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<Paper uid="P89-1020">
  <Title>A General Computational Treatment Of The Comparative</Title>
  <Section position="3" start_page="161" end_page="161" type="metho">
    <SectionTitle>
2 The Underlying System
</SectionTitle>
    <Paragraph position="0"> Proteus QAS answers natural language queries relevant to a domain of student records. It is highly modular and contains fairly standard components which perform: 1. A syntactic analysis of the sentence using an augmented context-free grammar consisting of a context-free component which defines the grammatical structures, a restriction component which contains welbformedness constraints between constituents, and a lexicon which classifies words according to syntactic and semantic categories.</Paragraph>
    <Paragraph position="1">  2. A syntactic regularization of the analysis using Montague-style compositional translation rules to obtain a uniform operator-operand structure.</Paragraph>
    <Paragraph position="2"> 3. A domain analysis of the regularized structure to obtain an interpretation in the domain.</Paragraph>
    <Paragraph position="3"> 4. An analysis of the scope of the quantitiers. null 5. A translation to logical form.</Paragraph>
    <Paragraph position="4"> 6. Retrieval and answer generation.</Paragraph>
    <Paragraph position="5">  The syntactic analyzer also covers general coordinate conjunction by containing a conjunction metarule mechanism which automatically adds a production containing conjunction to certain context-free definitions.</Paragraph>
  </Section>
  <Section position="4" start_page="161" end_page="162" type="metho">
    <SectionTitle>
3 The Syntactic Analysis
</SectionTitle>
    <Paragraph position="0"> of the Comparative In Section 1.1 it was shown that the comparative resembles other complex syntactic structures. This observation suggests that the comparative could be treated as general coordinate conjunctions, wh-relative clauses, and certain subordinate and adverbial clauses  by the syntactic analysis component of the system. If the system can already handle these structures, the extension for the comparative is straightforward. This approach has the advantage of utilizing the system's existing machinery to process comparative structures which are very complex and diverse; in this way a minimal amount of effort results in extensive coverage. For example, to cover conjunction-like comparative structures, the production containing possible conjunctions was modified to include than; to include relative-clause-like comparatives, the production containing words which can head relative clauses was also modified to include than. Analogous minor grammar changes were made for the other types of similar structures shown above. Using this approach, a comprehensive comparative extension was obtained by a trivial modification of only a small number of grammar productions.</Paragraph>
    <Paragraph position="1"> Thus, a conjunction-like comparative structure such as Sentence la. in Section 1.1 would be analyzed as consisting of an object which contains a conjoined noun phrase more apples CONJ 0 oranges where the value of CONJ is than, and where a quantifier phrase similar to more has been omitted which occurs with oranges. A relative-clause type of comparative structure such as Sentence 5a. would be analyzed as a relative clause than we invited 0 adjoined to more guests. Those constructions that are unique to the comparative, as shown in Sehtences 8 through 11, have to be uniquely defined. For example, the comparative clause in Sentence 8 is defined as a clause where the predicate is omitted, whereas the comparative clause in Sentence 9 is defined as a measure phrase.</Paragraph>
    <Paragraph position="2"> Although the comparative syntactically resembles other structures, this type of similarity does not carry over to the underlying structure or to the semantics of the comparative, as will be discussed shortly.</Paragraph>
    <Paragraph position="3"> There are also some syntactic differences between the comparative and the structures it resembles. For example, the comparative has zeroing patterns that are somewhat different from those associated with conjunctions: + John slept more than Mary \[slept\].</Paragraph>
    <Paragraph position="4"> - John slept and Mary \[slept\].</Paragraph>
    <Paragraph position="5"> The comparative constructions also have scope marker constraints that are not applicable to non-comparative structures. These differences are handled by special add-on constraints that specifically deal with the comparative, and do not interfere with the other restrictions.</Paragraph>
    <Paragraph position="6"> The treatment of the comparative marker is complicated because it can occur in a large number of different locations in the head clause 2, as illustrated by a few examples below: null He wanted to travel to more countries than he was able to.</Paragraph>
    <Paragraph position="7"> He is taller than Mary.</Paragraph>
    <Paragraph position="8"> He ate 3 more apples than Mary did.</Paragraph>
    <Paragraph position="9"> He ate more in the fall than in the winter.</Paragraph>
    <Paragraph position="10"> Because the comparative marker can occur in such a variety of locations and also be deeply embedded in the head clause, it cannot be conveniently handled in the BNF component of the grammar. Instead, the constraint component deals with this problem by means of special constraints that assign and pass up the comparativ e marker; other constraints test that the comparative clause is in the scope of the marker.</Paragraph>
  </Section>
  <Section position="5" start_page="162" end_page="164" type="metho">
    <SectionTitle>
4 Underlying Structure
</SectionTitle>
    <Paragraph position="0"> Basically, linguists such as Chomsky \[3,4\], Bresnan \[2\], Harris \[10\], and Pinkham \[13\] agree on fundamental aspects concerning the underlying structure of the comparative.</Paragraph>
    <Paragraph position="1"> They regard its underlying structure as consisting of two complete clauses where information in the comparative clause which is identical to information in the head clause is required to be zeroed.</Paragraph>
