A Language for the Statement of Binary Relations 
over Feature Structures 
Graham Russell Afzal Ballim Dominique Estival Susan Warwick-Armstrong 
ISSCO, 54 rte. des Acacias 
1227 Geneva, Switzerland 
elu@divsun.unige.ch 
Abstract 
Unification is often the appropriate method for 
expressing relations between representations in 
the form of feature structures; however, there 
are circumstances in which a different 
approach is desirable. A declarative formalism 
is presented which permits direct mappings of 
one feature structure into another, and illustra- 
tive examples are given of its application to 
areas of current interest. 
1. Introduction 
Benefits arising from the adoption of 
unification as a tool in computational linguis- 
tics are well known: a declarative, monotonic 
method of combining partial information 
expressed in data structures convenient for 
linguistic applications permits the writing of 
sensible grammars that can be made indepen- 
dent from processing mechanisms, and a grow- 
ing familiarity, in both theoretical and compu- 
tational circles, with the techniques of 
unification fosters fruitful interchange of ideas 
and experiences. There are, however, occa- 
sions when unification alone is not an 
appropriate tool. In essence, unification is a 
ternary relation in which two structures, when 
merged, form a third; it is less attractive in cir- 
cumstances where the relation to be expressed 
is binary - when one would like to manipulate 
a single feature structure (FS), perhaps simu- 
lating the direct transformation of one FS into 
another. 1 The present paper introduces a 
declarative formalism intended for the expres- 
sion of such relations, and shows how it may 
be applied to some areas of current interest. 
The formalism in question is based upon a 
notion of 'transfer rule'; informally, a set of 
such rules may be considered as characterizing 
We are indebted to Jacques Jayez for comments on an 
earlier draft of this paper. 
1 Clearly there is a sense in which such relations can 
be viewed as ternary: T(FI, R, F2), where 171 and 172 are 
• 17Ss, and R is the rule set which relates them. 
a binary relation over a set of feature struc- 
tures, the properties of that relation depending 
on the content of the particular rule set in use. 
Transfer rules associate the analysis of one FS 
with the synthesis of another; they may be 
thought of as a specialized variety of pattern- 
matching rule. They are local in nature, and 
permit the recursive analysis and synthesis of 
complex structures according to patterns 
specified in a format closely related to that 
widely employed in unification-based compu- 
tational linguistics. Indeed, the interpretation 
of transfer rules involves unification, albeit in a 
context which restricts it to the role of a 
structure-building operation. 2 
In the remainder of this paper we provide a 
brief specification of the transfer rule formal- 
ism, discuss its interpretation, outline two 
alternative rule application regimes, and illus- 
trate the use of the formalism in the areas of 
machine translation and reduction of FSs to 
canonical form. We conclude with an over- 
view of continuing strands of research. 
2. Rule Format and Interpretation 
2.1. General Remarks 
A transfer rule consists of four parts: 
(i) a role name; 3 
(ii) a set of constraint equations describing a 
FS; 
(iii) a set of constraint equations describing a 
FS; 4 
2 The rule formalism is thus monotonic, being unable 
to effect changes in the input representation, and con- 
stmcting the output by means of unification. 
3 The rule name plays no part in the interpretation of 
roles, but provides a convenient reference for tracing 
their ordering and application. 
4 The equations in each of (ii) and (iii) must he 
uniquely rooted. The current implementation disallows 
disjunction in the equation sets for this reason. 
- 287 - 
(iv) a (possibly empty) set of 'transfer 
correspondence statements' - equations 
describing transfer correspondences that 
must hold between variable bindings esta- 
blished in (ii) and (iii). 
A transfer rule relates the two FSs it describes 
either directly or indirectly, via the rule's 
transfer correspondence statements; in order 
for the relation to hold between the source and 
destination FS, it must hold between the FSs to 
which any transfer-variables are bound. An 
example of a transfer rule is given below: 
:T: exampled 
:LI: <* a b> = XI 
<* c d> = YI 
:L2: <* p q> = X2 
<*p r>ffiY2 
:X: Xl <=> X2 
YI <=> Y2 
This rule establishes a correspondence between 
the two feature structures shown below, (1) 
being the FS described by the equations under 
'Ll' and (2) by those under 'L2': 
The correspondence is licensed provisionally 
for this FS pair by "example-l"; it is licensed 
absolutely for a pair of FSs (1') and (2') having 
the same root as (1) and (2) respectively only 
if: 
(i) (1') contains sub-FSs (z unified with X1 
and \[3 unified with Y1 in (1), 
(ii) (2') contains sub-FSs y unified with X2 
and 8 unified with 3(2 in (2), and 
(iii) the same type of correspondence is 
licensed, possibly by some other rule, 
between (x and y and between \[~ and 8. 
