sides (rhs) indicate the content of the corresponding target FS. These rules are applied recursively to successively smaller collections of source language A:Vs.</Paragraph>
    <Paragraph position="3"> This is, of course, just a straightforward adaptation of the traditional transfer method to a A:V data structure in place of a tree, in particular, it re~mbles a classical transt~:r system in being 'structural' i.e. in involving the decomposition of source structures into smaller objects (on the lhs), and the actual construction of target strUctures (on the rhs). This is essentially the approach employed in ELU (Estival et al 1990) and MiMo2 (van Noord et al 1990).</Paragraph>
    <Paragraph position="4"> Though there is not much discussion of the treatment of referential dependencies in tmnst'er in these formalisms, it is easy to see how one can deal with re-entrances which naturally fall within the scope of one transfer rule. In ELU, tot example, such re-entrances can be translated by binding the re-entrant paths within the structure to rite same variable and stating n correspondence between the relevant source side and the target side variables, in this way the re-entrance is translated as one structure. In MiMo2 the re-entrant paths are separately translated, but the re-entrance is explicitly mentioned on source and target side, requiring token-identity between the results of the separate translations. However, these structure based formalisms do not have any method for geucral~ing this to cases where re-entrances are not 'local'. This is serious, because phenomena classically regarded as involving Wh-Movement (e.g. Wh-Questions, Topicalization, Relativisation, etc.), are typically of this kind, and for these phenomena, the formalisms can provide no general treatment.</Paragraph>
    <Paragraph position="5"> Of course, there are a number of ways in which one might try to remedy this inadequacy.</Paragraph>
    <Paragraph position="6"> For example, one could unfold the re.entrances as type identities (i.e. reinterpret the DAG as a tree), or 'thread' shared values through the structure, in such a way that they become local (cf. standard gap threading techniques to reduce unbounded dependencies to local ones). However, none are satisfactory. The former looses information, so that source FS and target FS are no longer equivalent, and causes problems in generation, where some method must be found for ensuring that lexical content is not duplicated, and appears in the right place). Threading techniques are unattractive because of the (often extreme) complication they introduce in grammars and representations. 2</Paragraph>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
2.2. Constraint Based Approaches
</SectionTitle>
      <Paragraph position="0"> In this section, we will outline the approach to the translation of non-local re-entrances proposed in Kaplan et al (1989).</Paragraph>
      <Paragraph position="1"> In LFG projections are linguistically relevant mappings or correspondences between levels, whether these mappings are direct or involve function composition (Kaplan (198&amp;quot;0, Halvorscn and Kaplan (1988), Dalrymple (1990) and Dalrymple et al (1990)). By means of these projections, equations can be stated which codescribe elements of the two levels related by the projection. The standard projections are V (normally expressed in terms of t and ~,, from c-structure to f-structure), and o (variously from c- and f-structure to semantic structures).</Paragraph>
      <Paragraph position="2"> Kaptan et al extend this approach to provide what amounts to a transfer lormalism for LFG. 3 In their proposal, the equational language of LFG is used to state bilingual constraints or correspondences between elements of source and target structures. They introduce mapping functions x (between f-structures) and T' (between semantic structures). Achieving translation can be thought of ns specifying and resolving a set of constraints on target structures, constraints which are expressed by means of the &amp;quot;~ and x' functions.</Paragraph>
      <Paragraph position="3"> The formalism permits a wide variety of source-target correspondences to be expressed: and ap can be composed, as can x' and o. Equalions specifying translations are added to (source language) lexiual entries and c-structure rules.</Paragraph>