    <Paragraph position="2"> Harris' work is particularly suitable for computational purposes because he claims that one underlying structure is the source of 2This phrase was used by Bresnan \[2\] to refer to the clause of the comparative that contains the comparative marker.</Paragraph>
    <Paragraph position="3">  all comparative forms. We modified his interpretation somewhat to obtain a more convenient form for computation. In our version, the underlying structure contains a main clause where the comparison is the primary relation; each quantity in the relation contains an embedded clause specifying the quantity being compared. An example of this form is shown below for the sentence John ate more apples than Mary, which resembles a conjunction-like comparative structure where the verb phrase has been omitted: Nx \[John ate Nx apples\] &gt; N2 \[Mary ate N2 apples\] This form is also appropriate for all the different comparative forms shown in Section 1.1. For example, the underlying form for a relative-clause-like comparative, such as Sentence 5a. is: N1 \[Nx guests visited us\] &gt; N2 \[we invited N2 guests\] The underlying form for a sentence such as a man taller than John visited us is slightly different because the comparative structure itself is embedded in a noun phrase. The main clause is a man visited us, and the comparative structure is a clause adjoining a man, whose underlying structure is: NI \[the man is N1 tall\] &gt; N2 \[John is N2 tall\] The notion that there is one underlying form for all comparatives has important implications for a computational treatment: * Regularization procedures can be written to transform all comparative structures into one standard form consisting of a comparative operator and two complete clauses which specify the quantities being compared.</Paragraph>
    <Paragraph position="4"> * In the standard form, each clause of the comparative operator is a simpler structure which can be processed using basically the usual procedures of the system. This means that further processing does not have to be modified for the comparative. null This process can be illustrated by a simple example. When the sentence more guests than we invited visited us is regularized, a structure consisting of an operator connecting two complete clauses is obtained: (&gt; (visited (er guests) (us)) (invited (we) (than guests))) The symbols er and than, shown above, roughly correspond to quantities being compared, and in subsequent processing they are each interpreted as denoting a certain type of quantity. Notice that each clause of the comparative is also in operator-operand form where generally the verb of a sentence is considered the operator and the subject and object (and sometimes sentence adjunct phrases) are considered the operands z. Each of the two clauses can be processed in the usual manner provided that er and than are treated appropriately. This will be described further in Section 5 which contains a discussion of semantics and the comparative.</Paragraph>
    <Paragraph position="5"> The regularization process was modified to be a two phase process. The first phase uses ordinary compositional translation rules to perform the standard regularization so that the surface analysis is transformed into a uniform operator-operand form. The compositional regularization procedure is effective for fairly basic sentence structures but not for complex ones such as the comparative. The compositional rules associated with comparative structures only include labels categorizing the type of comparative structure. The second phase, written specifically for the comparative, completes the regularization process by filling in the missing elements, permuting the structures to obtain the correct operator-operand form, and supplying the appropriate quantifiers er and than to the items being comparativized. An example of this process is shown for the relative-clause type of comparative in more guests than we invited visited as, where the comparative clause than we invited is analyzed syntactically as being a right adjunct modifier of guests.</Paragraph>
    <Paragraph position="6"> 3However, if the predicate is an ad~ectlvsl phrase, the adjective is considered the operator and the verb be the tense c~-rier. Thus, ignoring tense information, the regularized form of John is t611 is: (tall (John)).  There are a few key points that should be made concerning the regularization procedures. The Montague-style translation rules could not readily be used to regularize the comparative constructions as they were defined in the context-free component. To use the rules, the grammar would have to be modified substantially because the translation of the comparative is different and more complex than that of the structures it resembles. In particular, it would then not be possible to use the general conjunction mechanism to obtain coverage of that type of comparative structure. In the case of the usual relative clause, the regularized form is also substantially different from the regularized form of the relative-clause type of comparative shown above. For a typical relative clause, such as that we invited 0 in g.ests that we invited visited us, the regularized form occurs as a clause embedded in the main clause as follows: (visited (guests (invited (we) 0)) (us)) The second important point is that because of regularization further processing of sentences containing a comparative is significantly simplified and only minor changes are required specifically for the comparative. In Prote,s QAS, as well as other NLP Systems, several other processing components are needed after syntactic regularization until the final result is obtained. Therefore a significant result of our approach is that subsequent components do not have to be modified for the comparative. As long as the underlying system can handle adjectives, degree expressions, quantifiers, and adverbs, the remainder of the processing of sentences with the comparative is basically no different than the processing of ordinary sentences because at that point the comparative is represented as being composed of fundamental linguistic entities.</Paragraph>
  </Section>
  <Section position="6" start_page="164" end_page="165" type="metho">
    <SectionTitle>
5 Semantics of the Com-
</SectionTitle>