Complex FSs are analysed and constructed 
recursively as a result of the passage of control 
through transfer variables. / 
In the abstract, transfer rules have no 
inherent directionality; the two FSs above may 
be visualized interchangeably as input and out- 
put, or 'source' and 'destination'. When com- 
piled for a particular application, however, 
they are interpreted directionally, the domain 
of the transfer relation being collectively 
characterized by the equation sets labelled 'LI' 
and the range by those labelled 'L2', or vice 
versa. One may then think of compiled 
transfer rules as having a 'left-hand' or 'input' 
and a 'right-hand' or 'output' side, the former 
describing a source FS and the latter a destina- 
tion FS. We shall use these terms freely in 
contexts where directionality is at issue, and 
assume that the rules have been compiled 
accordingly. 
2.2. Interpretation 
The relation of transfer between a source FS X 
and a destination FS A is defined recursively in 
terms of the quintuple (R, ¢bx(R), ~p(R), 
T(R), O(Z)), where R is a rule, ~(R) and 
• p(R) are, respectively, the FSs induced by the 
left-hand and right-hand equation sets in R, 
T(R) is the set of transfer correspondence 
statements in R, and O(Y~) is the result of con- 
vertin\[\[ any path-final variables in Z to con- 
stants:-' 
Z stands in the transfer relation to A with 
respect to Riff: 
(i) (b~.(R) subsumes (~(Y-), and 
(ii) ~p(R) unifies with A, and 
(iii) for each % e T(R), the sub-FSs of 5"- and A 
unifying with the transfer variables men- 
tioned in 'c stand in the transfer relation 
with respect to some rule in the currently 
accessible rule set. 
The first clause of this definition states the con- 
dition under which a rule is a candidate for 
application to a given input FS. The second 
states the condition under which a rule is a 
candidate for application to a given output FS. 
Note that the operations differ; whereas the 
matching in (i) is based on subsumption, the 
action in (ii) employs unification. As a conse- 
quence, the FS q)p(R) is added to the output FS 
A. The third clause imposes the further condi- 
tion that, in order for \]: and A to be related by 
R, any FSs they contain which are explicitly 
connected via variable binding and a transfer 
correspondenc e statement in T(R) are also 
related. 
As will be~ seen from clause (iii) of the 
definition, a complex FS is traversed from root 
to terminals, control being passed via variables 
in tran~er equations, and the extent of each 
sub-transfer (i.e. how much of the input FS is 
consumed at each stage) being determined by 
5 It may well be the case that, in certain applications 
or envixonments, source FSs will not contain such vari- 
ables; the possibility must be acknowledged nevertheless, 
since non-declarative rule interactions may otherwise oc- 
CUlt'. 
- 288 - 
the path specifications in the left-hand side 
equation set of the currently active rule. Possi- 
ble paths through the FS from a given point are 
determined collectively by the left-hand side 
equations of all rules, together with their 
transfer correspondence statements. 
Because FSs are finite and acyclic, termina- 
tion is guaranteed as long as there is no rule of 
the form shown below. This is able to apply 
(in the 'L1-->L2' direction - we ignore the 
converse) without consuming part of the 
source FS: 
:T: infinite-recursion :LI: <*>-- X 
:L2" ... :X: X <--> Y 
Coherence of a destination FS with respect to a 
source FS and a set of transfer rules is ensured 
by the formalism; material can only be intro- 
duced into a destination FS by the right-hand 
side of transfer rules which have successfully 
applied. Completeness, on the other hand, 
must be verified explicitly; every part of the 
source FS must be subsumed by a subpart of 
the FS obtained by unifying the FSs induced 
by the left-hand side patterns of every rules 
that has successfully applied. In the current 
implementation, it is possible to declare that 
certain subparts of a source FS are not to be 
transferred; in this case, it is the remainder of 
that FS which must be covered by the rules. 
3. Applications of the Formalism 
We now illustrate how the transfer rule formal- 
ism may be exploited, and indicate briefly how 
the rule invocation regime may vary. The 
machine translation example in the following 
section assumes parallel invocation of the rule 
set, while that involving reductions to canoni- 
cal form seems most amenable to the serial 
invocation of individual rules or subsets of 
rules. 
