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<?xml version="1.0" standalone="yes"?> <Paper uid="P88-1006"> <Title>A General Computational Treatment of Comparatives for Natural Language Question Answering</Title> <Section position="4" start_page="42" end_page="42" type="metho"> <SectionTitle> 3. Lexical Provisions for Comparatives </SectionTitle> <Paragraph position="0"> Our current repertoire of domain-independent lexical items associated with comparatives includes &quot;many', &quot;few', and &quot;much'; &quot;more', with 3 readings (er, er+many, er+much), following Bresnan (1972) and similar to Robinson (1982, p. 28); &quot;fewer (er+few); &quot;less', with 3 readings (less, er+few 6, less+much); several formatives and adverbials ('at', &quot;least', &quot;most', &quot;exactlY', &quot;precisely', &quot;only', &quot;just', &quot;half', &quot;again', &quot;times', &quot;percent'); and a handful of spelled-out ordinals ('thirds&quot; etc.). Though not stored in the lexicon, both integers and floating-point numbers (of.</Paragraph> <Paragraph position="1"> &quot;3.45 inches') are also involved in comparativization.</Paragraph> <Paragraph position="2"> The domain-dependent portion of the lexicon includes members of the open categories of adjectives, measure nouns, and comparative inflections of adjectives. The scanner output for the comparative of the adjective A is er +A (e.g. &quot;larger&quot; becomes er+large).</Paragraph> </Section> <Section position="5" start_page="42" end_page="43" type="metho"> <SectionTitle> 4. Syntax for Comparatives </SectionTitle> <Paragraph position="0"> The basic syntax for comparatives adheres to the meta-rules given in Section 1.2. As indicated in the parse tree of Figure 1, COMPAR is never a primary tree node but is instead a daughter of the node being comparativized. Furthermore, since our grammar has recently taken on somewhat of an X-bar flavor (cf. Jackendoff, 1977), the complement for a comparativized item is found as either its sister or its parent's sister. Complex comparatives derive from left-recursive structures. 7 Our present grammar for comparatives is set up partly by meta-rules 8 and partly by hand-coded rules relating to such idiosyncracies as &quot;more than 3 inches in length&quot; (however, of. &quot;more than 6 in number*).</Paragraph> <Paragraph position="1"> 6. To the possible horror of the prescriptive grammarian, this accounts for such attrecities as &quot;less books'.</Paragraph> <Paragraph position="2"> 7. Though our parser operates top-down, we've incorporated a general mechanism for left recursinn that's also utilized by possessives (e.g. &quot;the newest car's company's largest compatitor's smallest car').</Paragraph> <Paragraph position="3"> 8. Meta-rules are also used to produce the grammar for relative clauses, yes-no questions, and a host of other structures (e.g. various slash categories) from a hand-coded grammar for basic declarative sentences.</Paragraph> <Paragraph position="4"> S. Parse Tree Normalization ' Letting Node{<X>} denote a node of the normalized parse tree associated with an element of type <X>, comparatives involve the replacement</Paragraph> <Paragraph position="6"> where <Arg> corresponds to an optional noun phrase, <Etcx> captures non-elided material associated with the matrix clause, and the 2-place-relation denoted by <Rel> is the most interesting (and by far the most complex) element produced.</Paragraph> <Paragraph position="7"> The algorithm that produces it converts &quot;more', &quot;less&quot;, and &quot;times&quot; respectively into +, -, and *. This process is left recursive; the relational operator is determined from the highest MODE, and by default it is assigned to be _.9 As indicated below, these algebraic and arithmetic symbols will be preserved in the executable expression unless the word being comparativized indicates a downward direction on the scale applicable to it (e.g. &quot;fewer', &quot;shorter'), in which case they will be reversed (e.g. >i becomes and -~ becomes -). Each 2-place-relation is the body of a 2-place lambda whose variables, P and A, are associated with values obtained from a parameter and an argument against which a comparison is being made. Some example 2-place-predicates are mere than 166 h~les leag more than IS feet ling When the measure noun appearing in an English input differs from that by which the objects being tested are measured, as indicated by the second example above, a scalar conversion is required.</Paragraph> </Section> <Section position="6" start_page="43" end_page="45" type="metho"> <SectionTitle> 6. Semantics for Comparatives </SectionTitle> <Paragraph position="0"> The semantics of comparativization involves converting a one-place predicate into another one-place predicate by performing arbitrarily complex operations on it. For example, if &quot;large car&quot; has been defined as a car whose length exceeds 190 inches, thetl, letting &quot;A&quot; denote a noun phrase complement, some examples are</Paragraph> <Paragraph position="2"> no lealger than A twice as leog as A t- wide 3 laches mora thaa twi~ as long as A</Paragraph> <Paragraph position="4"> where each of these right-hand-sides is the body of a one-place predicate whose single variable is x.</Paragraph> <Paragraph position="5"> As a second example, comparative quantifiers such as &quot;more than 6&quot; are handled by an identical process ldeg, as indicated by Ii x has --any y,. Size {y I Jhs(x,y)} ;~ x has more tham 6 y's Size {y \[ Has(x,y)\] > 6 x Im mere y'. em A Size {y I nt, s(x,y)} > Size blt~(A,y)} x Im at lem 2 me~ Size {y \[ Hgix,y)} y's tim A ~ 2 + Size \[y \] l-I~(A.y)} where the initial Constant denotes some arbitrary constant.