Machine Translation Using Isomorphic 
UCGs 
John L. BEAVEN* 
Pete WHITELOCK 
Department of Artificial Intelligence 
University of Edinburgh 
80 South Bridge 
Edinburgh EH1 1HN 
Scotland 
Abstract 
This paper discusses the application of Unification Categorial 
Grammar (UCG) to the framework of Isomorphic Grammars for 
Machine Translation pioneered by Landsbergen. The Isomorphic 
Grammars approach to MT involves developing the grammars of 
the Source and Target languages in parallel, in order to ensure 
that SL and TL expressions which stand in the translation rela- 
tion have isomorphic derivations. The principle advantage of this 
approach is that knowledge concerning translation equivalence of 
expressions may be directly exploited, obviating the need for an- 
swers to semantic questions that we do not yet have. Semantic and 
other information may still be incorporated, but as constraints on 
the translation relation, not as levels of textual representation. 
After introducing this approach to MT system design, and 
the basics of monolingual UCG, we will show how the two can 
be integrated, and present an example from an implemented bi- 
directional Engllsh-Spanish fragment. Finally we will present some 
outstanding problems with the approach. 
1 Background and Introduction 
The aim of this paper is to explore how the linguistic theory known 
as Unification Categorial Grammar can be adapted to the general 
methodology of Machine Translation using Isomorphic Grammars, 
as pioneered by Landsbergen and others in the ROSETTA team 
\[Landsbergen 87a, b\]. 
UCG is one of several recent grammar formalisms \[Calder et al. 
86, Karttunen 86, Pollard 85\] which are highly lexicalist, i.e. rules 
of syntactic combination are not a language-specific component of 
the grammar, but are very general in character, and combinatory 
information is primarily associated with lexical items. 
Lexical items are represented by sets of feature-value pairs 
(where the values may be themselves sets of such pairs}, and are 
combined by unification into objects of the same type. The lan- 
guage defined is thus the closure of the lexicon under the combi- 
natory rules. 
Landsbergen's work on Isomorphic Grammars follows Monta- 
gue's approach of having a one-to-one correspondence between 
syntactic and semantic rules. A syntactic rule Rs/, in the Source 
Language corresponds to a syntactic rule RTL in the Target Lan- 
guage if and only if they are both associated with the same seman- 
tic operation Rsem. The translation relation is then defined in a 
precise manner and it can be guaranteed that well-formed expres- 
sions in the Source Language are translatable, as there will be an 
expression in the Target Language that is derived in a correspond- 
ing way, and can therefore be considered as a possible translation 
of it. 
*Supported by a studentship from the Science and Engineering Research 
Council. 
According to Landsbergen, writing isomorphic grammars is a 
way of being explicit about the "tuning" of SL and TL grarmnars 
that is essential for reliable MT. The present paper is an attempt 
to adapt this approach to a type-driven mapping between syntax 
and semantics. 
2 Isomorphic Grammars 
We can recognise two basic relations of relevance in translation. 
namely, "possible translation" (which is symmetric}, and "best 
translation" given the current context and much extra-linguistic 
knowledge (which is not symmetric}. We take the task of the lin.~ 
guistic component of an MT system to be a correct and complete 
characterisation of the former, and will have nothing further to 
say about the latter. 
An important problem that arises in an interlingual translation 
system is what Landsbergen \[Landsbergen 87b\] calls the "subset 
problem". If the analysis component generates a set L of interlin° 
gum expressions, and the generation component accepts a set L I 
of them, the only sentences that can be translated are those that 
correspond to expressions in the intersection L N L ~. If the gram-. 
mars of the source and target languages are written independently, 
there is no way of guaranteeing that they map the languages into 
the same subset. 
The problem arises because a sufficiently powerful system of" 
interlingual representation will contain an infinite number of log- 
ically equivalent expressions that represent a meaning of a given 
Source Language expression. Of course, the Source Language 
grammar will only associate a single one of these with a given 
SL expression. However, in the absence of specific tuning, this 
is not guaranteed to be the same one that the Target Language 
grammar associates with any of the translation equivalents. 
Therefore, SL and TL grammars must be tuned to each other. 