3.1. Machine Translation 
Perhaps the most obvious application for the 
formalism presented here lies in the domain of 
machine translation. The transfer model of 
MT may be thought of as involving three dis- 
tinct mappings; from the source language 
expression to a source linguistic representa- 
tion, from the source representation to a target 
representation, and from this to an expression 
in the target language. The first and last of 
these are to be performed by parsing and gen- 
eration with natural language grammars, but, 
while proposals have been made to combine 
some of the three stages (e.g. Kaplan et at., 
1989), there are advantages in treating the 
intermediate, transfer, stage independently. 
As an example, consider the FSs shown 
below: 6 
(3) \[sem Ipred schwimmen \]\] 
args (<1> sem pred Maria) 
Lmod sem pred gem 
(4) Isem \[pred aimer \[ )1 args 
(<I> sem pred Maria, 
<2> sem pred nager\] 
args (#I)\] 
(3) and (4) are possible representations for the 
German sentence Maria schwimmt gem, and 
the French sentence Maria aime nager, both of 
which might translate into English as 'Maria 
likes swimming'. Note that, whereas (3) has 
the predicate which translates 'swim' at the top 
level, and contains a modifier gem which 
might be glossed as 'gladly', (4) embeds the 
'swim' predicate within an argument to the 
main predicate aimer 'like', and links the first 
argument of aimer to the first argument of 
nager by means of a re-entrancy. 7 
The set of rules given below together estab- 
lish a transfer relation between (3) and (4): s 
Note the use of a list, indicated by '(... )', to encode 
arguments in these FSs, the identification of elements on 
such a llst by e. 8. '<1>', and re-entrancy flagged by '#'. 
7 Clearly, one could employ a similar analysis for the 
German sentence by making gem an 'equl' predicate like 
aimer - this would amount to simplifying transfer by 
shifting complexity from the transfer rules into the Gear- 
man grammar. 
8 This is not quite true; the variables 'Tf and 'Tg' in 
the rule "gem-aimer" will bind to lists (the empty list in 
this case), and we therefore require additional generic 
list-transfer rules that will have the effect of passing 
through a list, recursively transferring heads and tails. 
Implementations for systems that lack the list data type 
will naturally be able to dispense with this. In addition, 
the lexical transfer rules assume the presence in the 
current set of a rule consuming the '<* sere pred>' 
paths terminating in Paul and Maria. 
- 289 - 
:TA: Paul Paul 
:TA: Maria Maria 
:T: schwimmen-nager 
:LI: < * sere pred > = schwimmen 
<* sere args> = \[Xg\] 
:L2: < * sem pred > = nager 
<* sem args> = \[Xf\] 
:X: Xg <=> Xf 
:T: gem-aimer 
:LI:<* sem pred> = Rg 
<* sem args> = \[AglTg\] 
<* sem mod sere pred> ffi gem 
:L2: < * sere pred> ffi aimer 
<* sere args> = \[Af, Vf\] 
<* sem args> = \[Af, Vf\] 
<Vf sere args> = \[AfiTf\] 
:X: Rg <-> Rf 
Ag <=> Af 
Tg <--> Tf 
< Vf sem pred > ffi Rf 
The pair of rules ':TA:PaulPaul' and 
':TA: Maria Maria' are 'lexical transfer rules'; 
they state a transfer relation between atomic 
FSs (i.e. words, in the context of MT), rather 
than complex ones, and, further, do so without 
reference to the context of these FSs. They are 
equivalent to e.g. 
:T: Maria Maria 
:LI: <*> = Maria 
:L2: < * > = Maria 
:X: - 
The re-entrancy in FS (4), in which the first 
argument associated with the predicate aimer 
is also the argument associated with the 
embedded predicate nager, is of some interest 
in connection with transfer. Taking (4) as the 
source, application of "gern-aimer" results in 
the binding of both instances of the variable 
'Af' to the sub-FS indexed as '<1>' which is 
subject to the relevant transfer correspondence 
statement and whose corresponding destination 
sub-FS (in this case identical) will be present 
in the overall destination FS as the first ele- 
ment on the argument list of schwimmen. Rev- 
ersing the direction, with (3) as the source, the 
variable 'Ag' is bound to the sub-FS indexed 
as '<1>', whose corresponding destination 
sub-FS is similarly present in the overall desti- 
nation FS, this time as the first element in both 
argument lists, and, moreover, owing to the 
identity of variables in "gern-aimer", unified 
rather than duplicated. Re-entrancy may thus 
be detected in the source FS and created in the 
destination; naturally, responsibility for 
correctly analysing structures confining re- 
entrancies, and enforcing them where desired 
in output structures, lies with the writer of 
transfer rules. 
