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<?xml version="1.0" standalone="yes"?> <Paper uid="P88-1005"> <Title>QUANTIFIER SCOPING IN THE SRI CORE LANGUAGE ENGINE</Title> <Section position="4" start_page="33" end_page="36" type="metho"> <SectionTitle> RULES AND PREFERENCES </SectionTitle> <Paragraph position="0"> Many of the following rules have appeared in wrious forms in multiple places in the literature, and most natural language processing systems include some mechanism for selecting a preferred quantifier scoping. However, the published descriptious of many of those systems' capabilities tend to be cursory, with the scoping rules utilized in the LUNAR system still among the best described in the NLP literature. Because of space limitations, it is not possible to cite much of this discussion, nor to compare this system to others.</Paragraph> <Paragraph position="1"> Rule 1 A quantifier A that is not in the restric.</Paragraph> <Paragraph position="2"> tion of quantifier B and that occurs within the scope of B cannot oeLgcope any of the quantifiers in the restriction of B.</Paragraph> <Paragraph position="3"> Rule 2 If a quantifier is raised past an operator, then any quantifier that occurs within its restriction must also be raised past that operator.</Paragraph> <Paragraph position="4"> These rules, presented by Hobbs and Shieber (1987), can best be explained with examples.</Paragraph> <Paragraph position="5"> A bishop visits e~er*j chapel by a ri,)er. (6) has an uuscoped logical form of visit'(qterm(a',B,bishop'(B)), qterm(every',C,and(chapel'(C), by'(C,qterm(a',R,river'(R)))))) The following is one of the possible permutations of the quemtifiers, but is not a valid scoping because the restriction of &quot;every&quot; (&quot;chapel by a river&quot;) has been fragmented: *quant(V,C,chapel'(C), quant(=l,B,bishop'(B), quant(=l, R,and(river'(R),by'(C, R)), visit'(B,C)))) Similarly, for the sentence John did not visit a chapel by a river. (7) the quantifier permutation *quant(3,C,chapel'(C), not(quant(3,R,and(river'(R),by'(C, R)), visit'(john',C)))) is not a possible scoping of the unscoped logical form</Paragraph> <Paragraph position="7"> Rule 3 For a set of quantijiers, which quantifier receives wide-scope preference can be determined by a pairwise comparison of the determiners. This comparison is based upon a combination of factors that include their relative strengths and surface positions, and whether or not either has been raised.</Paragraph> <Paragraph position="8"> In many systems, determiners are assigned numerical strengths and these values are compared to determine what scope should be assigned to each quantifier. Such a ranking is implicit in our preference rules and can be viewed as a first approximation of the relationships represented by our rules. Our algorithm permits a set of properties to be associated with determiners and for these to be used in ascertaining which determiner has wide-scope preference. The properties currently employed are surface position (the integer index of the determiner) and a Boolean value indicating when a quantifier has already been raised.</Paragraph> <Paragraph position="9"> Preference 3.1 There is a strong preference for %ach&quot; to outscope other determiners.</Paragraph> <Paragraph position="10"> That &quot;each&quot; is the strongest determiner is a common feature of most quantifier-scoping treatments. However, the evidence for the relative strengths of the remaining quantifiers is much less clear---our current ranking of them is an ad hoc blending of those in TEAM (Grosz ef al., 1987) and VanLehn (1978).</Paragraph> <Paragraph position="11"> Preference 3.2 There is a strong preference for WH.terms to outscope all determiners ezcepf &quot;each,&quot; which outscopes WH-terms.</Paragraph> <Paragraph position="12"> In the unscoped logical forms currently produced, WH-words (&quot;which,&quot; &quot;who,&quot; &quot;what&quot;) and phrases are represented as qterms. Our scopingpreference rules assign wide scope to &quot;each&quot; in Which ezams did each student pass? (8) There is a reported dialect in which sentences of the above form are judged to be malformed, but that dialect was not found among our informants.</Paragraph> <Paragraph position="13"> The design of our algorithm makes it easy to replace the current preferences with these.</Paragraph> <Paragraph position="14"> The definite determiner &quot;the&quot; is currently treated as a very strong quantifier, but this approach is not entirely satisfactory. Consider Every student passed the ezam. (9) The student in every race celebrated. (1O) The student in each race celebrated. (11) Every student in the race celebrated. (12) Each student in the race celebrated. (13) In (9)-(12), the preferred scopings are as predicted by the rules. However in (13), the preferred reading selected is the one with wide-scope &quot;each.