| { | |
| "paper_id": "W91-0108", | |
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| "date_generated": "2023-01-19T04:42:47.469916Z" | |
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| "title": "", | |
| "authors": [ | |
| { | |
| "first": "Henry", | |
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| "S" | |
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| "last": "Thompson", | |
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| "institution": "Human Communication Research Centre University of Edinburgh", | |
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| "abstract": "This paper explores the options available in the formal definitions of generation and, parasitically, translation, with respect to the assumed necessity for using a single grammar for analysis and synthesis. This leads to the consideratiOn of different adequacy conditions relating the input to the generation process and the products of analysis of its Output.", | |
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| "abstract": [ | |
| { | |
| "text": "This paper explores the options available in the formal definitions of generation and, parasitically, translation, with respect to the assumed necessity for using a single grammar for analysis and synthesis. This leads to the consideratiOn of different adequacy conditions relating the input to the generation process and the products of analysis of its Output.", | |
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| "section": "Abstract", | |
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| "text": "We start from the assumption of a constraint-based theory of linguistic description, which supports at least the notions of derivation and underlying form, in that the definition of grammaticality appeals to a relation between surface strings and some formal structure. We will attempt to remain agnostic about the shape of this formal structure, its precise semantics and the mechanisms by which a grammar and lexicon constrain its natUre in any particular case. In particular, we take no stand on whether it is uniform and monolithic, as in the: attribute-value matrices (hereafter AVMs) of PATR-II or HPSG, or varied and partitioned, as in the trees, AVMs and logical formulae of LFG. We will use the phrase products of analysis to refer to the set of underlying structures associated by a grammar and lexicon with a surface string, viz for a grammar G and sentence s e LG, we refer to the set of all products of analysis where we use A for the 'derives' relation. 1 We will also use ~s to refer to an arbitrary member of Xs.", | |
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| "section": "I. A SCHEMATIC DEFINITION OF ~GENERATES'", | |
| "sec_num": null | |
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| "text": "We will also assume that the formal structures involved support the notions of subsumption and its inverse, extension, as well as unification and generalisation. Whether this is accomplished via appeal to a lattice, or in terms of simlflations, will only become relevant in section IV.", | |
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| "section": "I. A SCHEMATIC DEFINITION OF ~GENERATES'", | |
| "sec_num": null | |
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| "text": "We can now provide schematic definitions of generation and, with a few further assumptions, translation. We say Definition 1.", | |
| "cite_spans": [], | |
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| "section": "I. A SCHEMATIC DEFINITION OF ~GENERATES'", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "F~(~,s) (a structure ~ generate~ a string s for grammar G) iff 3 ~s ~ ~(~s,~) 2", | |
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| "section": "I. A SCHEMATIC DEFINITION OF ~GENERATES'", | |
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| "text": "Most work to date on building generators from underlying forms (e.g. lIn this we follow Wedekind (1988) , where we use X/x for an arbitrary underlying form, as he uses \u00a2/~ for f-structure and Z/a for sstructure. 2Again our T is similar to Wedekind (1988) 's adequacy condition C. Wedekind 1988 , Momma and DSrre 1987 , Shieber, van Noord, Pereira and Moore 1990 , Estival 1990 , Gardent & Plainfoss~ 1990 ) have taken the adequacy condition T to be strict isomorphism, possibly of some formalismspecific sub-part of the structures Xs and X, e.g. the f-structure part in the case of Wedekind (1988) and Momma and DSrre (1987) . In the balance of this paper I want to explore alternative adequacy conditions which may serve better for certain purposes. Although some progress has been made towards implementation of generators which embody these alternatives, that is not the focus of this paper. As far as I know, aside from a few parenthetical remarks by various authors, only van Noord (1990) addresses the issue of alternative adequacy conditions--I will place his suggestion in its relevant context below.", | |
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| "start": 88, | |
| "end": 103, | |
| "text": "Wedekind (1988)", | |
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| "start": 239, | |
| "end": 254, | |
| "text": "Wedekind (1988)", | |
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| "end": 293, | |
| "text": "Wedekind 1988", | |
| "ref_id": "BIBREF10" | |
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| "start": 294, | |
| "end": 316, | |
| "text": ", Momma and DSrre 1987", | |
| "ref_id": "BIBREF4" | |
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| "start": 317, | |
| "end": 361, | |
| "text": ", Shieber, van Noord, Pereira and Moore 1990", | |
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| { | |
| "start": 362, | |
| "end": 376, | |
| "text": ", Estival 1990", | |
| "ref_id": "BIBREF0" | |
| }, | |
| { | |
| "start": 377, | |
| "end": 404, | |
| "text": ", Gardent & Plainfoss~ 1990", | |
