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<?xml version="1.0" standalone="yes"?> <Paper uid="P88-1007"> <Title>PARSING AND INTERPRETING COMPARATIVES</Title> <Section position="4" start_page="50" end_page="51" type="metho"> <SectionTitle> 3. CLAUSAL COMPARATIVES </SectionTitle> <Paragraph position="0"> Most authors are agreed that the case of clausal comParison is the simplest, and for this reason we tackle it first; despite this, it will be seen that there are a few tricky points. Our analysis is heavily based on Pinkham's, and virtually amounts to an implementation of the second section of her thesis; we start by summarizing what we see as the main ideas in her treatment.</Paragraph> <Paragraph position="1"> The fundamental notion in Pinkham's analysis is to assume that there is an implicit element present in a comparative clause, which is linked to the head of the comparison 1 in a way similar to that in which a trace or gap is linked to its controller. This &quot;trace&quot; always contains a quantifier-like component. (We will adopt Pinkham's notation and symbolize this as Q). It may consist of just the Q on its own, or else be an implicit NP composed of the Q together with other material from the head of the comparison.</Paragraph> <Paragraph position="2"> Pinkham argues that there are essentially three cases; these are exemplified in sentences 2a) - 2c). In the first of these, just the Q is extraposed; in the second, a Q together with the CN books, taken from the head more books. If the head contains a comparative adjective, as in 2c), then the extra material, consisting of the adjective and the main noun from the head, is obligatory. For a justification, and an explanation of several apparent exceptions, we refer to Pinkham, p. 33 - null 40.</Paragraph> <Paragraph position="3"> 2a) John bought more books than Mary bought (Q) records.</Paragraph> <Paragraph position="4"> 2b) John bought more books than Mary could carry (Q books).</Paragraph> <Paragraph position="5"> 2c) John bought a more expensive vase than Mary bought (a Q expensive vase).</Paragraph> <Paragraph position="6"> A scheme of this kind can readily be implemented using any of the standard ways of handling traces. In our system, which is based on Extraposition Grammar (Pereira 83), we use the &quot;extraposition list&quot; to move the material from the head to the place in the comparative clause where it is going to appear; this corresponds to use of the HOLD register in an ATN, or &quot;slash categories&quot; in a GPSG-like framework.</Paragraph> <Paragraph position="7"> Although this method appears to work well in practice, thre is a theoretical problem arising from the possibility of sentences with crossing extrapositions. We refer to the full paper for further discussion.</Paragraph> </Section> <Section position="5" start_page="51" end_page="56" type="metho"> <SectionTitle> 4. DIRECT INTERPRETATION OF NON-CLAUSAL COMPARISON </SectionTitle> <Paragraph position="0"/> <Section position="1" start_page="51" end_page="53" type="sub_section"> <SectionTitle> 4.1 Basic ideas </SectionTitle> <Paragraph position="0"> Our first implementation (Banks 86) was based on the conventional interpretation of comparatives: all comparatives are explicit or elliptic forms of clausal comparatives, making the analysis of comparison essentially a syntactic process. In (Banks & Rayner 87) we presented this in outline and then described some problems we had encountered, which eventually caused us to abandon the approach. Briefly, it turned out that the exact formulation of the syntactic copying process was by no means straightforward: there appeared to be a strong parallel with the well-known arguments against the analogous point of view for co-ordination constructions. (See e.g.</Paragraph> <Paragraph position="1"> (Dowty et. al. 82), p. 271). As an example, we presented sentence 3) 3) Everyone spent more money in London than in New York.</Paragraph> <Paragraph position="2"> which is problematic for a reduction account. We suggested instead that the sentence be thought of as being composed of the following components: the initial everyone, the contrasted elements London and New York, and the duplicated part, which could be rendered (roughly) as is a P such that P spent an amount of money in where _. In a Montaguegrammar-like formalism, this can then be given the following semantic analysis: &quot;Montagovian&quot; analysis of comparative (spent(x,y,z) is to be read as &quot;x spent amount y in the city z&quot;) than in New York 1. everyone 2. New York 3. London 4. spent m in 5. spent more in 6. spent more in London than in New York everyone spent more in London than in New York The key point is that the syntactic copying of the deletion approach has been replaced by a semantic operation, a double instantiation of a lambda-bound form. The following account summarizes how the idea is implemented within the structure of the SNACK-85 system.</Paragraph> <Paragraph position="3"> Semantic interpretation in SNACK-85 is performed by first converting the parse-tree to an intermediate form, which we call (following (Pereira 83)) a quant-tree. This is then subjected to rewriting rules before being converted into the final logical form. Normally, these rewriting rules formalize so-called scoping transformations; here, we will also use them to describe the interpretation of non-clausal comparison. The basic motivation is the same, namely to remove rules from the grammar which lack syntactic motivation.