&quot; Although both scopings of this sentence are logically equivalent (as are those for (9) and (12)), wide-scope &quot;the&quot; seems to he the preferred reading. Our algorithm does not distinguish between specific and nonspecific use of indefinite articles. It is debatable whether this belongs in quantifier scolP ing or in another part of the system.</Paragraph> <Paragraph position="15"> Preference 3.3 A logically weaker interpretation is preferred. This preference is strong when it maintains surface order, weak when it inverts surface order. 2 The quantifier order V'~ is weaker than ~/, accounting for the preferences in A man loves every woman. (14) Every man loves a woman. (15) In both sentences, the reading with wide-scope &quot;eeerf is the preferred one; the reading with wide-scope &quot;a&quot; is possible for (14), but is very strained for (15).</Paragraph> <Paragraph position="16"> Rule 4 Raising a quantifier out of certain syntactic constituents changes the strength of its determiner. null VanLehn presents an &quot;embedding hierarchy&quot; of the probability of a quantifier in the modifier of an NP being raised to have wider scope than the quantifier in the NP's head 2Vanl.mhn proposes a more general form of this preference--that, when comparing two quantifiers within the same ge~neral group, the &quot;more numerous&quot; one will have a preference for wider scope. For example, &quot;many&quot; would take wider scope over &quot;few.&quot; However, for everything except &quot;ever~'/&quot;a,&quot; such preferences appear to he very slight. PP > Reduced Relative Clause > Relative Clause A method frequently proposed to account for this distinction is to use, as a measure of the cost of raising, a count of the number of nodes in the syntactic structure over which the quantifier is raised. However, such accounts are acknowledged to have various deficiencies and to be overly sensitive to the syntactic representation used. We have chosen to permit rules to associate a cost for raising a quantifier with certain types of nodes (other nodes can be viewed as having zero costs). This capability of the system is currently invoked only on an all-or-nothing basis.</Paragraph> <Paragraph position="17"> Preference 4.1 A quantifier cannot be raised across more than one major clause boundary.</Paragraph> <Paragraph position="18"> A common rule in the quantifier-scoping literature is &quot;quantification is generally clause bound.&quot; While it is possible to generate sentences with acceptable readings when a quantifier has wider scope than the clause in which it occurs, we have been unable to find any examples showing that it can be raised out of two clauses.</Paragraph> <Paragraph position="19"> Preference 4.2 A quantifier cannot be raised out of a relative clause.</Paragraph> <Paragraph position="20"> This is a common restriction in many quantifier-scoping algorithms. In our system, this is not a special rule, but one of the preferences. Consequently, this could easily be modified from vever being permitted to being &quot;highly unpreferred.&quot; Rule 5 In unscoped logical form, quantifiers can occur within the scope of an opaque operator.</Paragraph> <Paragraph position="21"> Whether or not to raise such a quantifier outside that operator is determined by a pairwise comparison between the operator and the determiner in the quantifier, as well as by their relative surface position.</Paragraph> <Paragraph position="22"> Preference 5.1 There is a strong preference for &quot;some&quot; to outscope negation.</Paragraph> <Paragraph position="23"> Preference 5.2 There is a preference for negation to outscope %very.&quot; This preference is strong when it maintains surface order, weak when it doesn't.</Paragraph> <Paragraph position="24"> Different scopings of &quot;some&quot; and &quot;every&quot; under negation produce equivalent readings (3&quot;~ is equivalent to --V). The preferred scopings for the two sentences John did not see someone. (16) John did not see everyone. (17) have equivalent logical forms quant(3,P, person'(P),not(see'(john',P))) not(quant(V,e, person'(e),see'(john',e))) Similarly, the preferred scopings of sentences Someone did not see John. (18) Everyone did not see John. (19) have equivalent logical forms quant(3,P, person'(P),not(see'(P, john'))) not(quant(V,e.person'(P),see'(e, john'))) The reading of (16), which would assign narrow scope to &quot;some&quot; is produced by substituting &quot;an~ 's for &quot;some&quot; : John did not see anyone. (20) This has the following logical form (no other scopings exist): not(q ua nt(3, P, person'(P),see'(joh n', P))) , which is logically equivalent to quant(V,e, per$on '(e),not(see'(john' ,e))) , which corresponds to the strongly &quot;unpreferred&quot; readings of (16) and (17). Similarly, the sentence No one saw John. (21) which has a scoped logical form of quant(V,P, person'(P),not(see' (p,john'))) corresponds to the &quot;unpreferred&quot; scoping for (18) and (19).