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| { | |
| "start": 582, | |
| "end": 597, | |
| "text": "Wedekind (1988)", | |
| "ref_id": "BIBREF10" | |
| }, | |
| { | |
| "start": 602, | |
| "end": 624, | |
| "text": "Momma and DSrre (1987)", | |
| "ref_id": "BIBREF4" | |
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| "section": "I. A SCHEMATIC DEFINITION OF ~GENERATES'", | |
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| "text": "Work on translation (Sadler and Thompson 1991) suggests that a less strict definition of T is required. Consider the following AVM, from which features irrelevant to our concerns have been eliminated:", | |
| "cite_spans": [ | |
| { | |
| "start": 20, | |
| "end": 46, | |
| "text": "(Sadler and Thompson 1991)", | |
| "ref_id": "BIBREF5" | |
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| "section": "II. WEAKER FORMULATIONS", | |
| "sec_num": null | |
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| "text": "\"cat s pred like comp ipUbj red Figure 1. Exemplary 'underspecified' ~ E~at nn~ ] re.d Robi swim", | |
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| "section": "II. WEAKER FORMULATIONS", | |
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| "text": "Under the T is identity approach, this structure will not generate the sentence Robin likes to swim, even though one might expect it to. For although we suppose that somewhere in the grammar and lexicon there will be a constraint of identity between the subject of like and the subject of swim, which should be sufficient to as it were 'fill in' the missing subject, the strict isomorphism definition of T will not allow this.", | |
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| "section": "II. WEAKER FORMULATIONS", | |
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| "text": "If T were loosened to extension, the inverse of subsumption, this would then work 7(ks,Z) iff ~s subsumes thing which translation, straightforwardly (i.e. _~ ~, that is, ~s extends ~, ~s). It is just this sort of seems to be required for see for example Sadler and Thompson (1991) and the discussion therein of Kaplan et al. (1989) , where X for the desired target arises as a side effect of the analysis of the source, and Xs is additionally constrained by the target language grammar 3.", | |
| "cite_spans": [ | |
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| "start": 254, | |
| "end": 280, | |
| "text": "Sadler and Thompson (1991)", | |
| "ref_id": "BIBREF5" | |
| }, | |
| { | |
| "start": 311, | |
| "end": 331, | |
| "text": "Kaplan et al. (1989)", | |
| "ref_id": "BIBREF2" | |
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| "section": "II.1 Subsumption and extension", | |
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| "text": "Note that for Wedekind (1988) this move amounts to removing the coherence requirement, which prevents the addition of additional information during generation.", | |
| "cite_spans": [ | |
| { | |
| "start": 14, | |
| "end": 29, | |
| "text": "Wedekind (1988)", | |
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| "section": "II.1 Subsumption and extension", | |
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| "text": "Not surprisingly, therefore, implementation of a generator for T as subsumption is in some cases straight-forward--for the generator of Momma and DSrre, for example, it amounts to removing the constraints they call COHA and COHB, which are designed to implement Wedekind's coherence requirement.", | |
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| "section": "II.1 Subsumption and extension", | |
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| "text": "van Noord (1990) discusses allowing a limited form of extension, essentially to fill in atomic-valued features. This avoids a problem with the unconstrained approach, namely that it has the potential to overgenerate seriously.", | |
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| { | |
| "start": 4, | |
| "end": 16, | |
| "text": "Noord (1990)", | |
| "ref_id": "BIBREF9" | |
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| "section": "II.1 Subsumption and extension", | |
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| "text": "3Note that appealing to subsumption assumes that both the inputs to generation (~) and the results of analysis (Xs) are fully instantiated.", | |
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| "section": "II.1 Subsumption and extension", | |
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| "text": "For the above example, for instance, the sentence Robin likes to swim on Saturdays could also be generated, on the assumption that temporal phrases are not subcategorised for, as Zs in this case clearly also extends X. Rather than van Noord's approach, which is still too strong to handle e.g. the example in Figure 1 above, some requirement of minimality is perhaps a better alternative.", | |
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| "ref_spans": [ | |
| { | |
| "start": 309, | |
| "end": 317, | |
| "text": "Figure 1", | |
| "ref_id": null | |
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| "section": "II.1 Subsumption and extension", | |
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| "text": "What we want is that not only should ks extend X, but it should do so minimally, that is, there is no other string whose analysis extends X and is in turn properly extended by Xs. Formally, we want T defined as 4 Definition 2.", | |
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| "section": "II.2 Minimal extension I", | |
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| "text": "~(Zs,Z) iff Zs ~ X and 2s'~Xs' ~ ZA~S ~ ~s'", | |
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| "section": "II.2 Minimal extension I", | |