This is not a problem specific to interlingual translation: in the 
transfer approach to MT system design, this tuning is effected by 
an explicit transfer module. The use of Isomorphic Grammars 
is another way of being explicit about this, tuning the grammars 
themselves rather than their inputs/outputs, which offers a greater 
possibility of bi-directionality than the transfer approach. 
Landsbergen assumes the existence of compositional grammars 
for two languages, that is, grammars in which i) basic expres- 
sions correspond to semantic primitives and ii) each syntactic rule 
that builds up a complex linguistic expreaqion from simpler ones is 
paired with a semantic rule that builds the meaning of the complex 
expression from the meanings of the simpler ones. 
The tuning of grammars consists in ensuring that there it~ a 
basic expression in one grammar corresponding to each basic ex-~ 
pression in the other, and that for each semantic rule there is a 
corresponding syntactic rule in each grammar. Two expressions 
are then considered possible translations of each other if they can 
be derived from corresponding basic expressions by applying cor~ 
responding syntactic rules. In other words, they are possible transo 
lations of each other if they are built from expressions having the 
same rneaning, by using syntactic rules that perform the same se- 
mantic oper,tions. Note the lack of directional specificity in this 
definition of the "possible translation" relation. 
/ v 8 The ~monohngual) UCG formalis~n 
Many recent grarmnar formalisms \[Shieber 86\] represent linguistic 
objects as t~ts of attribute-.value pairs. Values taken by these 
attributes may be atomic, variables, or they may thenmelves be 
sets of attribate-value pairs, so these objects *nay be thought of as 
Directed Acyclic Graphs (DAGs), in which directed arcs represent 
feature% and the nodes at the end of these represent values. Such 
formalisms t~pically support re-entrancy, that is, they provide a 
mechanism 5)r specifying that object~s at the end of different paths 
are the same object. 
Unification Gategorinl Grarimaar is such a formalism, which 
combines a categorial treatment of syntax with semantics similar 
to Kamp's :Vliscourse Representation \[Kamp 81\]. Each linguistic 
expression licensed by the grammar corresponds to what is called 
a sign. A sigt~ consists of four main entries or features, which are 
explained below: 
1. phonology (orthography in the present cruse) 
2. synta): 
3. semantics 
4. The o:der in which the terms combine. 
Typical signs for the lexical entries Mary and sings *nay then 
look something like the following: 
phon: "Mary" 
synt: npA nmn: sing 
gen: fern 
Se~l: mary 
ord: Order 
and 
phon: sings 
phon: Pho i 
synt: sentA\[ tense: flu \]/ sFnt: npA 
sexfl: SeE~ 
oral: post 
sere." \[\]q\[siugs(E,Sem)\] 
ord. ~ O*der 
pets: 
snlg 
These are briefly explained below. Note that in the above ex- 
ample, as ehewhere, the Prolog-like convention is adopted that 
constants start with lower-case or are within quotes, and vari- 
ables start with upper-case. Also, for the sake of simplicity in 
an introductory example, the first example above differs from the 
standard UCG practice of typeoraising noun phrases, which follows 
Montague arm others. 
3.\]. Syntax 
There are 4 basic categories: nouns (noun), sentences (seat), noun 
phrases (np) and prepositional phrases (pp). These may be further 
specified by features (such as nuniher, gender, etc.). Features 
are indicated by the operator A. 
A category is either a basic category, or of the form A/B, 
where A is ~ category and B is a sign. Combination of signs 
is determined by the rule of function application, which allows a 
functor sign with syntax A/B to combine with an argument sign 
B t, to give a sign like the funetor sign but with syntax A. The 
combination is licensed if B and B' unify, and if the functor and 
argument signs appear in the order specified by the value of the 
order feature in B (if the order feature of an argument is pre its 
functor must precede it, and if it is poet the functor follows it). 
The unification may further instantiate variables in the functor 
sign (in particular, the semantics). Although Function Applica- 
tion is the main combination rule, there are a few important unary 
rules, such as Gap Deletion, pp-insertion, and others. Unlike many 
other extended Categorial Grammars, UCG does not have Func~ 
tional Composition, as a similar effect is achieved by the technique 
of Gap Threading, based on work by Johnson and Klein \]Johnson 
and Klein 86\]. However it is envisaged that a richer set of binary 
rules, and a reduction or elimination of unary rules, will be nec- 
