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<Paper uid="W91-0108">
  <Title>Structural Non- Correspondence in</Title>
  <Section position="3" start_page="57" end_page="58" type="metho">
    <SectionTitle>
III. THEORY-BASED TRANSLATION
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    <Paragraph position="0"> As mentioned above, the need to consider more carefully the nature of the adequacy conditions for the generation relation has arisen from developments in theory-based translation (Kaplan et al. 1989, Sadler and Thompson 1991, van Noord 1990).</Paragraph>
    <Paragraph position="1"> Although a range of different approaches fall ufider this description, they all share some amount of grammaticalisation of translation regularities. Furthermore, they all appeal to some form of reversibility or bi-directionality. Figure 6 below provides a schematic characterisation of all these approaches, where A and F are as before, and T is for an optional transfer  sation of translation The important point about these approaches is that the output of the analysis process is the input to the generation process. This is in contrast to previous transfer approaches, in which transfer produces some distinct new structure for input to generation. If a transfer component is included in the approaches I'm concerned with, as in van Noord (1990), its rules function to elaborate the product of analysis, not replace it, and they could without loss of generality be incorporated into the source and/or target grammars.</Paragraph>
    <Paragraph position="2">  Now we can formalise the picture in Figure 6 as follows: Definition 4.</Paragraph>
    <Paragraph position="3"> TP~_,c~(s,t) (a string s translate~o a string t for grammars Gs,Gt) iff ~ Xs ~ Aa(S,Xs) and F~(xs,t) The goal of this enterprise has been to provide a version of y which makes this a practical definition of theory-based translation, and it should be clear how all the phenomena which were used in section II to motivate the Definition 3 version of y are likely to arise in translation. In particular, the necessity for allowing the overlap between Xs and Xt to be less than total arises from the obvious asymmetry which will exist between the syntactic contents of the two---in whatever form is appropriate to the grammatical theory involved, Xs will contain a full syntactic analysis in the source domain, and possibly only a root S node for the target, while for Zt the situation will be reversed. The mini-maximal approach given above covers this case straight-forwardly.</Paragraph>
    <Paragraph position="4"> IV. BEYOND SUBSUMPTION The use of subsumption as the basis for my explorations of T has another problem, in that typically definitions of subsumption require that the structures to be compared share a common root. For reasons which would take too long to set out, this constraint too may prove over-strong in certain translation cases. By way of illustration, consider translating into a language in which overt performarives are required for all grammatical utterances. We would then find that the translation into this language of e.g. Robin swims would involve a higher predicate, so for various parts of the product of analysis, the appropriate relationship would hold not between root and root, but between root and sub-part. This suggests that a weaker relationship, perhaps the existence of a homomorphism, should replace subsumption in the definition of T.</Paragraph>
    <Paragraph position="5"> V. IMPLEMENTATION I have made some progress towards implementing a generator based on Definition 2 of section II. I believe it will be possible to provide an implementationl which is guaranteed to provide all and only the correct outputs if any exist, but may fail to terminate if no output is possible. The basic idea is to constrain the generator to produce results in node-cardinality order, that is, smallest first. In fact, there is some slop in the most straightforward way of implementing this, in that it is fairly simple to limit the number of ~ nodes allocated, but more difficult to constrain the number eventually usedi What is guaranteed, however, is that structures are produced in an order which respects subsumption, in th'at if Zs subsumes Zs', then it will be generated first. This in turn means that one can enforce the minimality constraint of Definition 2.</Paragraph>
    <Paragraph position="6"> The problem arises with certain classes of recursive definition, both the simple left recursion cases of more traditional grammars, and the more complex ones of categorial-style ones.</Paragraph>
    <Paragraph position="7"> My best guess for these is to anticipate that it would be possible to (semi)automatically ~prove that any such rule produced Via recursion a structure which was 'subsumed' (as per section IV above) by one with less recursion. This in turn would mean that provided some result had been found, the recursion could be terminated, since any further downstream result would fail the minimality constraint. If however no result could be found, there would be no basis for stopping the recursion other than a very ad-hoc shaper test (Kuno 1965), based on some more or less arbitrary (depending on the application) limit on the size of the expected output.</Paragraph>
    <Paragraph position="8"> At the moment I have no ideas on how to implement a generator which respects Definition 3.</Paragraph>
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