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| "text": "This rules out the over-generation of Robin likes to swim on Saturdays precisely because Xs for this properly extends ~s for the correct answer Robin likes to swim, which in turn extends the input X, as given above in Figure 1 . 4Hereafter I will Use the 'intensional' notation for extension, subsumption, unification and generalisation, using square-cornered set operators, as follows: ss E ls Ss subsumes ls; ls extends ss ss E ls ss properly subsumes ls; ls properly extends ss SSl U ss2=ls sslandss2unifytols lsl N ls2 = ss llsl and ls2 generalise to ss The intuition appealed to is that of the set operators applying to sets of facts (ssmsmaller set; Is--larger set).", | |
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| "ref_spans": [ | |
| { | |
| "start": 218, | |
| "end": 226, | |
| "text": "Figure 1", | |
| "ref_id": null | |
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| "section": "II.2 Minimal extension I", | |
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| "text": "Unfortunately, the requirement of any kind of extension is arguably too strong. We can easily imagine situations where the input to the generation process is over-specific. This might arise in generation from content systems, and in any case is sure to arise in certain approaches to translation (see section III below). By way of a trivial example, consider the input given below in Figure 2 . Figure 2 . Exemplary 'overspecified' X In the case where nouns in the lexicon are not marked for gender, as they might well not be for English, according to Definition 2 no sentence can be generated from this input, as Xs for the obvious candidate, namely Robin swims, will not extend X as it would lack the gender feature. But it seems unreasonable to rule this out, and indeed in our approachto translation to enforce the extension definition as above would be more than an inconvenience, but would rather make translation virtually unachievable. What seems to be required is a notion of maximal overlap, to go along with minimal extension, since obviously the structures in Figures 1 and 2 Figure 3 . Exemplary Z for overlap/extension conflict we will prefer Robin swims with Kim, with its extensions for the person and number features, as opposed to the non-extending Robin swims, because the latter overlaps less. Note that in the case of two alternatives with noncompatible overlaps, two alternative results are allowed by the above definition.", | |
| "cite_spans": [], | |
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| { | |
| "start": 384, | |
| "end": 392, | |
| "text": "Figure 2", | |
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| { | |
| "start": 395, | |
| "end": 403, | |
| "text": "Figure 2", | |
| "ref_id": null | |
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| { | |
| "start": 1072, | |
| "end": 1087, | |
| "text": "Figures 1 and 2", | |
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| }, | |
| { | |
| "start": 1088, | |
| "end": 1096, | |
| "text": "Figure 3", | |
| "ref_id": null | |
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| "section": "II.3 Maximal Overlap", | |
| "sec_num": null | |
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| "text": "Note that this approach is quite weak, in that it contains nothing like Wedekind's completeness conditionm if the grammar allows it, output may be produced which does not overlap large portions of the input structure, regardless of its status. For example structures which may be felt to be ungrammatical, as in Figure 4 below, may successfully generate surface strings on this account, i.e. Hours elapsed, despite 'leaving out' as 'important' a part of the underlying form as the direct object. Ki SmgJ m Exemplary 'ungrammatical' X If it is felt that generating anything at all from such an input is inappropriate, then some sort of completeness-with-respect-to-subcategorisedfor-functions condition could be added, but my feeling is that although this might be wanted for grammar debugging, in principle it is neither necessary nor appropriate.", | |
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| "start": 312, | |
| "end": 320, | |
| "text": "Figure 4", | |
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| "text": "Alternatively one could attempt to constrain not only the relationship between Zs and X, but also the nature of itself. In the example at hand, this would mean for instance requiring some form of LFG's coherence restriction for subcategorisation frames. In general I think this approach would be overly restrictive (imposing completeness in addition would, for exam-ple, rule out the Z of Figure 1 above as well), and will not pursue it further here.", | |
| "cite_spans": [], | |
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| { | |
| "start": 389, | |
| "end": 397, | |
| "text": "Figure 1", | |
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| "text": "It is interesting to note the consequences for generation under this defintion of input at the extremes. For X = T (or any structure with no grammatical subset), the result will be the empty string, if the language includes that, failing which, interestingly, it will be the set of minimal sentences(-types) of the language, e.g. probably just intransitive imperative and indicative in all tenses for English.", | |
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| "text": "The case of I X = ~ is trickier. If _L is defined such that it extends everything, or alternatively that the gener-al\u00b1sat\u00b1on of anything with \u00b1 is the thing itself, then 1) .1_ is infinite so 2) no finite structure can satisfy the maximal overlap requirement; but in any case \u00b1 fails to satisfy the first clause of 3, namely the unification of Zs and Z must not be \u00b1, since if Z is \u00b1 then Xs and Z unify to \u00b1 for any Zs.", | |