essary if the Isomorphic Grammars approach is to be extended to 
typologically diverse languages. 
3.2 Semantics 
The semantic formalism used in UCG is similar to Kamp's DRT, 
but with a Davidsonlan treatment of predicates. It is called InL 
(Indexed Language) and is described in \[Zeevat 86\]. A sentence 
like: 
If a linguist owns a donkey, she writes about it 
is represented in InL by: 
\[S1\]\[\[S2\]\[\[X\]linguist(X), \[Y\]donkey(Y), \[S2\]own(S2,Z,Y)\] 
==~ \[E\]write_about( E,X,Y)\]\] 
There is an important difference between InL and DRT: each 
formula introduces a discourse referent, or index ($1 and $2 above) 
which corresponds to the semantic object introduced by the for- 
mula. Since events, states etc. are primitive semantic objects, InL 
permits a first order treatment of modifiers. 
Indices contain information about the sortal nature of the dis- 
course referent in question. The sorts are coded into a subsump- 
tion lattice, and consist of bundles of features which may be uni~ 
fled. Unification ensures for instance that predicates have argu.- 
ments of the right sort. 
4 UCG and Isomorphic Grammars 
The principle of Isomorphic Grammars is realised in UCG by 
means of bilingual signs. Bilingual rules, which combine bilingual 
signs, may be defined in terms of how monolingual rules combine 
the monolinguM parts of the sign. 
As was mentioned, monolinguM UCG signs consist of four fea- 
tures: Phonology, Syntax, Semantics, and Order. A bilingual sign 
is merely a sign with top-level attributes source and target hav- 
ing monolingual signs as their values, and in which source se~ 
mantics and target semantics share their value. Since transla~ 
ties must preserve semantics, this sharing of values is a necessary 
condition. In the general case, however, it is not sufficient (sev 
section 5). 
The Bilingual sign can easily be decomposed into, or built up 
from, a Source sign and a Target sign (having a common Seman- 
tics), by a Prolog predicate 
decompose(Bllingual_Si~t, Source_Sign, Target_Sign). 
Combination of two monolingual signs is defined by two pred- 
icates: 
33 
source_combine(S1, S2. S). 
target_combine(Tl, T2, T). 
which combine their first two arguments to give the third. 
The crucial difference between these two predicates is as fol- 
lows: source_combine requires that the order feature of S1 and 
$2 is consistent with the phonology of S, while target_combine 
ensures that the phonology of T is consistent with the order of 
T1 and T2. This enables differences in word order in the Source 
and Target Languages to be accounted for, as shown below. 
The two monolingual modes of combination above are used to 
define bilingual combination through a predicate: 
bilingual_combine(B1, B2, B):- 
decompose(B1, S1, T1), 
decompose(B2, S2, T2), 
source_combine(S1, $2, S). 
target_combine(Tl, T2, T), 
decompose(B, S, T). 
The way in which differences in word order are dealt with may 
be illustrated by the translatioin equivalence between an adjective- 
noun combination in English and a noun-adjective combination in 
Spanish. For the sake of simplicity, only the features for phonol- 
ogy, syntax and order are included. 
The predicate source_comblne allows two combinations: 
(I) gz A/B s: C ----* ptm AWl W2 
o: pro 
(2) s: C p: W2 p~ WI W2 
o: post s: A/B ~ m A 
(where the active part of the functor sign unifies with the argu- 
ment sign) 
The predicate target_combine, on the other hand, allows the 
above two combinations, and in addition the two order-reversing 
ones: 
s: A/B m C ~ p: W2 Wl 
o: post s: A 
(4) e: C p: W2 p: W2 Wl s: A/B --4 .: A 
o: pre 
Let us then examine how the English expression red book gets 
translated into the Spanish llbro rojo, in which the order of the 
adjective and noun are reversed. 
The bilingual signs are: 
\[ sre:p: red 
tgtsp~ 
tgtzs: noun/ s:z post 
and 
\[ src:p: book 1 tgt:p: nbro 
grc:9~ noun tgt:s: noun 
These will get decomposed into their source and target con- 
stituents, which may only be combined using (1) and (3) above, 
respectively: 
34 
st noun p: book (1} p: red book m noun m noun a~ noun 
o: pre 
Currently, we assume the existence of four bilingual signs core 
responding to the English word red, since the Spanish adjective 
has four combinations of gender and number. Only that sign re~. 
resenting the contextually correct translation equivalence will be 
incorporated in the derivation. In a practical system, there would 
be a single bilingual sign whose Spanish component has disjunctive 
(or unspecified) values for gender and number, and the incorpora- 
tion of this sign into the derivation will eliminate the disjunction 
(or bind the variables). 
Unlike Landsbergen's approach, it is not necessary to specit~y 