      <Paragraph position="4"> For example (2) composes &amp;quot;~ and ap, identifying the 'r of the (source) SUBJ f-structure with the SUBJ attribute of the x of the f-structure associated with some node (the value of t), indicating that the translation of the value of the SUB3 slot in a source fdegstructure fills the SUB3 slot in the f-structure which is tile translation of that source 2 The possibility of a 'threading' aplnoech ia hinted at in van Noord et d (1990). The formalism described in Pu\[man (ed) (1991) seems to allow an intc~ating variation, where instead of threading infonalatiotl about non-local re-eaatmnee throttgh the ~oorce atmetom, it in threaded through the 'virtual' atructur~ that am built the tmlmfer mechanisms reeura~ through the aoenee structure. This still tk~e~ nol avoid the htmic objection to the toe of auch techhiquea, however.</Paragraph>
      <Paragraph position="5">  3 See Sadler ,t a/ (1990), Sadler and Thompson (1991), and Fmdler (1991) for further disctmaion of this apl~oach to MT.</Paragraph>
      <Paragraph position="6"> ACtES DI&amp;quot; COLING-92, NAmEs. 23-28 ^oral' 1992 7 2 9 l'goc, oV COLING-92, NA~'rEs, AUO. 23-28, 1992 f-structure.</Paragraph>
      <Paragraph position="7"> (2) T(tStmJ) - (Tt SUm)  In this approach, then, relations between different types of linguistic description (i.e. levels) are defined in terms of correspondence funetiom, not by means of the re.cursive application of rules to source language structures. In particular, notice thai tmmfer does not opomte compositionally on a source language feature structure, rather the analysis procedure collects sets of constraints on various structures, including ('0 constraints on target structures. The solution of a set of z equations is a (probably incomplete) target f-structure which must then be completed and validated by the target grammar. This allows information which is exhaustively determined by the target grammar to be ignored in the transfer prooms. 4 In this sense, the system is constraint-based, rather than structure baaed like the approaches described in 2.1. above, and it has different expteasive possibilities. null As regards relative clauses, Kaplan et al assume a reasonably standard LFG analysis: wh-relatives are represented as an attribute (here RELMOD) which contains a re.untrunce between the values of a RELTOPIC plLrese and a within-clause function (see (8) below). The approach to translating these dependencies involves stating separate correspondences for both the within clause function and the RELTOPIC function.</Paragraph>
      <Paragraph position="8"> For a simple example like (3), with English as source language, the rules are as in (4-7) and the English and (incomplete) French f-structures as in (8) and (9) (the indices here are simply informal devices to allow easy reference to pieces of f-structure).</Paragraph>
      <Paragraph position="9"> (3)a. The man who I saw.</Paragraph>
      <Paragraph position="10"> b. L'homme que j'ai vu.</Paragraph>
    </Section>
  </Section>
  <Section position="6" start_page="0" end_page="0" type="metho">
    <SectionTitle>
4 For * target tentence to be * Iran~tlon of *
</SectionTitle>
    <Paragraph position="0"> tource tente~e, the minimal ~mcture aatigned to the Utrget teatznce by the argot grammar mntt be *ubturned by the mlnim*l solution of the * and Z' coe-</Paragraph>
    <Paragraph position="2"> In the functional uncertaimy equation in (5), {XCOMP,COMP}* allows the 'gap' associated with the RELTOPIC to be inside zero or more COMPs or XCOMPs, and GF is an abbreviation for a set of paths including length one paths such as SUBJ, OBJ, etc., and paths of length two, such OBLto OBJ, which allows preposition stranding, as in man who i I replied to Hi</Paragraph>
    <Paragraph position="4"> The equations on rule (4), which are specifically for dealing with relative slrnctmr, s, are quite simple in themselves, and combine</Paragraph>
  </Section>
  <Section position="7" start_page="0" end_page="0" type="metho">
    <SectionTitle>
6 We ~umo that PRED-'QUE' ,ul~um~ the
</SectionTitle>
    <Paragraph position="0"> vmanta qua, qui,/aq~//e, (c)tc.</Paragraph>