    <Paragraph position="0"> parative Semantically the comparative denotes the comparison of two quantities relative to a certain scale. This interpretation is consistent with work in formal semantics ( \[12,11\], \[6,5\]), although our formalism is not the same.</Paragraph>
    <Paragraph position="1"> Since the comparative marker can occur with adjectives, quantifiers, and adverbs, we would like to integrate its semantic treatment with the semantics of those fundamental linguistic categories and also remain true to the semantics and syntax of the comparative. This can be done by noting that once the comparative is regularized, the comparative marker becomes a higher order operator connecting two clauses and what remains of the marker within each clause functions as a quantitative phrase. For example, the regularized form for/s John taller than Mary is: (&gt; (tall (DEG er) (John)) (tall (DEG than) (Mary)).) In this form er and than are each interpreted as a type of degree phrase that occurs with adjectives. In a question answering application such as that of Proteus QAS, each clause of the above form is equivalent to the regularized form of how tall is John, where how is also interpreted as a degree phrase modifying tall: (tall (DEG how) (John)) The interpretation of a sentence containing the comparative is therefore reduced to the interpretation of two similar simpler clauses, each containing an adjective operator and an  operand which is a degree phrase. Issues concerning the correct scale and criteria of comparison for adjectives are non-trivial, but are generally not different from those issues concerning adjectives not being comparativized. For example, determining the scale and criteria that should be used to interpret is John more refiable than Jim raises similar issues to those for ho~a reliable is Jim.</Paragraph>
    <Paragraph position="2"> The semantic treatment of adverbs generally parallels that of adjectives; the interpretation of quantifiers in the comparative form is also equivalent to the interpretation of certain interrogatives. For example, the regularized form of did John take more courses than Mary consists roughly of the two clauses John took er courses and Mary took than courses, which is treated analogously to how many in how many courses did John take.</Paragraph>
  </Section>
  <Section position="7" start_page="165" end_page="166" type="metho">
    <SectionTitle>
6 Quantifier Analysis
</SectionTitle>
    <Paragraph position="0"> An interesting problem involving the comparative concerns the scope of quantifiers when there is a higher order sentential operator such as the comparative. The problem is not discussed much in the literature, but was discussed by Rayner and Banks \[14\] when they described their treatment ofquantifiers for everyone spent more money in London than in New York. The basic issue is whether the quantifier every in everyone should be given wider scope than the comparative itself, in which case it is applicable to both clauses of the comparative. Our approach addresses this problem in a general way by adding a preliminary phase to the standard quantifier analysis. Our approach has several key features: * The replication of a quantified noun phrase does not lead to impossible scoping combinations, as frequently happens when these phrases are replicated for the purpose of obtaining a complete clause.</Paragraph>
    <Paragraph position="1"> * Our approach is applicable to all general higher order operators connecting two clauses.</Paragraph>
    <Paragraph position="2"> * The scope of quantifiers is determined in a late stage of processing so that cornmittment is not done prematurely.</Paragraph>
    <Paragraph position="3"> * A procedure using pragmatics and domain knowledge can easily be incorporated into the system as a separate component to aid in scope determination.</Paragraph>
    <Paragraph position="4"> In Proteus QAS, the scope of quantifiers is determined subsequent to the regularization and domain analysis components in a manner similar to other NLP Systems, as described by Woods \[16\]. The basic quantifer analysis procedure initially handled simple clauses, and therefore had to be modified to accommodate scope determination when a sentence contains a higher order operator such as a comparative or a coordinate conjunction. A preliminary quantifier analysis phase was added to find and label quantifiers which have a wider scope than the comparative. In addition, minor modifications were made to the component which translates the regularized form to logical form, in order to handle the translation of wider scope quantifiers.</Paragraph>
    <Paragraph position="5"> Generally, in the case of the comparative, the criteria used for determining whether or not a quantifier should have a wider scope involves the location of the quantifier relative to the comparative marker in the surface form.</Paragraph>
    <Paragraph position="6"> Usually, a preference is given to the wider scope interpretation if the quantifier precedes the marker. Using this approach, the sentence everyone spent more money in London than in New York is first interpreted syntactically as consisting of two complete clauses, which are roughly everyone spent er money in London and everyone spent than money in New York. The semantics of each clause is interpreted the same as that of a simpler sentence how much money did everyone spend in London. The preliminary quantifier analysis phase prefers the reading where the scope of everyone is wider than the comparative operator because everyone precedes more. The sentence is translated to logical form so that the quantified expression YX : person(X) occurs outside the comparative operator, and therefore has scope over both c|auses of the comparative. The interpretation is roughly:</Paragraph>
    <Paragraph position="8"> A different scope interpretation is obtained for more students read than wrote a book, where the two clauses are er students read a book and than students wrote a book. The narrow scope interpretation of a in a book is obtained because a follows more. In this case, the quantified expressions for each clause of the comparative are completely independent of the other.</Paragraph>
  </Section>
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