that the rules which combine the SL and TL expressions must be 
the same. Because of the type-driven mapping between syntax and 
semantics, if two pairs of signs stand in the translation relation, 
then so will the pair of signs resulting from their combination, 
regardless of the rule used. 
5 Current Difficulties 
There are several important difficulties that remain unsolved. The 
first one is how to handle the differences in the freedom of word 
order in two languages. For instance, Spanish word order is rel- 
atively free compared to English. It conveys important stylistic 
information that should be capturdd in the translation, but which 
at present gets lost. Another aspect of the same problem is that 
we would like to be able to recognise all possible word orders in 
Spanish, without generating them all (as some are intelligible but, 
sound awkward). 
A possible solution to this could be to include some measure 
of the degree of "markedness" of a construction in each language. 
The translation process would attempt to keep the markedness of 
the two constructions as close as possible to each other. If the 
grammar specifies that Spanish sentences may be more "marked" 
than the English, the more marked would never be generated, 
though they could be analysed. 
Another problem is how the set of basic bilingual signs is to 
be characterised. That the semantics of SL and TL signs unify is 
a necessary condition for them to stand in the relation of trans- 
lation equivalence. It is however insufficient in two ways. First, 
it must be the case that there is no more specific sign in either 
language whose semantics unifies with that of the other language, 
and which is of similar markedness. Secondly, it must be the 
case that the semantics of the two signs will continue to unify re~. 
gardless of the derivations into which the signs are incorporated. 
For instance, suppose that the English word leg is associated with 
the semantics \[leg~of(X,Y)\], and the Spanish word pieraa with 
\[leg_of(X,Y),human(Y)\]. Although these semantic values do not 
contradict each other, they will if Y becomes bound to a non- 
human entity. In this case, the solution is clear ° a further bilino 
gual sign must be constructed in which English leg is paired with 
Spanish pats, having the semantics \[leg_of(X,Y),not(human(Y))\]. 
Then, either the derivation will eliminate one or the other equiva.- 
lence, or both translations will be produced, which is the desired 
result. 
It is possible that one monolingual component of a bilingual 
lexical sign will not be a basic expression in that language. Instead, 
it must be explicitly constructed in order to be paired with a basic 
expression in the other language. The unification-based semantics 
gives an indication of when such a sign-construction process must 
take place. The flexible categorial approach to the construction of 
constituents allows the non-standard categories needed to be built. 
in a sense, ell the hard work of this approach takes place at this 
point. See \[Whitelock 881 for a discussion of the issues involved. 
Finally, ghore is a cluster of problems that impinge on the 
question of ,:omputatlonal efficiency. It seems unavoidable that 
certain bilinl~ual signs will need to incorporate either discontinuous 
or null constituents, or both, ti'om one or the other of the languages- 
conce ).'J~led. 
g Co~tclusion 
This paper presents a view of MT that is based on the direct spec- 
ification of a computable description of a recursive translation re- 
lation. We :~mve proposed a system of simultaneous constraints 
placed on ist,morphie derivation trees in SL and TL whose leaves 
,~re elements of a finite set of bilingual signs and whose internal 
nodes stand in a type-driven compositional relationship to their 
daughters. \[~ is the combioation of unification and categorial 
techuiquc.,.~ ~hat makes this idea particularly feasible. The non- 
st, andard co~,stituents made available in a thll categorial calculus 
enables iso~lorphic derivation trees to be built; the partiality of 
the signs aml their combination by unification allows the expres- 
sion of very precise constraints that both derivations must satisfy. 
The p,~rtiality of semantic representations is also crucial in deter- 
mining the set of equivalences - the bilingual lexicon - that form 
the basis of lhe recursive translation relation. 
There remain many problems with realising this approach in 
s. practical I~ystem. However, we believe that there are significant 
advantages to be gained by a direct statement of the translation 
relation between two languages that is at once declarative, com- 
putable and linguistically well-ibunded. 

