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<Paper uid="P92-1031">
  <Title>CONNECTION RELATIONS AND QUANTIFIER SCOPE</Title>
  <Section position="3" start_page="0" end_page="242" type="intro">
    <SectionTitle>
0. INTRODUCTION
</SectionTitle>
    <Paragraph position="0"> Many natural language sentences have more than one possible reading with regard to quantifier scope. The most widely used methods for scope determination generate all possible readings of a sentence with regard to quantifier scope by applying all quantifiers which occur in the sentence in all combinatorically possible sequences. These methods do not make use of the inner structure and meaning of a quantifier. At best, quantifiers are constrained by external conditions in order to eliminate some scope relations. The best known methods are: determination of scope in LF in GB (May 1985), Cooper Storage (Cooper 1983, Keller 1988) and the algorithm of Hobbs and Shieber (Hobbs/Shieber 1987). These methods assign, for instance, six possible readings to a sentence with three quantifiers. Using these methods, a sentence must be disambiguated in order to receive a semantic representation. This means that a scope-ambiguous sentence necessarily has several semantic representations, since the formalisms for the representation do not allow for scope-ambiguity.</Paragraph>
    <Paragraph position="1"> It is hard to imagine that human beings disambiguate scope-ambiguous sentences in the same way. The generation of all possible combinations of sequences of quantifiers and the assignment of these sequences to various readings seems to be cognitively inadequate.</Paragraph>
    <Paragraph position="2"> The problem becomes even more complicated when natural language quantifiers can be interpreted distributively as well as collectively, which can also lead to further readings. Let us take the following sentence from Kempson/Cormack (1981) as an example: Two examiners marked six scripts.</Paragraph>
    <Paragraph position="3"> The two quantifying noun phrases can in this case be interpreted either distributively or collectively. The quantifier two examiners can have wide scope over the quantifier six scripts, or vice versa, which all in all can lead to various readings. Kempson and Cormack assign four possible readings to this sentence,  Davies (1989) even eight. (A detailed discussion will follow.) No one, however, will make the claim that people will first assign all possible representations with regard to the scope of the quantifiers and their distribution, and will then eliminate certain interpretations according to the context; but this is today's standard procedure in linguistics. In many cases, it is also almost impossible to determine a preferred reading.</Paragraph>
    <Paragraph position="4"> The difficulties that people have when they are forced to disambiguate such sentences (to explicate all possible readings) point to the fact that people only assign an underdetermined scope-ambiguous representation in the first place.</Paragraph>
    <Paragraph position="5"> Such a representation of the example sentence would only contain the information that we are dealing with a marking-relation between examiners and scripts, and that we are always dealing with two examiners and six scripts. This representation does not contain any information about scope. On the basis of this representation one may in a given context derive a representation with a determined scope. But it may also be the case that this information is sufficient in order to understand the sentence if no scope-defining information is given in the context, since in many cases human beings do not disambiguate such sentences at all. They use underdetermined, scopeless interpretations, because their knowledge often need not be so precise. If a disambiguation is carried out, then this process is done in a very natural way on the basis of context and world knowledge. This points to the assumption that scope determination by human beings is performed on a semantic level and is deduced on the basis of acquired knowledge.</Paragraph>
    <Paragraph position="6"> I will present a formalism which works in a similar way. This formalism will also show that it is not necessary to work with many sequences of quantifiers in order to determine the various readings of a sentence with regard to quantifier scope.</Paragraph>
    <Paragraph position="7"> Within this formalism it is possible to represent an ambiguous sentence with an ambiguous representation which need not be disambiguated, but can be disambiguated at a later stage. The readings can either be specified more clearly by giving additional conditions, or they can be deduced from the basic ambiguous reading by inference. Here, the inner structure and the meaning of quantifiers play an important role. The process of disambiguation can only be performed when additional information that restricts the number of possible readings is available. As an example of such information, I will treat anaphoric relations.</Paragraph>
    <Paragraph position="8"> Intuitively speaking, the difference between assigning an undertermined representation to an ambiguous sentence and assigning a disjunction of all possible readings to this sentence corresponds to the difference between the following statements*: &amp;quot;Peter owns between 150 and 200 books.&amp;quot; and &amp;quot;Peter owns 150 or 151 or 152 or ... or 200 books.&amp;quot; It goes without saying that both statements are equivalent, since we can understand &amp;quot;150 or 151 or ... or 200&amp;quot; as a precise specification of &amp;quot;between 150 and 200&amp;quot;. Nevertheless, there are procedural differences in processing the two pieces of information; and there are cognitive differences for human beings, since we would never explicitly utter the second sentence. If we could represent &amp;quot;between 150 and 200&amp;quot; directly by a simple formula and not by giving a disjunction of 51 elements, then we may certainly gain great procedural and representational advantages.</Paragraph>
    <Paragraph position="9"> The deduction of readings in semantics does not of course exclude a consideration of syntactic restrictions. They can be imported into the semantics, for example by passing syntactic information with special indices, as * The comparison stems from Christopher Habel.</Paragraph>
    <Paragraph position="10">  described in Latecki (1991). Nevertheless, in this paper I will abstain from taking syntactic restrictions into consideration.</Paragraph>
  </Section>
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