3.2. Reduction to Canonical Form 
It is often the case that a grammar assigns just 
one of a range of logically equivalent represen- 
tations to a sentence; designers of grammars 
for use in analysis generally take care to ensure 
that the result of parsing a non-ambiguous sen- 
tence is a unique semantic representation, and 
multiple representations are seen as the hall- 
mark of (pre-theoretical) ambiguity. In gen- 
eration, as Shieber (1988) and Appelt (1989) 
observe, a situation may arise in which the 
representation supplied as input to the process 
(perhaps by another program) is not itself 
directly suitable, but is logically equivalent to 
one that is. The use of distinct grammars for 
parsing and generation could provide a solu- 
tion to this problem, but it raises others con- 
nected with management of the resulting sys- 
tem. An alternative is to define equivalence 
classes of representations, and reduce all 
members of a class to the single canonical 
form which the grammar can map into a sen- 
fence. Exactly how the classes and reductions 
are defined will doubtless depend on many fac- 
tors; we consider here some of the standard 
logical equivalences exploited in reducing 
arbitrary expressions of the propositional cal- 
cuius to disjunctive normal form. 
:T: not-not 
:LI: <* op> ffi not 
<* val 1 op> ffi not 
<* val 1 val 1> = Y 
:L2: <*> ffi X 
:X: X <ffi> Y 
:T: not-or 
:LI: <* op> ffi not 
<* val 1 op> = or 
<* val 1 val 1> = XI 
<* val 1 val 2> = X2 
:L2: <* op> = and 
<* val 1 op> ffi not 
<* val 1 val 1> ffi Y1 
<* val 2 op> = not 
<* val 2 val 1> = Y2 
:X: XI <ffi> Y1 
X2 <ffi> Y2 
The two rules shown above express 
equivalences which are more familiar as: 
--,(-,p) ~ p 
and 
-,(p v q) ~-~ (-,p ^ -,q). 
the 
- 290 - 
The mode of application required here is rather 
different from that described in the preceding 
section, for a context in which "not-not" 
applies may not exist prior to the application of 
"not-or". Consider the three FSs below: 
(5) op not 
val op not 
val 1 
Q 
(6) "op 
val 
and 
1 \]°Pal n°t \[~1 
2 \[OPval not Q\]I 
.ot\]\] 
Given (5), the desired result is (7), by way of (6). 
A suitable context for the role "not-not" is created 
by "not-or"; note, however, that this context exists 
only in the destination FS, and not in the source. 
What is required is a serial mode of invocation, as 
opposed to the parallel mode assumed for the MT 
application, with the 'output' of one rule serving as 
the 'input' to another. An alternative would be to 
formulate transfer rules that encompass a wider 
context; drawbacks of such an approach would be 
that it is not possible to cater for all contexts, and 
that, in attempting to do so, one would dimini.~h the 
locality and thus the transparency of the rules. 
There are several possibilities for imple- 
menting serial rule invocation; the most 
straightforward involves taking an output FS 
as the input to another pass through the rule 
set. In this case, vacuous application of the 
rule set must be detected in order to ensure ter- 
mination. 
It will not normally be desirable to apply 
canonicalization rules 'in reverse': the effect 
will be to derive all forms that are logically 
equivalent to the input, and, if the relevant 
equivalence classes are not finite, the process 
will not terminate. Consider the rule "not- 
not"; its presence in a rule set compiled with 
'L2' as the left-hand side will result in the 
derivation of forms involving, at each point, an 
embedding of the source FS under a progres- 
sively higher even number of nots. This is as 
it should be, however, given the semantics of 
transfer rules outlined in section 2, since, in 
this direction, the rule characterizes a relation 
whose range is not finite. Individual applica- 
tions of the rule terminate, nevertheless. 
4. Conclusion 
We have presented what is to our knowledge 
the first formalization and implementation of a 
type of rule and control regime intended for 
use in situations where it is desired to produce 
the effect of transforming one feature structure 
into another. 9 
The formalism described above has been 
implemented as part of ISSCO's ELU l°, an 
enhanced PATR-II style (Shieber, 1986) 
unification grammar environment, based on the 
UD system presented by Johnson and Rosner 
(1989). ELU incorporates a parser and genera- 
tot, and is primarily intended for use as a tool 
for research in machine translation. Use of 
transfer rules in translation has not so far 
brought to light instances where the serial rule 
invocation regime described in section 3.2 
proves necessary. ELU grammars permit the 
use of typed feature structures (cf. Johnson and 
Rosner, op. cit., Moens et al., 1989) in gram- 
mars; although the present transfer rule format 
does not, they are clearly a desirable addition, 
since they would provide a means of exerting 
control over rule interactions. 