References

\[Calder et al. 86\] Calder, J., Moens, M. and Zeevat, H. (1986) A 
UCG interpreter. ACORD Deliverable T2.6. Centre for Cog- 
nitive Science, Edinburgh University. 

\[Johnson and Klein 86\] Johnson, M. and Klein, E. (1986) Dis- 
course, ~naphora and parsing. In Proceedings of the 11th 
International Conference on Computational Linguistics and 
the 24th Annual Meeting of the Association for Computa- 
tional Liv~,guistics, Institut lure Kommunikationsforschung und 
Phonetik~ Bonn University, Boon, August 1986. 

\[Kamp 81\] I/amp, It. (1981) A theory of truth and seroantic 
representation. In Groenendijk, J.A.G., Janssen, T.M.V. and 
Stokhof, M.B.J. (Eds) Formal Methods in the Study of Lan- 
guage, Vo1136, pp 227-322. Amsterdam: Mathematical Centre 
'lh'acts. 

\[Karttunen 86\] Karttunen, L. (1986) Radical Lexicalism. CSLI- 
86-68, Centre for the Study of Language and Information, 
Stanford University, California. 

\[Landsbergen 878\] Landsbergen, J. (1987). Isomorphic Grammars 
and their Use in the ROSETTA Translation System. In King, 
M. (Ed) Machine Translation Today: the State of the Art. Pro- 
ceedi~gs of the Third Lugano Tutorial, Lugano, Switzerland, 
2--7 April 1984. Edinburgh University Press. 

\[Landsberge~ 87b\] Landsbergen, J. (1987) Montague Grammar 
and Machine 'l.k'anslatioa. In Whitelock et aL (Eds). Liguis- 
tic Theorz and Computer Applications. Academic Press. 

\[Pollm'd 85\] Pollard, C. (1985). Lectures on tlPSG. Unpublished 
lecture l~otes, GSLI, Stanford University. 

\[Shieber 86\] Shieber, S. (1986) An Introduction to Unification- 
based Ap~,roaehes to Grammar. Lecture Notes Number 4. Cen- 
ter for tim Study of Language and Information, Stanford Uni- 
versity. 

\[Whitelock 88\] Whitelock, P. (1988) The Organisation of a Bilin- 
gual Lexi,~on. DAI Working Paper, Dept. of Artificial Intelli- 
gence, "(hfiq. of Edinburgh. 

\[Zeevat 86\] 7.eevat, H. (1986). A specification oflnL. Unpublished 
Internal ACORD Report. Centre for Cognitive Science, Uni- 
versity of Edinburgh. 

\[Zeevat 87\] Zeevat, H., Klein, E., and Calder, J. (1987). Unifica- 
tion Categorial Grammar. In Haddock, N., Klein, E. and Moro 
rill, G. (Eds) (1987). Working Papers in Cognitive Science, 
Vo|. 1: Categodal Grammar, Unification Grammar and Pars- 
ing. Centre for Cognitive Science, University of Edinburgh. 
