We say that translation from Lj to Lj is st_r_i_ç_tl_y_ compositional if there is mapping T from 6j=<Cj > to Gj =<Cj,flj> such that:

As will become apparent, these definitions imply a very restricive theory of translation, one which is much too strong to be usable. However, before dis­cussing its inadeguacy, we will make the ideas invol­ved more concrete by describing a notatiun for Bs and Ts which is strongly committed to these ideas, and by discussing a very simple example of the use nf the notation. The description is rough and not precisely formalised, but should give an idea of the issues i nvolved.

Notation for constructors and atoms:

atom ::- (name, feature description) constructor::= (name,feature description)[argspec*!

argspec::= (name, feature description) (In fact, atoms are simply constructors with arity 0, but we will preserve the intuitive distinction here). The feature theory we assume here is extremely simple: a feature description is a set of attrihute-value pairs. The 'name' is just a distinguished fea­ture representing the intuitive linguistic basis Df the language being described (thus, it might be a syntactic category, a syntactic relation, or a seman­tic relation as appropriate). Notice that this name need not be unique. Each constructor lias in addition a unique abbreviatory constructor name which is used by the T-rules.

The language L generated by a G is a set of well-formed abject (wfo's) such that:

Every atom is a wfo; and if c„ is a constructor of arity n, and each of uj, un is a wfo, then cn i ui, ..., an is a wfo.

This very simple syntax for Bs will lead to over-generation ~- for example, it will allow up construc­tors with two arguments as a wfo, even if the first argument is a verb, and the second is a preposition. For this reason we supplement the purely syntactic description with a semantics based on applying con­structors to arguments. We will thus normally be concerned only with the subset wfns that are also constructs, in the following sense:

Every atom is a construct! a constructor applied to some arguments yields a construct providing the argu-m e n t s u,ni_f _y_ with the appropriate argspecs of the constructor.

Examples (fnr a constituent structure language): atoms: aBKampie = (example, {cat^n, num=5ing})

The syntax and semantics of Ts is roughly as follows. Syntactically, a T-rule is of the form: Ihs ==> rhs, where lhs and rhs are atoms or constructors of source and target language Gs respectively. For example, the following might be T-rules relating a level based on syntactic relations with one based on semantic rela­tions for the atoms corresponding to the verbs 1 ike anci IlLL- (They are both assumed to assign subject and object relations to their dependents syntactically. They are assumed to assign respectively, experience!-and patient, and agent and patient to their semantic dependents. Since the leading linguistic idea at both levels is relational, and the nature of the relation cannot be determined for constructs in iso­lation, the name feature of atoms and constructors is 'blank' at these levels).

The semantics of this is that all source language atoms which unify with the lhs are translated to all target language atoms which unify with the rhs.

The following might be a constructor to constructor T-rule for the same two levels :

15) c5ubj-ubj cexp-pat meaniny that any source language construction built by applying c5Ubj — obj t° some arguments uj, ... u„ is translated by applying cEXp_j,at to the translations of ui. •■■, "n

This syntax and semantics for T-rules implements the idea of strict compositionality defined above.

This model is elegant, but inadequate, given the way natural languages appear to be. What strict composi-tionality requires is at least a rather strong homo-morphi5m hetween the languages related by a T. It is easy to find examples where this looks implausible.

For example, consider the common need to re-Drder members of a construction in translation; or the need to eliminate 'formal' items which are a part of constructions in one language (one level) but not in another- (perhaps re-expressing some information they carry as part of a feature), as in (6)j or the kind of simple structural change involved in going from a level which has both S and VP constructions to one which has verb, subject, and object as members of a single construction (7); or the need to re-analyse an item which is part of une construction in one lan­guage, as part of another construction in translation (B).

'■Sl-finitel jules understand it 1 t rely-on Cnp sandy 11

Uf course, one could easily vary assumptions about representations so that these examples disappear, but other examples conflicting with the new assumptions will be just as easy to find. Notice that though, for simplicity, we have chosen examples that are close to the surface of one language (English), there are many examples of this kind between languages:

(9) Cjules zwemt graag] "HjuleBj likeslei to swimll 'Lexical holes' such as English exhibits with respect to Dutch (English has no adverb 'likingly' to trans­late graag) , and idioms such as give a hand will normally give rise to the need for non-strictly com­positional translations, for obvious reasons. As a more general example, it is often the case that what is expressed lexically or syntactically in one lan­guage is expressed morphologically in another. Thus, modality is often expressed by inflection in Romance languages, and by combinations of separate lexical items in Germanic languages, and correspon­dences between compounds in Germanic languages, and syntactic constructions in Romance languages (as in (111) are very common. Treating this kind of thing will certainly lead to non-strictly compositional translations somewhere.