A third area in which the transfer rule for- 
realism might be applied concerns the manipu- 
lation of re-entrant structures. While re- 
entrancy is in general a useful property of FSs, 
the complexity entailed by its presence is in 
some cases unwelcome; the method of genera- 
: 9 Van Noord (1990) describes the use of a standard 
unification grammar to successively instantiate a single 
feature structure embodying meaning representations for 
both source and target language expressions in a machine 
translation application. Similarly, the transfer rules of 
Zajac (1990) express a relation between subparts of a sin- 
gle complex structure. Such an approach does not appear 
suitable for the appl/cation discussed in section 3.2 
above. 
10 "Environnement Linguistique d'Unification" 
- 291 - 
tion proposed by Wedekind (1988), for exam- 
ple, requires that the LFG-style f-structures 
which form the input to the generation process 
be 'unfolded' into unordered trees. This may 
be done with a suitably formulated rule set of 
the kind introduced here. The present rule for- 
mat is unable to preserve the information that 
distinct sub-FSs in a destination FS arise from 
the duplication of a single, re-entrant, sub-FS 
in the source. Ways of incorporating this abil- 
ity into the rule formalism are under considera- 
tion, one possibility being the addition of an 
indexing mechanism that would flag sub-FSs 
as originating in a re-entrancy. 
A companion paper describes an interpreta- 
tion of transfer rule sets in terms of a partial 
ordering with respect to the specificity of rules, 
and discusses linguistic and computational 
motivations for this view; it also comments in 
greater detail on the rule interaction problems 
referred to in fn. 3, and on issues of termina- 
tion, completeness and coherence in transfer. 
Here, we simply note that, in the current 
implementation, it is possible to declare to the 
system the path set of a source FS that is to be 
subject to transfer, so as to provide rim-time 
notification ff inadequacies in the rule set 
result in a specified sub-FS being neglected. 
With respect to a given rule set and source FS, 
however, correctness of the transfer process is Assured. 
References 
Appelt, Douglas E. (1989) "Bidirectional 
Grammars and the Design of: Natural 
Language Generation Systems", in Y. 
Wilks (ed.) Theoretical Issues in Natural 
Language Processing; 19.9-205. Hillsdale, 
NJ: Laurence Erlbaum. 
Johnson, Rod and Mike Rosner (1989) "A 
Rich Environment for Experimentation 
with Unification Grammars". Proceedings 
of the Fourth Conference of the European 
Chapter of the Association for Computa- 
tional Linguistics, Manchester, UK, April 
10th-12th 1989; 182-189. 
Kaplan, Ronald M., Klans Netter, Jiirgen 
Wedekind, and Annie Zaenen (1989) 
"Translation by Structural Correspon- 
dence". Proceedings of the Fourth Confer- 
ence of the European Chapter of the Asso- 
ciation for Computational Linguistics, 
Manchester, UK, April 10th-12th 1989; 
272-281. 
Moens, Marc, Jo Calder, Ewan Klein, Mike 
Reape, and Henk Zeevat (1989) "Express- 
ing Generalizations in Unification-based 
Grammar Formalisms". Proceedings of the 
Fourth Conference of the European 
Chapter of the Association for Computa- 
tional Linguistics, Manchester, UK, April 
10th-12th 1989; 174-181. 
Shieber, Stuart M. (1986) An Introduction to 
Unification-Based Theories of Grammar. 
CSLI Lecture Notes no. 4, CSLI, Stanford. 
Shieber, Smart M. (1988) "A Uniform Archi- 
tecture for Parsing and Generation". 
Proceedings of the 12th International 
Conference on Computational Linguistics, 
Budapest, August 22nd--27th, 1988; 
614-619. 
van Noord, Gertjan (1990) "Reversible 
Unification Based Machine Translation". 
Proceedings of the 13th International 
Conference on Computational Linguistics, 
vol.2, Helsinki, Finland, August 20th-24th, 
1990; 299-304. 
Wedekind, Jiirgen (1988) "Generation as 
SWacture-Driven Derivation". Proceedings 
of the 12th International Conference on 
Computational Linguistics, Budapest, 
August 22nd-27th, 1988; 732-737. 
Zajac, R~ai (1990) "A Relational Approach to 
Translation". Proceedings of the Third 
International Conference on Theoretical 
and Methodological Issues in Machine 
Translation of Natural Language, Austin, 
Texas, June llth-13th, 1990. 
- 292 - 