</Paragraph> <Paragraph position="25"> One of LUNAR's scoping rules was that in the antecedent of &quot;if-then&quot; statements, quantifiers &quot;some&quot; and &quot;anf should be assigned wide scope, and that &quot;a&quot; and &quot;every&quot; should be given narrow scope. If such antecedents were treated as a negative environment (or equivalent thereto), the foregoing preferences could produce this effect.</Paragraph> <Paragraph position="26"> SThe CLE system does not currently provide a treatmerit of &quot;,n~.&quot; However, within the qu~ati~er-scoping compon~t, &quot;4n~&quot; is treated ~ ~ potenti~dly ambiguotm between the usual universal quantifier, free-choice &quot;any,&quot; and a ~cond form, polarity-sensitive &quot;anlt,&quot; which occurs in conjunction with negative-polarlty items. Polarity-~mitive &quot;anlh&quot; is treated as & narrow.cope existelxtied quantifier (Ladtmaw, 1980).</Paragraph> <Paragraph position="27"> Preference 5.3 There is a strong preference for free-choice &quot;any&quot; to have wider scope than modals. There is a strong preference for all other determiners that occur within the scope of a modal to have narrower scope than that modal.</Paragraph> <Paragraph position="28"> Did some student take every testf (22) Does some student take every test? (23) Some student took every test. (24) Some student takes every test. (25) Some student is taking every test. (26) For sentences (23), (25), and (26), there are two acceptable quantifier scopings. However, for (22) and (24), the scoping in which &quot;every&quot; is assigned narrower scope seems to be strongly preferred. We ascribe this to the presence in the logical form of a modal operator corresponding to the past tense. This effect is accentuated in (27), which exhibits an ambiguity resulting from whether &quot;some teacher&quot; is scoped inside or outside the modal, corresponding to (28) and (29), respectively: Some teacher took every course. (27) Last summer, some teacher took every coarse(28) As a student, some teacher took every course~29) The scoping in which &quot;every&quot; outscopes &quot;some ~ is possible, although unpreferred, for the reading * (28); but it is not a possible scoping for (29) in any dialect that we have encountered.</Paragraph> <Paragraph position="29"> Rule 6 If polarity-sensitive &quot;any&quot; occurs within a clause in which its trigger does not occur, it must be raised out of that clause.</Paragraph> <Paragraph position="30"> De Dicto/De Re The mechanism described here can provide an account for the de dicto/de re distinction. null Another ambiguity associated with quantifier terms is whether or not the referent is required to exist. In PTQ (Montagne, 1973), the sentence John seeks a unicorn. (30) is assigned a de dicto reading (which does not require that any unicorns exist), seek'(~john ',%~(P,q uant(3,X,u nlcorn '(X),'P(X)))) and a de re reading (which requires the existence</Paragraph> <Paragraph position="32"> In PTQ, this distinction is produced by syntactic rules. Cooper (1975, 1983) demonstrated that a mechanism using a store could produce both readings from a single logical form.</Paragraph> <Paragraph position="33"> Our mechanism obtains similar results. Starting from the unscoped logical form seek'Cjohn','A(P,:P(qterm(a',X,unicorn'(X))))) with the intension operator &quot; treated as being optionally opaque, both readings are produced by the quantifier-scoping algorithm described here.</Paragraph> <Paragraph position="34"> Additional (unwarranted) scopings are not produced because these are the only two sites at which quantifiers can be pulled from the store.</Paragraph> <Paragraph position="35"> Nonrule There is a strong preference for a noun phrase in a prepositional phrase complement to outscope the head noun.</Paragraph> <Paragraph position="36"> This criterion is used in many quantifier scoping mechanisms. It is a good heuristic, but it is not a reliable rule. In John visited every house on a street. (31) John visited every house with a dog. (32) the heuristic correctly predicts the preferred stoping for (31), but fails for (32). 