    <Paragraph position="1"> S ACTas DE COLING-92. NANTES, 23-28 Aot~r 1992 7 3 0 PRoc. OF COLING-92. NANTES) AUG. 23-28. 1992 with the equations given in the lexical entries (6) and (7) to create a re-untrance in the target structure (9) corresponding to that in (8). This can be seen by looking at the relevant constmints, in (10), which are derived from these roles in relation to (8) and (9). Since x is a function, ( fx RELTOPIC) and ( ft OBJ) must he the same token. Hence the desired re-entrance falls out automatically.</Paragraph>
    <Paragraph position="3"> Thus, it appears that, in principle, this approach requires neither the addition of special apparatus, nor modifications to the treatment of grammatical phenomena that do not involve reentrance. null Unfortunately,, this approach is only capable of producing intuitively correct structures in cases where the conditions on unbounded dependencies are parallel in the source and target languages. On closer inspection, the example Kaplan et al use to demonstrate their approach does not work correctly, giving the ungrammatical (11c) instead of the correct (llb). (11)a The letter which I have answered.</Paragraph>
    <Paragraph position="4"> b. La tettre h laquelle j'ai r~pondu.</Paragraph>
    <Paragraph position="5"> The letter to which 1 have responded c. *La lettre laquelle j'ai r~pondu h.</Paragraph>
    <Paragraph position="6"> The letter which I have responded to The c-structure rules and annotations required here include (4) and (5), and the lexical entry for answer, which includes the information in (12). The source f-structure produced by these roles is (13).</Paragraph>
    <Paragraph position="8"> From these rules, the following x equations arise, in relation to (13):</Paragraph>
    <Paragraph position="10"> However, these yield the incorrect f-structure (15) (if we assume details filled in from the monolingual gmmrrmr), corr~ponding to the ungrammatical string (11c), with a strande, d</Paragraph>
    <Paragraph position="12"> The pmhtem in this case arises because the relativised p~itiom in English and French are not identical. Although it seems at flint sight that the approach nicely preserves re-entrances in tramlation, in fact what happens is that the source grammar dictates what will be re-entrant on the target side. Thus, though the Kaplan et al approach provides a simple method for projecting source language re-entrances onto the target language structures, the method is insufficiently flexible in the scope allowed for variation between source and target structures.</Paragraph>
  </Section>
  <Section position="8" start_page="0" end_page="0" type="metho">
    <SectionTitle>
3. Using Underspeclflcatlon
</SectionTitle>
    <Paragraph position="0"> Characteristic of the approaches de.acrthed in 2.1. and 2.2. is that they mmslate beth 'ends' of a re-entrance. Because in structure based systems the translation relation is defined entirely by rules, the scope of the re-entrances that can be handled is limited by that of rules. A constraint based approach avoids this problem -under the approach described in 2.2 separate x correspondences are supplied for both paths involved in the re-entrance (both the source RELTOPIC, and the source within-clause function). Because these correspondences apply x to f-structure descriptions which evaluate to the same object, a target re-entrance is automati7 'l'his representation embodiee an number of que~tiotmble ~umptiotm about the treatment of r, which not relevant to the di~u~io~.</Paragraph>
  </Section>
  <Section position="9" start_page="0" end_page="0" type="metho">
    <SectionTitle>
ACRES DE COLING-92, NAN'I .a~s, 23-28 AOt)r 1992 7 3 l PROC. OV COLING-92, NAi~rES, AUG. 23-28, 1992
</SectionTitle>
    <Paragraph position="0"> ually established, whose value is the translation of this object. However, as we have seen, this approach does not permit factorization of source and target oriented information in these cases.</Paragraph>
    <Paragraph position="1"> In this section we will explore a solution to this problem which involves restricting &amp;quot;~ correspondences to just one of the paths involved in the source re-entrance, allowing a constraint based treatment of cases including those in (11) above. 8 Tiffs possibility is not easily available in 'structure based' approaches, and represents a genuine advantage of a constraint based approach.</Paragraph>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
3.1. Different Re.entrances in Source and
Target
</SectionTitle>