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| "text": "Finally note that in cases where substantial material has to be supplied, as it were, by the target grammar (e.g. if a transitive verb is supplied but no object), then Definition 3 would allow arbitrary lexicalisations, giving rise to a very large number of permissible outputs. If this is felt to be problem, then ~estricting (in the sense of (Shieber 1985) ) the subsumption test in the second half of Definition 3 to ignore the values of certain features, i.e. pred, would bepstraight-forward. This would have the effect of producing a single, exemplary lexicalisation for each significantly different (i.e. different ignoring differences under pred) structure which satisfies the minimaximal requirements.", | |
| "cite_spans": [ | |
| { | |
| "start": 344, | |
| "end": 358, | |
| "text": "(Shieber 1985)", | |
| "ref_id": "BIBREF6" | |
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| "text": "One potential problem clearly arises with this approach. It stems from its dependence on subsumption and its friends. Since subsumption, in at least some standard formulations (e.g. Definite Clause Grammars) fails to distinguish between contingently and necessarily equivalent sub-structures, we will overgenerate in cases where this is the only difference between two analyses, e.g. for Kim expects to go and Kim expects Kim to go on a straight-forward account of Equi. One can respond to this either by saying that this is actually correct, that Equi is optional anyway (wishful thinking, I guess), or by adding side conditions to Definition 3 which amount to strengthening subsumption etc. to differentiate between e.g. the two graphs in Figure 5 . As I do not at the moment see any way of expressing these side conditions formally without making more assumptions about the nature of underlying forms than I have so far had to (c.f. for example ,)\u00b0 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 . 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 component. Figure 6 . Schematic characterisation 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. Now we can formalise the picture in Figure 6 as follows:", | |
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| "text": "Figure 5", | |
| "ref_id": "FIGREF2" | |
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| "text": "Figure 6", | |
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| "text": "Figure 6", | |
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| "text": "Figure 6", | |
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| "section": "II.4 A Problem with the Mini-maximal Approach", | |
| "sec_num": null | |
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| { | |
| "text": "Definition 4.", | |
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| "section": "II.4 A Problem with the Mini-maximal Approach", | |
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| "text": "TP~_,c~(s,t) (a string s trans-late~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 theorybased 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.", | |
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| "text": "(xs,t)", | |
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| "section": "II.4 A Problem with the Mini-maximal Approach", | |
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| { | |
| "text": "The mini-maximal approach given above covers this case straight-forwardly.", | |
| "cite_spans": [], | |
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| "section": "II.4 A Problem with the Mini-maximal Approach", | |
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| "text": "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.", | |
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| "section": "IV. BEYOND SUBSUMPTION", | |
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| }, | |
| { | |
| "text": "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.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "IV. BEYOND SUBSUMPTION", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "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.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "V. IMPLEMENTATION", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "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. 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.", | |
| "cite_spans": [ | |
| { | |
| "start": 711, | |
| "end": 722, | |
| "text": "(Kuno 1965)", | |
| "ref_id": "BIBREF3" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "V. IMPLEMENTATION", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "At the moment I have no ideas on how to implement a generator which respects Definition 3.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "V. IMPLEMENTATION", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "(Shieber 1986) where subsumption is defined in terms of a simulation plus an explicit requirement on the preservation of token identity), I will leave this point unresolved.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "", | |
| "sec_num": null | |
| } | |
| ], | |
| "back_matter": [ | |
| { | |
| "text": "The work reported here grew out of work carried out while the author was a visitor to the Embedded Computation and Natural Language Theory and Technology groups of the Systems Science Laboratory at the Xerox Palo Alto Research Center. These groups provided both the intellectual and material resources required to support that earlier work, for which thanks. Many of the ideas presented here were first articulated in discussions with Jo Calder and Mike Reape, and many of the HCRC coffee room regulars also contributed patience and suggestions-my thanks to them all. Thanks also to Klaus Netter, in particular for first calling to my attention the behaviour of Definition 3 with respect to the extreme cases.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "ACKNOWLEDGEMENTS", | |
| "sec_num": null | |
| } | |
| ], | |
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| "FIGREF1": { | |
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