A CONSTRAINT-BASED APPROACH TO 
TRANSLATING ANAPHORIC DEPENDENCIES 
Louisa 5'adler 
Doug Arnold 
Department of Language & Linguistics, 
University of Essex, Wivenboe Park, 
Colchester, CO4 3S0, UK 
(louisa@esscx.ac.uk;doug@essex.ac.uk) 
Abstract 
The normal method for representing ana- 
phoric dependencies in Unification Based gram- 
mar tbrmalisms is that of re-entrance. In this 
paper, we address the problems that this 
representational device poses when such formal- 
isms are used for translation. We demonstrate 
the inadequacies of existing proposals, and 
describe an approach which exploits the expres- 
sive possibilities of the equational constraint 
language in LFG and involves an inferential 
procedure combining undempecification in the 
statement of bilingual correspondences with the 
use of target language knowledge. 
1. Introduction 
The normal method for representing ana- 
pboric dependencies in Unification Based (UB) 
grammar formalisms is that of re-entrance 
(often indicated graphically by means of sub- 
scripts, as in (lb)). The interpretation is that two 
or more attributes share (are pointers to) a sin- 
gle 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. 
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. 
(la) Linguists try to employ linguists. 
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. 
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- 
(lb) 
"PRED 'try<SUBJ, XCOMP>' 
fPRED 'linguist" / 
SUBJ fl \[IIUM PL 
\[PERS 3rd 
PLIED 'employ<SLrBJ, OBJ>" 
KCOMP ISUBJ fl\[\] 
/ \[PRED 'linguist' \] 
PL / 
\[ \[PE~s 3rd \] 
lems are considerable, but have been generally 
ignored in the literature. Section 2 will review 
existing approaches, pointing out the problems. 
Section 3 describes the approach, which pro- 
vides a straightforward treatment of cases where 
filler-gap dependencies are subject to different 
constraints in source and target languages (e.g. 
where one language allows, and the other for- 
bids, Preposition Stranding). In exemplifying 
this, we will focus on the treatment of relative 
clauses. 1 
2. Existing Approaches 
2.1. Transfer Bused (Structural) Approaches. 
Perhaps the most obvious way to use a 
LIB formalism for translation is to use a stan- 
dard UB grammar formalism in analysis to pro- 
duce a feature structure (FS), which is a collec- 
tion 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©r¢, we dL~ctma ca~,es where filler-gap 
~ntkndm in one language oorreapond to 
antecedent-pco~oun dependencies in another. 
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. 
This is, of course, just a straightforward adapta- 
tion 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 strUc- 
tures (on the rhs). This is essentially the 
approach employed in ELU (Estival et al 1990) 
and MiMo2 (van Noord et al 1990). 
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 natur- 
ally 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 men- 
tioned 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, Relativisa- 
tion, etc.), are typically of this kind, and for 
these phenomena, the formalisms can provide 
no general treatment. 
Of course, there are a number of ways in 
which one might try to remedy this inadequacy. 
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). How- 
ever, 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 dupli- 
cated, and appears in the right place). Threading 
techniques are unattractive because of the (often 
extreme) complication they introduce in gram- 
mars and representations. 2 
2.2. Constraint Based Approaches 
In this section, we will outline the 
approach to the translation of non-local re- 
entrances proposed in Kaplan et al (1989). 
In LFG projections are linguistically 
relevant mappings or correspondences between 
levels, whether these mappings are direct or 
involve function composition (Kaplan (198"0, 
Halvorscn and Kaplan (1988), Dalrymple (1990) 
and Dalrymple et al (1990)). By means of these 
projections, equations can be stated which co- 
describe 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). 
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 trans- 
lation can be thought of ns specifying and 
resolving a set of constraints on target struc- 
tures, constraints which are expressed by means 
of the "~ and x' functions. 
The formalism permits a wide variety of 
source-target correspondences to be expressed: 
and ap can be composed, as can x' and o. Equa- 
lions specifying translations are added to (source 
language) lexiual entries and c-structure rules. 