</Paragraph> <Paragraph position="4"> We introduce four new kinds of nodes in addition to those defined in (Pereira 83): we call these comparands, comparative-objects, comparisons, and comparison-placeholders. They interact as follows.</Paragraph> <Paragraph position="5"> (Stage 1) At the syntactic level, we view the comparative object as a constituent in its associated comparative AP; when the parse-tree is transformed into the quant-tree, the AP gets turned into a comparand node, in which there is a comparative-object subnode representing the comparative object. (Stage 2)Rewriting rules then move the comparative-object out of the comparand, leaving behind a placeholder. This is a triple consisting of the compared predicate (the adjective, adverb or whatever), and two logical variables (the &quot;linking&quot; variables), which correspond to the lambda-bound variables y and ~ above. (Stage 3) The &quot;raised&quot; comparative-object node is a 4-tuple. It consists of represents the comparand NP or PP.</Paragraph> <Paragraph position="6"> The rewriting rules move it upwards until it finds a quant node that it can be compared against. At the moment, the only compatibility requirements are that the quant node and the comparative-object's quant subnode not have incompatible case-markings. This could be improved upon; one way would be to define preference heuristics which gave higher priority to comparisons between quant nodes whose variables are of similar type. The result of merging the two nodes is a comparison node, which is a 5-tuple</Paragraph> </Section> <Section position="2" start_page="53" end_page="56" type="sub_section"> <SectionTitle> and P </SectionTitle> <Paragraph position="0"> When the quant-tree is converted into logical form, there should thus be only comparison nodes and placeholder nodes left, with the placeholders &quot;below&quot; the comparisons. In the final stage, the portion of the quant-tree under the comparison node is duplicated twice, and the linking variables instantiated in each copy in the manner described above. So in the &quot;inner&quot; copy, P gets instantiated to a a form 2y:comp(y,y'), where comp is the type of comparison and y and y' are the degree variables; in the &quot;outer&quot; copy, P is instantiated to the value of the inner form.</Paragraph> <Paragraph position="1"> In the next two subsections, we go further to show how a similar analysis can be used to assign a correct semantics to two other kinds of comparative construction without any recourse to C-ellipsis.</Paragraph> <Paragraph position="2"> 4.2. Comparatives with &quot;s-operators&quot; In this section, we are going to examine comparative constructions like those in 4a), 4b) and 4c). These have a long and honourable history in the semantics literature; 4c) is a famous example due to Russell.</Paragraph> <Paragraph position="3"> 4a) Mary had more friends than John had expected.</Paragraph> <Paragraph position="4"> 4b) Most people paid more than Mary sa/d.</Paragraph> <Paragraph position="5"> 4c) John's yacht was longer than I thought.</Paragraph> <Paragraph position="6"> In order tohandle examples like these within our framework, we need a syntactic representation which does not involve ellipsis. Our solution is to introduce a syntactic constituent which we call an &quot;s-operator&quot;: we define this implicitly by saying that an &quot;s-operator&quot; and a sentential complement combine to form a clause. 1 Thus the italicized portions of the sentences above are deemed to be s-operators, and in each of them the s-operator's missing complement is viewed as a kind of null pronoun.</Paragraph> <Paragraph position="7"> Although this move may in English seem syntactically quite unmotivated, there are other languages where evidence can be found to support the claim that these pronouns really exist. In Russian, where comparative constructions very closely follow the English and Swedish patterns, they can optionally appear in the surface structure as the pronoun ~ 1&quot;0. The following sentence illustrates this. OH K~H'I'I4,rl 60JII, LUe KHWr qeH ~ 3TO He bought more books than I ~T0 n~Ma~.</Paragraph> <Paragraph position="8"> thought.</Paragraph> <Paragraph position="9"> Semantically, the analysis of such sentences is exactly parallel to that in the preceding subsection. Comparing 4b) with 3), the &quot;initial part&quot; is most people, and the &quot;contrasted elements&quot; are the s-operator Mary said and an implicit trivial s-operator which we can write as (it is true that). The &quot;duplicated part&quot; is the predicate is a P such that P paid amount of money where . We can sketch a &quot;Montagovian&quot; analysis similar to that in table 2 &quot;Montagovian&quot; analysis of s-operator comparative (paid(x,y) is to be read as &quot;x paid y amount of money&quot;) 1. most people 2. Mary said 3. (it is true tha0 4. paid 5. paid more than Mary said 6. (it is true tha0 paid more than Mary said 7. most people paid more than Mary said</Paragraph> <Paragraph position="11"> The implementation of this analysis in terms of quant-tree rewriting rules involves only a slight extension of the method described in section 4.1 above.</Paragraph> <Paragraph position="12"> The reader is referred to the program code in the full paper for the concrete details.</Paragraph> <Paragraph position="13"> 4.3. &quot;Parallel&quot; phrasal comparatives Comparative constructions of the type illustrated in 5a) have been the object of considerable controversy. The orthodox position was that they were &quot;parallel&quot; constructions: 5a) would thus be a reduced form of 5b).</Paragraph> <Paragraph position="14"> 5a) More women than men read '1-Iouse and Garden&quot;.