The solution to this problem adopted by Landsbergen (1984) in Rosetta is to 'tune' the Bs to each other, thereby ensuring that they are homomorphic, and that something close to strict compositionality can be preserved. (In fact, Landsbergen requires the trans­lation relation to be symmetric, so the grammars turn out to be isomorphic). This preserves the elegance of the model, but at the expense of the elegance of the linguistic theories and descriptions (the Mul and MuB) , which become extremely complex, and potentially unusable. For example, it requires give a hand to and helpen. and graag. and like to to be treated alike. Providing a systematic and general character­isation of a theory of representation which allows this seems highly problematic. What one expects is that the representational theory will become unlearn-able in the sense described above. A second objec­tion to this approach is the obvious one that it eliminates the modularity that is potentially avail­able with this model (each G can be thought of as a module, e.g.). This reduces its attractiveness from a developmental point of view, particularly where multi-1ingual MT involving large numbers of lan­guages, or wide coverage (hence collaboration of large numbers of individuals) is envisaged.

For these reasons, we have preferred to explore an alternative approach, which involves allowing some relaxations of strict compositionality. The fol­lowing three relaxations have been proposed :

(i) To allow variables on either side of T rules :

with the meaning: translate any expression formed by applying c27 to three arguments by an expression formed by applying c3B to the translation of the second and third arguments. This relaxation allows for re-orderings, deletions, and reduplications by T-rules, and seems an entirely natural extension of strict compositionality.

(ii) To allow functions made up of constructors, atoms, and variables of the appropriate Gs on either side of T-rules, e.g.

Notice that since the output of such a translation rule is still an expression in the target language (i.e. an expression built by applying target G con­structors to target constructs), this relaxation still yields 'one shot' translation.

(iii) To allow the choice of the target constructor (function) to be dependent on properties of the argu­ments involved. For example, one does not want all Cv pp] constructions to be treated like rely on in (8), and the exceptional translation behaviour of idioms, and constructions involving lexical holes is clearly dependent on the presence of particular pro­perties within constructions (e.g. the presence of particular lexical items):

with the meaning: translate constructions formed by applying c35 to three arguments by constructions formed by applying c46 to their translations, provi­ding the second argument of c35 unifies with a fea­ture description where the attribute fl has the value vl, and the translation of the third argument unifies with a feature description where the attribute f2 has the value v2.

Though there is no provision for wild notational devices such as path variables, these relaxations greatly increase the power of the notation, to an extent which is problematic, given our methodology. We would naturally like to impose restrictions, so that we can preserve the idea that in compositional translation the translation of a whole is some 'rea­sonably straightforward' function of the translation □f its parts. One possibility is to impose special restrictions (or alternatively restrict some relaxa­tions) to certain translators (e.g. one would like the transfer translators to he as near as possible restricted to some kind of atom-atom translator). More generally, one might require that at most one side of a T-rule be a function (in the sense of relaxation (b)), or to require that context sensitive T-rules may only refer to attributes of particular arguments (e.g. attributes of the heads of construc­tions, perhaps, or to only allow them to test for the presence of particular lexical items among their arguments). There are interesting methodological and empirical problems involved in trying to find approp­riate restrictions, but we will not pursue them here, since (as will appear in the fallowing section), the notation is still restrictive enough for there to be a theoretical commitment which deserves discussion.

2. The theoretical commitments pf the model.

The attractiveness of our model as a framework for practical and theoretical MT derives from its modula­rity and its orderliness in the main. Practically, it ensures that translation proceeds via a series of representations which are described explicitly, and which therefore have to be capable of systematic description, and it ensures that the language gene­rated by applying a sequence of translators is always a subset of a language that has been explicitly described. It thus comes as close as possible to excluding 'hybrid' representations, and ensuring that representations languages will be 'learnable'. More­over, the separation of Gs and Ts, and the use of a semantics based on unification provides a high degree of declarativeness, and the homogeneity and uniformi­ty of the model may be of practical benefit. The separation of Gs and Ts also provides a high degree of modularity, so, e.g. different Gs can in principle be developed in parallel, and the effects of modifi­cations may often be localised to one G and the adjacent Ts. This is developmentally attractive.