      <Paragraph position="0"> Suppose that no &amp;quot;~ equations are stated on the c-structure rules introducing the RELTOPIC attribute, and a &amp;quot;c correspondence is stated only over the path terminating in the within clause (thematic) function. What results would be a French f-structure like (16), which differs from (15) only in the absence of a RELTOPIC, and would correspond to the string j'ai r~pondu h laquelle ('I have responded to which'):</Paragraph>
      <Paragraph position="2"> In order to produce an f-structure corresponding to (lib), i.e. a translation of (lla), we must ensure that an appropriate value for a RELTOPIC attribute is given. There are three sources of potentially useful information here.</Paragraph>
      <Paragraph position="3"> First, there is some source-oriented information -- the solution to the functional uncera Kaplan tt a/propose jmt such n treatment in cases like the trantlmtion of J~hn is likely to su Mary -- II C/~tt probab/C/ qu*, ./tan wrra Mar/C/. No X ~rrenlm,adence is given for the SUBJ of I/kc/y, ~ the f-stntclure laumnlatad with John i8 only related to s target f.~OucturC/ in the thematic imeitiom (SUBJ ot r ate). The French monolingual lexicx~ supplies in expletive SUBJ for pcobab/t. However, Kaplan #t a/ do not considC/~ the pt~dbility of dealing with 'unbounded' re.entrances in this way.</Paragraph>
      <Paragraph position="4"> tainty equation associated with the XP node in the English c-structure. The solution of the functional uncertainty equation in this case happens m be (tRELTOPIC)-(tOBJ). By me application of a general schema, we can derive a x equation from this, which in this case is (17), which (again in this case) is equivalent to (18).</Paragraph>
      <Paragraph position="5">  (17) (xt RELTOPIC)- T(t O13.1) (18) (x? RELTOPIC) - (xtOBL~o O13.1)  The method for doing this involves taking the functional uncertainty, namely tRELTOPIC = t{XCOMP,COMP}* GF, and adding (xtREL-TOPIC)-x(ta ) lbr every solution ct of the uncertainty on the right-hand side. This gives (18) as one solution.</Paragraph>
      <Paragraph position="6"> Of course, this cannot simply be added to the other x equations (if it were, it would establish a re-entrance between RELTOPIC and OBLso O13.I, which would give an ungrammatical result, with a stranded preposition, as in (11c) above).</Paragraph>
      <Paragraph position="7"> Second, the monolingual target grammar will contain a constraint to ensure that, if RELTOPIC is present, some path within the RELTOPIC attribute contains the attribute value pair WH-+. This is required to prevent the 'topicalizing' (i.e. wh-movement fronting within the relative clause) of any XP which does not contain a wh-phrase. Simplifying slightly, we take this equation to be: (19) (T RELTOPIC{OBJ, POSS}* WH) -c+ Third, the target grammar itself contains a functional uncertainty equation for establishing a relation between RELTOPIC and some within-clause function, which, for the sake of argument we could assume to be us in (20).</Paragraph>
      <Paragraph position="8"> Notice that this is more restrictive than the corresponding English constraint, which allowed identity between the values of a wide variety of GFs and the RELTOPIC. This restricts it to SUBJ, O13.I, and 'thematic' OBLiques (which includes OBLgo), excluding the possibility of preposition stranding.</Paragraph>
      <Paragraph position="10"> Intuitively, the source-derived equation (18) is used to provide the information that there should be a RELTOPIC attribute in the AC1T.S DE COLING-92, NANTES. 23-28 AOt~n&amp;quot; 1992 7 3 2 P~oc. OF COL1NG-92. NAN'\] ES, AUG. 23-28, 1992 target f-structure. It can he interpreted defcasibly in combination with the target information to lind the closest possible solution consistent with the target grammar. This closest solution emerges from comparing the constraint with the functional uncertainty equations for the target language. In the case of relative clauses, at least, there are two target functional uncertainty equations o- the first expresses a re-entlance between the value of RELTOPIC and the value of some within clause function, and the second requires RELTOPIC to contain a WH~+ path ((1.9) and (20)).</Paragraph>