</Paragraph> <Paragraph position="15"> 5b) More women read &quot;House and Garden&quot; than men read &quot;House and Garden&quot;.</Paragraph> <Paragraph position="16"> Pinkham, however, gives good reasons for supposing that this is not the case, and that the construction is in some sense base generated phrasal (p.121123). It will presumably not come as a revelation to hear that we agree with this idea, though we express it in a somewhat different way.</Paragraph> <Paragraph position="17"> Our interpretation of Pinkham's analysis recasts the more ... than... construction as a special kind of determiner. We introduce an extra rule for NP formation: in addition to the normal NP --~ Det + CN, we also have NP --~ CompDet + CN + CN. (The details can be found in the full paper). This allows us as usual to give the constituent structure without use of ellipsis, and then to interpret it using a suitable predicate-copying operation. Once again we illustrate with a Montague-style example.</Paragraph> <Paragraph position="18"> &quot;Montagovian&quot; analysis of &quot;paraUel&quot; phrasal comparative (reads(x,y) is to be read as &quot;x habitually reads y&quot;) 1. women 2. men 3. more 4. more women than men 5. &quot;House and Garden&quot; 6. read &quot;House and Garden&quot; 7. more women than men read &quot;House and Garden&quot; ~: woman(x) ~x: man(x) XP~.QM~ more(P, Q, R) M~,: more(~x: women(x), Xx: men(x), R) ~.x: x = &quot;H & G&quot; Xx: read(x,y) n y =&quot;H & G&quot; more( ~x: women(x), Xx: men(x), ~x: read(x,&quot;H & G&quot;)) It is interesting to compare our treatment with that suggested in (Keenan & Stavi 86) (p.282-284) for comparative adjectival constructions like that in 6a); they argue convincingly that these are to be regarded as directly interpreted, rather than as &quot;reduced forms&quot; of sentences like 6b). It seems to us that their arguments can be adapted to support the analysis of &quot;parallel&quot; phrasals given above; so if we were to extend their example, we would have that 6b) in its turn was also to be interpreted directly, rather than considered a reduction of 6c).</Paragraph> <Paragraph position="19"> 6a) More male than female students passed the exam.</Paragraph> <Paragraph position="20"> 6b) More male students than female students passed the exam.</Paragraph> <Paragraph position="21"> 6c) More male students passed the exam than female students passed the exam.</Paragraph> </Section> </Section> <Section position="6" start_page="56" end_page="57" type="metho"> <SectionTitle> 5 &quot;SIMPLE&quot; PHRASAL COMPARATIVES </SectionTitle> <Paragraph position="0"> We finally turn our attention to a third type of comparative construction, which does not properly seem to fit into any of the patterns given above.</Paragraph> <Paragraph position="1"> We start by giving in 7) - 9) some examples of the kind of sentence we have in mind.</Paragraph> <Paragraph position="2"> 7) Mary seems brighter than most pupils.</Paragraph> <Paragraph position="3"> 8) He ran faster than the world record. 1 9) John needs a bigger 2 spanner than the No. 4.</Paragraph> <Paragraph position="4"> Pinkham uses constructions like these as her key examples when demonstrating the existence of base-generated phrasal comparatives. Looking for instance, at 9), we claim with Pinkham that the most natural solution is to treat bigger spanner than the No. 4 as a dosed constituent with a semantic interpretation which does not involve the rest of the sentence. It may not be obvious at first why this should be so, and we pause briefly to examine the possible alternatives.</Paragraph> <Paragraph position="5"> Firstly, suppose that we tried to use a reduction/predicate copying account.</Paragraph> <Paragraph position="6"> This would make 9) a form of 9a): 9a) John needs a (big to extent X) spanner, X such that John needs the (big to extent Y) No. 4. spanner, X>Y.</Paragraph> <Paragraph position="7"> implying that John needs the No. 4.</Paragraph> <Paragraph position="8"> This is clearly wrong; the &quot;needs&quot; isn't copied in any way, and in fact the scope of any copying operation must be limited to the phrase bigger spanner than the No. 4. If we are absolutely bent on using copying, it appears to us that the only way in which it can be done is to treat 9) as derived from 9c) through 913) 9b) John needs a spanner which is bigger than the No. 4.</Paragraph> <Paragraph position="9"> 9c) John needs a spanner which is (big to extent X), X such that the No. 4 is (big to extent Y), X > Y.</Paragraph> <Paragraph position="10"> To be honest, we can't completely discount this approach. However, since it makes bigger than the No. 4 into a constituent in the intermediate 9b), we think it simpler to interpret the phrase structure directly, as is illustrated in the following Montagovian analysis.</Paragraph> <Paragraph position="11"> Montagovian analysis of &quot;simple&quot; phrasal comparative (needs(x,y) to be read as &quot;x needs something of which the predicate y holds&quot;) 1. John 2. needs 3. No. 4 4. big 5. spanner 6. the 7. more 8. more big than the No. 4 9. a bigger spanner than the No. 4 10. John needs a bigger spanner than the No. 4 the(Xz: type__of(x, No. 4), kz: 3y': big(z,y') A (y > y')) Tables It will be apparent that bigger than the No. 4 turns up as a constituent here too, and thus our solution is in a sense equivalent with the alternate one proposed above. This is a striking illustration of the difficulties that can attend any efforts to make rigorous comparisons between different syntactic-semantic analyses of natural-language constructions.</Paragraph> </Section> class="xml-element"></Paper>