</Paragraph> <Paragraph position="6"> In general, comparativizing a one-place predicate takes place as follows.</Paragraph> <Paragraph position="7"> 1. Find (a) an appropriate one-place function and (b) an associated relational operator that tells which direction on a linear scale indicates having &quot;more&quot; of the property. 2. Apply the relational operator located above to the modality of the comparison to determine the relational operator that will appear in the IR+. If the relational operator of the definition being comparativized is either > or >i, use the mode occurring in the IR; otherwise, &quot;reverse&quot; the mode by doing what would be a negation but leaving untouched the - portion of the operator. Thus, the reversal of < is >, the 9. This addresses the inherent ambiguity of as/as structures without an adverbial element, such as &quot;exactly&quot; or &quot;at least'. Thus, &quot;people with 3 children&quot; is interpreted as people with exactly reversal of ~< is />, and so forth. Similarly, +, and - are switched.</Paragraph> <Paragraph position="8"> 3. Determine the argument being compared against (possibly a constant).</Paragraph> <Paragraph position="9"> 4. Link these pieces together. If the argument was not constant (e.g. &quot;... longer than at least 3 foreign cars'), wrap its scope around the resulting expression.</Paragraph> <Paragraph position="10"> For example, if &quot;short car&quot; has been defined as &quot;x is short': Length(x) < 160 then the 1-place function and relational operator are determined in step 1 to be Length and <~, and thus we have &quot;shorter than A&quot; -&quot;* Leagth(x) < IAalgtk(A) &quot;exactly 3 inches shorter than A&quot; --* LentO(x) - Izs~(A) - 3 7. Comparatives Containing a Wh Element In addition to recognizing wh elements associated with a relative or interrogative clause, 12 TELI recognizes the word how when it appears in place of a quantity, e.g. &quot;how long&quot; (cf. &quot;6 inches long') and &quot;how many more&quot; (of. &quot;6 more't3). Wherever wh appears, however, we treat its semantics as roughly &quot;solve for wh such that'. In the case of interrogative pronouns (e.g. &quot;what'), this leads rather obviously to an internal representation asking for a SET. In the case of &quot;how', this treatment is also in order since it represents a (quantity) NP. For simplicity, we produce an expression containing an unbound wh and later give it wide scope. 14 In particular, subsequent processing involves moving the wh element upward in the logical form tree 18 by performing appropriate transformations.</Paragraph> <Paragraph position="11"> 12. To see that wh is less than a &quot;word', consider pairs such as what~that, where~there and when~then. The advantage of recognizing sub-word units us the primitives on which syntax and/or semantic analysis is based should come as no surprise to anyone acquainted with the structure of languages other than English, which is unusual in coming so close to being treatable solely at the word level.</Paragraph> <Paragraph position="12"> 13. As stated earlier, we have adopted derivations suggested by Bresnan (1973) such as -er+many---qnore. In the case at hand, we must assume something like Q+many--*Q, where Q denotes a quantity. 14. The scope is wide but not global because of inputs such as &quot;How many cars does each US company make?&quot; 15. Of course, our algebraic-logical forms, based on operators and their associated arguments, amount to being trees. For illustration, consider the absurdly complicated example &quot;Buick makes 3 more than how many percent more cars than Audi?&quot; the comparative portion of whose internal</Paragraph> <Paragraph position="14"> At this point, we proceed with semantic processing, ignoring for the moment the presence of the unbound WH element. In the case at hand, this leads to This process is not dependent on the position in which the wh occurred, and thus takes the place of sl~:ial-pu~ interpretation routines for &quot;how many,, &quot;How <Adjective>', and so forth. 17 8. Discussien Thus far, we have presented an overview of our treatment of comparatives, with as much detail as we're able to supply in a conference-length paper. Although we can offer no substantive empirical evidence with TELI (e.g. results of use by nonauthors), we believe some of the techniques we've presented can be put to use by the reader. Further information, especially with regard to the interaction of comparatives with a variety of other types of constructs, can be found in Bailard and Stumberger (1987).</Paragraph> <Paragraph position="15"> 16. The sentence is ambiguous, with readings indicated by &quot;3 more than \[how many percent\]&quot; and &quot;\[3 more than how manyl percent'. As indicated earlier, we presently take the reading that favors the use of left reenrsion.</Paragraph> <Paragraph position="16"> 17. Problematic situations can arise in which simple algebraic operations aren't sufl~cienct. For example, in examples such as &quot;Cars were sold to people with how many children?', we must move wh past a logical quantifier, rather than the arithmetic operators as shown above.