4 This heuristic is not part of our scoping algorithm; we believe that its effects are part of the processing consigned by us to the second phase of quantifier scoping (future work).</Paragraph> </Section> <Section position="5" start_page="36" end_page="38" type="metho"> <SectionTitle> BASIC ALGORITHM </SectionTitle> <Paragraph position="0"> The first level of our scoping algorithm generates the possible scopings, as described by Hobbs and Shieber (1987). However, we implemented ~ this with a different algorithm, partly for reasons of effEciency and partly because it could be easier expanded to include additional capabilities. The performance of the Hobbs and Shieber algorithm deteriorates as the number of quantifiers in the sentence increases---our analysis is that it spends a significant amount of time repeatedly traversing the logical form and doing structure copying (their goal was to produce a provably correct algorithm, not a highly efficient one). Our algorithm traverses the unscoped logical form, collecting the qterms (quantifier terms) into a store; then as the scoping for each qterm is determined, it is pulled out of the store, producing a scoped logical form.</Paragraph> <Paragraph position="1"> For a sentence with four qusatifiers, our algorithm is typically an order of magnitude faster than that presented by Hobbs sad Shieber.</Paragraph> <Paragraph position="2"> A simple example of the use of the store is provided by the sentence &quot;John saw a student,&quot; which has an unscoped logical form of see'(john',qterm(a',X,student'(X))) After quantifier scoping has placed the qterm in the store, the logical form is</Paragraph> <Paragraph position="4"> The scope for this quantifier is the whole sentence, so the qterm is puned out of the store to produce the scoped logical form quant(3,X,studeet'(X), see'~iohn',X)) The sentence &quot;Few students pass most ezamg' has the unscoped logical form pass'(qterm(few',X,student'(X)), qterm(most'.V.exam'(V))) After the qterms have been extracted, the remaining logical form sad the store are</Paragraph> <Paragraph position="6"> A qterm can have other qterms in its restriction sad our quantifier store is a structured collection (unlike the stores of Cooper sad LUNAR).</Paragraph> <Paragraph position="7"> The structure of qterms in the store corresponds to their relative positions in the unscoped logical form. For example, the unscoped logical form for &quot;every student in a college attends the lecture' is atten d'(qterrn(every' ,X,and(student'(X), in'(X,qterm(a',Y,college'(Y))))), qterm(the',Z,lecture'(Z))) When such qterms are placed in the store, this relationship is maintained by representing the collected qterms as trees (called qtrees), with the outer qterm as the root and those in its restriction as daughters:</Paragraph> <Paragraph position="9"> Consequently, the store is a forest of such qtrees, and the qterms occurring in the restriction of a qterm are themselves a forest of qtrees and are treated as if they were a store.</Paragraph> <Paragraph position="10"> As qterms are collected, they are inserted into the store in inverse order of preferencc c.g., the qterm that has narrowest-scope preference appears at the front of the list representing the forest. In implementing this algorithm in Prolog, we found that it was considerably easier to generate the scopings by working from the narrowest to the widest scope, rather than rice versa. As the various permutations of the quantifiers are generated, equivalent scopings are detected, and all but the most preferred one are then filtered out. In the following, both scopings of each sentence are logitally equivalent: Every student takes every test.</Paragraph> <Paragraph position="11"> Every student takes each test.</Paragraph> <Paragraph position="12"> A student takes a test.</Paragraph> <Paragraph position="13"> Some student takes a tes~.</Paragraph> <Paragraph position="14"> Each student takes the test.</Paragraph> <Paragraph position="15"> Eeery student takes the test.</Paragraph> <Paragraph position="16"> The student takes every test.</Paragraph> <Paragraph position="17"> In (33), (35), (37), sad (39), the preferred order is the same as the surface order, while in (34), (36), sad (38), the stronger quantifier occurs second in surface order, sad the scoping that corresponds to surface order is discarded. Filtering of equivalent permutations is achieved simply by comparing the qtree currently being pulled from the store with the preceding one; if the qusatifiers in their head qterms are logically equivalent, this quantifier scoping is discarded unless the qtree being pulled has wide-scope preference over its predecessor (in which case the other logically equivalent ordering will be discarded).