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<Paper uid="C92-3127">
  <Title>A HYBRID SYSTEM FOR QUANTIFIER SCOPING</Title>
  <Section position="1" start_page="0" end_page="0" type="metho">
    <SectionTitle>
A HYBRID SYSTEM FOR QUANTIFIER SCOPING
1. Introduction
</SectionTitle>
    <Paragraph position="0"> A prominent source of ambiguity confronting natural language processing systems is ambiguity of quantifier scope relations. For example, the sentence Some target was hit by every arrow has one reading on which the quantified noun phrase (NP) some target has wider scope than the quantified NP every arrow (some particular target got hit by all the arrows), and another reading on which every arrow has wide scope (each arrow hit some target or other). Many factors influence preferred scope readings.</Paragraph>
    <Paragraph position="1"> Semantic factors, for example: in Sam served one beer to all customers, we prefer wide scope for all because the alternative reading entails the unlikely scenario of patrons huddled around a single beer mug. Syntactic factors: e.g.</Paragraph>
    <Paragraph position="2"> embedded prepositional objects often scope over heads, as in Every teacher at some high school joined the union, whereas heads usually assume scope over NPs contained in a relative clause, as in Every teacher who is at some high school joined the union. Lexical factors (i.e. the lexical identity of quantifiers): e.g. each tends toward wide scope and a toward narrow scope. Linear order is a factor - leftmost quantifiers tend to have wide scope - and there are others as well.</Paragraph>
    <Paragraph position="3"> Given the relevance of different factors, a question arises: how can a system determine a scope reading based on the combination of factors present in any given sentence? The standard approach has two parts: f'wst, assign measures to the scoping influences of specific factors taken individually, and second, integrate the individual measures. The first task is performed by various &amp;quot;specialists&amp;quot;. A system may have a lexical specialist which represents the wide scope tendency of each, a specialist which represents the inverse scoping tendency of an embedded prepositional object, a specialist which represents the tendency of quantifiers to scope according to linear order, and so on. The system will prefer those scope orders for which fint(fspecl, fspec 2 .... ) is optimal, where lint is the integrating function and each fspec i is a specialist. For example, in the system of Grosz et. al. (1987), the specialists are called &amp;quot;critics.&amp;quot; Given a candidate scope order, the &amp;quot;left-right&amp;quot;</Paragraph>
  </Section>
  <Section position="2" start_page="0" end_page="0" type="metho">
    <SectionTitle>
ARNOLD J. CHIEN
PRC Inc.
1500 PRC Dr., 5S3; McLean, VA 22102 USA
</SectionTitle>
    <Paragraph position="0"> chien arnold@po.gis.prc.com critic deducts points for each deviation from left-to-right scope order; the &amp;quot;quantifier strength&amp;quot; critic (i.e. lexical specialist) uses a numerical ranking of quantifiers to add and deduct points depending on how closely the candidate order respects the ranking; and so on. The integrating function fint simply adds up the critics' points, though Grosz et. al. allow that the critics' judgments may need to be variously weighted in some fashion. To my knowledge all current systems use an &amp;quot;integration of specialists&amp;quot; (henceforth IS) approach, though not always as explicitly as Grosz et. al.; e.g. lint often is implicit in the order in which various specialized rules or preferences are tested in the clauses of a complex conditional. See e.g. van Lehn (1978), Woods (1978), Allen (1987), Hurum (1988), Moran (1988). (Note that the common categorization of IS systems does not deny the myriad differences of detail between systems; indeed the functional characterization is useful because it abstracts over these differences.) There is an alternative to IS. In what I will call &amp;quot;hybridization,&amp;quot; different factors are conjoined before any scope judgment is made. A system hybridized for lexical and syntactic factors has no lexical or syntactic specialists, but rather a single function, call it flex-syn, whose input is the conjunction of lexical and syntactic factors in a sentence. Given an input with quantifiers ql and q2 and (relevant) syntactic features s 1, ..., Sn, such a system computes flex-syn(ql, q2,sl ..... Sn) rather than fint(flex(ql, q2), fsynl(Sl ) ..... fsynn(Sn)).</Paragraph>
    <Paragraph position="1"> The advantage of this is that scope intuitions can be recovered directly. Take the tendency for an embedded prepositional object to scope over a head NP. This tendency varies depending on the quantifiers involved, among other things. In e.g.</Paragraph>
    <Paragraph position="2"> Every man on some committee abstained, there is a preference for the embedded NP to assume wide scope, but in A man on many conn,nittees abstained, the preference seems reversed. A prepositional phrase (PP) specialist in an IS system will not know how the preference changes when a and many quantify the head and the embedded object; since it is a specialist, it does not consider lexical input. Rather, the ACRES DE COL1NG-92, NANTES, 23-28 AOt'rr 1992 8 6 0 PROC. OI: COLING-92, NANIES, AUG. 23-28. 1992 system must turn to the lexical specialist, which for its part knows e.g. that a usually takes narrow scope, but not how the behavior of a and many varies with specific environments, such as embedded PP constructions. 1t is hard to see, then, how any integration of these specialists could prescribe a scoping of a over many in an embedded PP context, since both prefer the reverse scoping. (An additional ordering specialist may prefer the correct scoping but without ad hoc weighting, the integrated preference will still be incorrect.) But there is no problem in a hybrid system, because the values flex.syn(every, some, head-embedded-PP) and flex~syn(a, many, head-embedded-PP) are coml~letely independent, as opposed to having a PP specialist in common, and can be specifiext however intuitions dictate. Scope judgments are based on all the lexical and syntactic factors present, rather than on each factor taken in abstraction tY=om the others.</Paragraph>
    <Paragraph position="3"> My case for hybridization does not rely on counterexample, but on the flmdamentally murky nature of IS. Consider an analogy.</Paragraph>
    <Paragraph position="4"> Suppose there is election data showing, for any pair of candidates and any state, the relative vofiug preference when the candidates ran in the state. How should we design a system to produce a preference given two candidates and a state? A natural approach would be to simply retrieve the datum based on the candidate and state input together. But on an IS approach, a &amp;quot;candidate&amp;quot; specialist would measure a tendency over all states of the relative performance of the two given candidates; a &amp;quot;state&amp;quot; specialist would measure a tendency over the relative performances of all candidates, taken pairwise, in the given state; then somehow the two measures would be integrated. The problem here is that whereas the desired datum is a simple, the computation is barred on complex abstractions over much data other than the desired, relevant bit. That is the basic difficulty of an IS system, which the PP example was meant to illustrate.</Paragraph>
    <Paragraph position="5"> Though semantic and pragmatic factors also influence scope, they are not central to my current concern: the design of a &amp;quot;base&amp;quot; scoping unit which can be ported to different domains and adaptively extended, and which can be improved in~,wementatly as bits of real-world knowledge are gradually added to the system (as with Grosz et.</Paragraph>
    <Paragraph position="6"> al. 1987, Moran 1988, and Hurum 1988).</Paragraph>
    <Paragraph position="7"> Hence the focus on syntactic and lexical factors, which make up most of the domain-independent factors. I will return to this issue in section 3.</Paragraph>
  </Section>
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