For example (2) composes "~ and ap, identifying 
the 'r of the (source) SUBJ f-structure with the 
SUBJ attribute of the x of the f-structure associ- 
ated with some node (the value of t), indicating 
that the translation of the value of the SUB3 slot 
in a source f°structure 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. 
3 See Sadler ,t a/ (1990), Sadler and Thompson 
(1991), and Fmdler (1991) for further disctmaion of this 
apl~oach to MT. 
ACtES DI" COLING-92, NAmEs. 23-28 ^oral' 1992 7 2 9 l'goc, oV COLING-92, NA~'rEs, AUO. 23-28, 1992 
f-structure. 
(2) T(tStmJ) - (Tt SUm) 
In this approach, then, relations between 
different types of linguistic description (i.e. lev- 
els) are defined in terms of correspondence 
funetiom, not by means of the re.cursive appli- 
cation 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, includ- 
ing ('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 gram- 
mar. This allows information which is exhaus- 
tively determined by the target grammar to be 
ignored in the transfer prooms. 4 In this sense, 
the system is constraint-based, rather than struc- 
ture baaed like the approaches described in 2.1. 
above, and it has different expteasive possibili- 
ties. 
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 RELTO- 
PIC function. 
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 refer- 
ence to pieces of f-structure). 
(3)a. The man who I saw. 
b. L'homme que j'ai vu. 
4 For • target tentence to be • Iran~tlon of • 
tource tente~e, the minimal ~mcture aatigned to the 
Utrget teatznce by the argot grammar mntt be •ub- 
turned by the mlnim•l solution of the • and Z' coe- 
ttndnL 
(4) 
NP --~ NP S ~ 
tRELMOD-~ 
"~(t RELMOD)'('~ t RELMOD) 
x( \[ RELTOPIC)-(x~, RELTOPIC) 
(5) 
S' --* XP 
(tRELTOPIC) - ~, 
(t {XCOMP,COMP}* GV3 - 
(6) see: V 
PRED-'see<SUBJ,OBJ>' 
x(t SU~')-(T t strm3 
z(tom)=(Ttom) 
(7) who: N 
PRED-'who' 
HUMAN-+ 
('~ tPRED FN)='OUE '6 
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 
(8) 
IRELTOPIC e2 \[PRED 'who'\]\]\] 
(9) 
\[RELTOPIC f2 \[PRED 'QUE'\] \] \] 
The equations on rule (4), which are 
specifically for dealing with relative slrnctmr, s, 
are quite simple in themselves, and combine 
6 We ~umo that PRED-'QUE' ,ul~um~ the 
vmanta qua, qui,/aq~//e, ©tc. 
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 con- 
stmints, 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. 
(1o) 
( fl RELTOPIC) - x( e t RELTOPIC) - x(e,-z) 
( fi O13,1) = ~( el 0~) = ~(e2) 
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 re- 
entrance. 
Unfortunately,, this approach is only capa- 
ble of producing intuitively correct structures in 
cases where the conditions on unbounded 
dependencies are parallel in the source and tar- 
get languages. On closer inspection, the example 
Kaplan et al use to demonstrate their approach 
does not work correctly, giving the ungrammati- 
cal (11c) instead of the correct (llb). 
(11)a The letter which I have answered. 
b. La tettre h laquelle j'ai r~pondu. 
The letter to which 1 have responded 
c. *La lettre laquelle j'ai r~pondu h. 
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). 
(12) 1' PRED='answer<SUBJ, OBJ>' 
('~'PRED FN)='r6pondre<SUBJ, OBLso>' 
~(tSLrm)-(~ISLU3J) 
z(tOm)=(TtOBL~ Ore) 
(13) 
\[RELTOPIC e2 \[PRED 'which'\]\] l 
I PRED 'answer<SUBJ'OBJ>' /\[ 
From these rules, the following x equations 
arise, in relation to (13): 
(14) z( ~' RELTOPIC)-(-¢ t RELTOPIC) 
x( eT.)=(ftRELTOPIC) 
z(1' OBJ)-('t 1' OB~o OID) 
T( e2)-( flOBLso OBJ) 
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 
preposition. 7 
(15) 
RELTOPIC f2 \[PRED 'QUE'\] 
PRED 'r6pondre<SUBJ, OBI.~>' 
~ELMOD f, SUBJ f3 \[PRED 'je'\] 
OBL~o \[PRED 
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. 