</Paragraph> <Paragraph position="18"> Logically equivalent scopings can also be produced when a quantifier is raised out of the restriction of another. However, the quantifier permutations that produce equivalent scopings by raising are a subset of those produced by permuting siblings: null Every student in every race celebrated. (40) A student in a race celebrated. (41) Some student in a race celebrated. (42) Each student in the race celebrated. (43) Every student in the race celebrated. (44) The student in every race celebrated. (45) Note that the scopings for (40) and (45) are not logically equivalent. The scopings in the others axe logically equivalent, but in (41) and (43), the preferred scoping is the one corresponding to constituent structure, whereas in (42) and (44), the preferred scoping has the NP from the PP raised to have wider scope over the head noun.</Paragraph> <Paragraph position="19"> When a qtree is pulled from the store, the algorithm tries to produce additional permutations by raising subsets of qterrns (actually of qtrees) out of that qtree's restriction. When a qtree is raised, it is put back into the store---since qtrees are being assigned scope from narrowest to widest, this ensures that a raised qtree will receive wider scope than the qtree out of which it was raised.</Paragraph> <Paragraph position="20"> Because a raised qtrse may have its strength reduced when it is placed back in the store (an option in our system), a set of logically equivalent scopings could have all instances filtered out by a naive implementation. The problem arises in the following manner. Before the qtree is raised, the algorithm determines that the unraised scoping is logically equivalent to a raised one and that the latter is preferred, so it discards the former. When the qtree is raised and its strength reduced, it becomes weaker than the qtree out of which it was raised. The algorithm detects that the raised scoping is logically equivalent to an unralsed one, and determines--on the&quot; basis of the current strengths--that the unraised scoping is preferred, so it now discards the raised one. This problem is avoided by doing some additional bookkeeping.</Paragraph> <Paragraph position="21"> The current implementation of the above rules is very coarse-grained. The &quot;score&quot; indicating whether or not a quantifier should be assigned wide scope over another quantifier, logical form operator (e.g., a modal, negation), or syntactic constituent is one of four values: always (narrow scope is impossible), never (wide scope is impossible), pref (wide scope is preferred, but narrow scope is acceptable), and unpref (narrow scope is preferred). In the current implementation of the above preferences, a strong preference to take wider scope is treated as an instance of always, and a weak preference is treated as pref. For example, Preferences (3.1)-(3.3) are given by the following rules, in which Pref is the preference of a determiner Detl to take wider scope over another determiner Det2: if Detl and Det2 are both &quot;each&quot;:</Paragraph> <Paragraph position="23"> otherwise, if Detl is &quot;each&quot; (and Det2 is not), Pref = always otherwise, if Detl is an interrogative determiner, Pref-- always otherwise, if the logical forms for Detl and</Paragraph> <Paragraph position="25"> Overshoot The method described here results in .some quantifiers' being assigned scopes that are wider than appropriate, relative to other predicates (but not quantifiers) in the logical form.</Paragraph> <Paragraph position="26"> The sentence &quot;John visited every person on a committee&quot; has an uuscoped logical form of visit'(john',qterm(every',P, and(person'(P), on'(P, qterm(a',C,committee'(C)))))) and its preferred scoping is quant(V,P, quant(3,C,committee'(C), and(person'(P),on'(P,C))), visit'Cjohn'.P)) Note that person'(P) is independent of C; thus it can be outside the scope of the quantifier for C quant(V,P, and(person'(P), quant(q,C,committee'(C),on'(P,C))), visit'~iohn', P)) Such transformations can have a significant impact on the performance of the system, substantially reducing the processing time of queries for even a modest database. Rather than pass additional information so that quantifiers could be pulled at the correct point in the traversal of the logical form, we chose to let the scoping algorithm &quot;overshoot&quot; its mark and then lower the quantitiers to the correct position. This was considerably easier to implement, and it does not seem to have any performance penalty in our system.</Paragraph> </Section> class="xml-element"></Paper>