      <Paragraph position="11"> If the source-derived equation is consistent with the target constraints, then it is chosen. If it is not, then the closest solution is chosen. Note that the shortest path in (19) would have just the wh-item in RELTOPIC (the OBJ of the preposition). But this is ruled out by (20), which disallows OBLg o OBJ as the hottom of the mm~rtainty path. The &amp;quot;closest&amp;quot; solution is defined as the pemfissibie solution whicfi contains the minimal solution of the equation  (19) (which requires RELTOPIC to contain a +WH item). In this case, that solution is: (21) (1' OBL~o) - (1' RELTOPIC) (22) (~' RELTOPIC OBJ WH) - +  In cobiuation with the other constraints, this will give a representation like (23), corresponding, to (11)b, as intended.</Paragraph>
      <Paragraph position="12">  In this case, since French requires pied-piping rather than preposition stranding, the closest solution turns out to be the one which involves the attribute-value structure which contains the one specified in the source-oriented constraint, with no other containing possible structure intervening. But the mechanism can be applied equally well to derive &amp;quot;smaller&amp;quot; RELTOPIC phrases from &amp;quot;larger&amp;quot; structures, as in the English -* French pair in (24), and can be extended to deal with 'strategy mismatches' of the kind exemplified in (25), whine a 'gap' in one language corresponds to a resumptive pronoun in another (see Arnold and Sadler 1992). (24)a The nmn \[ whose wife \]i 1 have seen \[\]i b L'homme dout i j'ai vu \[ la femme \[\]i \] the man of-who I-have seen the wife (25)a l'uomo ehe mi donmndn \[ chi abbia vista \]\] h the manl of whom I wonder who l hel saw \[\]j It is worth considering why this sort of method is not readily usable in 'structure bused' approaches. A~,~ here, the basic idea would be to translate the material in rite within clause position only, ignoring the RELTOPIC position, and then create a re-entrance on the target side.</Paragraph>
      <Paragraph position="13"> There are at least two problems. First, in stun&gt; tuml approaches, the normal operation of lmnsi~er requires soure kind of completeness check to eusure that all parts of the source structure are translated. Nomlally, this can be interpreted as a check that every path in the source object has been visited. Thus, for this approach to work, one would need rule.,; that explicitly translate the value of RELTOPIC us nil ('deleting' it). One could, alternatively, try to redefine completeness in terms of translation of all values (since the RELTOPIC and the within clause position have the same value, translating either would count as translating both). This would mean one could avoid the rules explicitly deleting the RELTOPIC, but it is not clear what consequences it would have elseo where. The second problem is more serious. The output of transfer will produce a structure like man \[ \[\] 1 have seen who\], and one will need roles to create a link between the RELTOPIC position (/\]), and who. But one cannot, in gen~ eral, assume that such rules will exist. For example, they will not exist if the target grammar creates links as part of the parsing process titat creates A:V structures (e.g. if they are associated with c-structure rules), and even if they ate rules that can be applied to already condeg structed A:V structurns, it cannot be guaranteed that they will apply to configurations such as this (since they will have been written to apply to cases where the lexical material (who) fcommands the 'gap'; but in the structures output from transter, the relationship will be the reverse.</Paragraph>
    </Section>
  </Section>
  <Section position="10" start_page="0" end_page="0" type="metho">
    <SectionTitle>
Ac'l~s I)E COLING-92, NAmI.:S, 23-28 AOl'rr 1992 7 3 3 Prtoc:. OF COLING-92, NANII.:S. AUG. 23-28. 1992
4. Conclusion
</SectionTitle>
    <Paragraph position="0"> We have shown in this paper that the approach to transfer between feature structures introduced in Kaplan et al 1989 can be exploited to deal with the translation of anaphoric dependeneins. Our proposal exploits the constraint based (rather than structure based) nature of the approach, and the flexibility that comes from being able to underspecify various parts of the translation relation, and allow infornmtion (i.e. constraints) from source language, and target grammar to interact with bilingual information.</Paragraph>
  </Section>
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