Methodologically and theoretically the model is at­tractive in a number of ways. The complexity of T-rules provides a very simple and effective evaluation metric against which to judge competing proposals about representational levels (so it is relatively easy to find arguments why there should or should not be intermediate representations of a certain sort). And it provides a level of abstraction at which linguists and implementers can communicate easily. However, perhaps the most important advantage of the model is that it decomposes the 'problem of MT', and provides a framework for investigating some interes­ting and apparently manageable sub-problems. Some of these are discussed in a preliminary way here.

This notation, and hence the model that it instan­tiates, in effect provides a context free grammar notation augmented by a simple feature theory based on unification, and (via the T rules) the capacity for certain transformations. We have no demonstra­tion of the weak genenerative capacity of the nota­tion, but one suspects it is at least as powerful as the notations of LFG (Kaplan & Bresnan 1982), or FUG (Kay 19B5). Taking full advantage of relaxations (a)-(c) below may well yield Turing machine capacity. While this makes it likely that the notation provides some treatment of all translational1 y relevant pheno­mena, it is still rather restricted as regards des­criptive or expressive capacity, and there is no guarantee that the treatment will be 'natural', ap­propriate, or even practically usable.

One approach to the issue of usability is the provi­sion of user friendly abbreviations (e.g.), and it is fairly easy to imagine some conventions which would take this basic (Mu2) notation and make it more usable as a programming language for linguists (i.e. a Mul 'user language').

Some of the major modifications to the model which have been proposed include:

(a) The introduction of special versions of construc­tor application in place of unification, for example, in the treatment of co-ordinate constructions. The properties of co-ordinate constructions are partly determined by the fact that they inherit the common features of their elements, 50 the feature descrip­tion of the construction should be the generalisation (roughly self consistent intersection of the feature descriptions) of the elements, rather than their unification.

(b) The introduction of Kleene star to avoid deeply recursive structures in the treatment of construc­tions which allow arbitrary numbers of arguments (e.g. most constructions can include an indefinitely large number of PP modifiers). Since the syntax of Gs requires specific reference to the arity of constructors, the obvious way of dealing with this phe­nomena in the basic notation is to have recursive constructors (e.g. a constructor that combines an np and a pp to form an np), yielding structures such as:

This treatment is not obviously incorrect, but it is not necessarily the most intuitively satisfactory treatment either, and it can have the undesriable effect of burying the lexical heads of constructions arbitrarily far down inside them.

(c) A closely related point is that the model des­cribed is committed to representation languages where members of constructions are strictly ordered (CC32: a,bl is a different abject from Cc32! -- e.g.

the latter may fail to unify to give aconstruct, while the former succeeds). This may not always be very natural, especially where relational languages are concerned: since the elements of constructions are distinguished by their roles, they do not also need to be distinguished positional1 y.

A number of modifications along these lines are being discussed in the project. They are not unproblematic (or even obviously correct), for example, (b) and (c) above both suggest that constructors be treated as operations on sets, rather than lists of arguments. Apart from changing the formal nature of construc­tors, a problem will arise in going from unordered representation languages to ones which are ordered, motivating an extension to the T-rule notation. Ne­vertheless, they seem to within a reasonable distance of (and hence compatible with) the essentials of the basic model.

A consequence of the CFG basis of the model is that constructs are always hierarchical objects similar to tree structures (each application of a constructor yields a new level of structure, intuitively). The model is most naturally applied in the description of linguistic phenomena that can be thought of hierar­chically, and in translating between languages that capture such phenomena. Thus, it is naturally ap­plied in the description of phrase and relational structures (though cf above), and given the unifica­tion based semantics, in dealing with phenomena such as agreement between members of constructions.

Moreover, though the 'naturalness' of the treatment is perhaps more questionable, it provides interes­ting, and apparently workable accounts of a number of phenomena that are not obviously hierarchical. For example: it is reasonably easy to see how the relaxa­tions of strict compositionality allow a treatment of functional control and unbounded syntactic dependen­cies (Arnold et al, 1985 sketches a crude, but straightforward treatment exploiting the possibility Df having functions composed of target G constructors and variables in T-rules).