3. Using Underspeclflcatlon 
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 sys- 
tems 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 con- 
straint 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 func- 
tion). Because these correspondences apply x to 
f-structure descriptions which evaluate to the 
same object, a target re-entrance is automati- 
7 'l'his representation embodiee an number of que~- 
tiotmble ~umptiotm about the treatment of r, which 
not relevant to the di~u~io~. 
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 
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. 
In this section we will explore a solution to this 
problem which involves restricting "~ correspon- 
dences 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. 
3.1. Different Re.entrances in Source and 
Target 
Suppose that no "~ equations are stated on 
the c-structure rules introducing the RELTOPIC 
attribute, and a "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'): 
(16) 
PRED 'rtpondre<SOBJ, OBLgo>' \] \] 
l/ I 1// 
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. 
First, there is some source-oriented infor- 
mation -- the solution to the functional uncer- 
a Kaplan tt a/propose jmt such n treatment in cases 
like the trantlmtion of J~hn is likely to su Mary -- II ¢~tt 
probab/¢ qu*, ./tan wrra Mar/¢. No X ~rrenlm,adence 
is given for the SUBJ of I/kc/y, ~ the f-stntclure laum- 
nlatad with John i8 only related to s target f.~Ouctur¢ 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 consid¢~ the 
pt~dbility of dealing with 'unbounded' re.entrances in 
this way. 
tainty equation associated with the XP node in 
the English c-structure. The solution of the 
functional uncertainty equation in this case hap- 
pens 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). 
(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. 
Of course, this cannot simply be added to 
the other x equations (if it were, it would estab- 
lish a re-entrance between RELTOPIC and 
OBLso O13.I, which would give an ungrammati- 
cal result, with a stranded preposition, as in 
(11c) above). 
Second, the monolingual target grammar 
will contain a constraint to ensure that, if REL- 
TOPIC is present, some path within the REL- 
TOPIC attribute contains the attribute value pair 
WH-+. This is required to prevent the 'topical- 
izing' (i.e. wh-movement fronting within the 
relative clause) of any XP which does not con- 
tain 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). 
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. 
(20) 
(t RELTOP1C) = 
(t {COMP, xcoiPI*{strm, OBJ, OBL~}) 
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" 1992 7 3 2 P~oc. OF COL1NG-92. NAN'\] ES, AUG. 23-28, 1992 
target f-structure. It can he interpreted defcasi- 
bly 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)). 
If the source-derived equation is con- 
sistent 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 hot- 
tom of the mm~rtainty path. The "closest" solu- 
tion 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. 
(23) 
RELTOPIC h I \[PRED 'QUE' 
\[oBJ \[WH + 
PRED 'r6pondre<SUBJ, OBLgo>' 
RELMOD fl SUBJ f:~ \[PRED 'je'\] 
OBLgo fz \[ \] 
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 con- 
tains 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 "smaller" 
RELTOPIC phrases from "larger" 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 pro- 
noun 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 posi- 
tion only, ignoring the RELTOPIC position, and 
then create a re-entrance on the target side. 
There are at least two problems. First, in stun> 
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 gram- 
mar creates links as part of the parsing process 
titat creates A:V structures (e.g. if they are asso- 
ciated with c-structure rules), and even if they 
ate rules that can be applied to already con° 
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) f- 
commands the 'gap'; but in the structures output 
from transter, the relationship will be the 
reverse. 
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 
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 ana- 
phoric 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 infor- 
nmtion (i.e. constraints) from source language, 
and target grammar to interact with bilingual 
information. 
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ACRES DE COLING-92. NANTES. 23-28 AOt~" 1992 7 3 4 P~oc. OF COLING-92. NANTES, AUO. 23-28, 1992 