</Paragraph> <Section position="1" start_page="45" end_page="45" type="sub_section"> <SectionTitle> 8.1 Related Work </SectionTitle> <Paragraph position="0"> Although the literature describing implemented NL processors contains many examples of comparative constructions (cf. Kirsch (1964) for a wealth of early examples), at least two qualifications may be given concerning the current &quot;state of the art&quot; of comparative treatment. First, the majority of the examples appearing in the literature are quite simple 18 (e.g. &quot;more than $250&quot;) and can be prepared for by specifying a 2-place predicate in advance that's effectively equivalent to the 2-place predicate we construct from an underlying 1-place predicate by way of coercion into a 1-place function. This allows one to avoid some slippery problems of movement (which we have adressed but have certainly not disposed of), to ignore morphological subtleties (e.g.</Paragraph> <Paragraph position="1"> recognizing the &quot;er&quot; of &quot;larger&quot; or &quot;more&quot; as -er, a &quot;word&quot; to be input to the parser), and to take other shortcuts. 19 Second, although examples of various types of comparatives are not hard to come by, accounts of the actual mechatdsms that treat comparatives are harder to find, as are specific statements of the generality which authors believe themselves to have provided for.</Paragraph> </Section> <Section position="2" start_page="45" end_page="45" type="sub_section"> <SectionTitle> 8.2 Levels of Representation </SectionTitle> <Paragraph position="0"> The architecture of TELI resembles that of similarly motivated question answering systems (cf. Grosz et al, 1987; Hafncr and Godden, 1985; Bates and Bobrow, 1983 and Bates et al 1985) by comprising a linear sequence of processing stages which produce successively -lower&quot; level representations of the input. 2deg Although our parse tree format is rather conventional, 21 what we have called &quot;normalized 18. Evidence of the gap between what's been studied and what may actually be important is expressed, in the context of pronoun resolution, in Hobbs (1978, p. 343) as follows: &quot;There are classes of examples from the literature which are not ... handled by the algorithm, but they occur rarely in actual texts, and in view of the fact that the algorithm fails on much more natural and common examples, there seems to be little point in greatly complicating the algorithm to handle them.&quot; 19. The extent to which &quot;shortcuts&quot; are justified, from either a psychological or system designer's standpoint, is not clear. As a possibly bizarre example, consider the word &quot;after', which could be treated as &quot;-er .aft than', where .aft is the Anglo-Saxon root (extant only on I:card ship) from which current English word derives. A perhaps even more bizarre opportunity may exist for treating &quot;rather&quot; as &quot;-er .rathe', where &quot;.rathe&quot; is a Middle English adverb meaning &quot;quickly'. 20. We're using &quot;low&quot; to refer to level of abstraction. Perhaps ironically, successively higher levels of cognitive information are involved in producing these &quot;lower&quot; level representation.</Paragraph> <Paragraph position="1"> 21. The methods whereby TELI produces parse trees are less conventional than the trees it produces, due to our provision for having the parser enforce agreements automatically while it is running, rather than doing subsequent filtering.</Paragraph> <Paragraph position="2"> parse tree&quot; and &quot;algebraic-logical form&quot; correspond rather loosely to what in the literature are often called &quot;logical form&quot; and &quot;meaning representation', respectively. Furthermore, in the most recent work with TELI, meaningful distinctions between modules have become blurred, although the relative order in which operations are carried out is largely the same.</Paragraph> <Paragraph position="3"> In seeking to compare our formalisms and processing strategies with others that have been proposed, we have found terms such as &quot;logical form&quot; being used in the literature in quite vague and often incompatible ways. Furthermore, we know of no compelling arguments that suggest that a psychologically plausible model of human information processing will require intermediate levels such as parse trees, logical forms, and the like.</Paragraph> <Paragraph position="4"> Is it even clear that there ought be be a finite number of successive &quot;levels&quot;, whatever they might be? We are increasingly doubtful that the trappings spawned by linguists and philosophers can be put in a bag, sprinkled with Common Lisp, shaken, and expected to yield robust natural language processors.</Paragraph> <Paragraph position="5"> More of an interdisciplinary effort may be required than has yet been seen.</Paragraph> </Section> <Section position="3" start_page="45" end_page="45" type="sub_section"> <SectionTitle> 8.3 Curreat Work </SectionTitle> <Paragraph position="0"> The representation given in Section 5 fundamentally restricts us from handling comparatives whose complement is more than one level above the word being comparativized (e.g. &quot;John persuaded his students to contribute to more museums than Bill did'). Our current work involves producing normalized parse tree structures of roughly the form</Paragraph> </Section> </Section> <Section position="7" start_page="45" end_page="46" type="metho"> <SectionTitle> (COMPAR.2 Ci <Co..p> ('COMP~-I Ct-) -.) </SectionTitle> <Paragraph position="0"> where the COMPAR-1 and <Comp> structures correspond to the COMPAR structure given in Section 5; Ct provides for co-indexing when multiple comparativizations are present; and the first &quot;...&quot; allows for arbitrarily many levels. This calls upon us to modify the semantic processing presented in Section 6, making it resemble the treatment given to wh elements as described in Section 7.</Paragraph> </Section> class="xml-element"></Paper>