<?xml version="1.0" standalone="yes"?>
<Paper uid="C90-3034">
  <Title>A Quantifier Scoping Algorithm without A Free Variable Constraint</Title>
  <Section position="6" start_page="192" end_page="192" type="evalu">
    <SectionTitle>
5 Pronouns
</SectionTitle>
    <Paragraph position="0"> Introduchlg complex noun phrase led to increased complexity in the H&amp;S algorithm. The introduction of structure such as 5. Every man saw a plcture of himself where &amp;quot;him&amp;quot; is bound by &amp;quot;every man&amp;quot; leads to yet more. Take the representation of 5. as 6. saw(&lt;,,very x man(x)&gt;,&lt;a y picture(y,x)&gt;) Applying &lt;every x man(x)&gt; first, via the H&amp;S mechanism, gives (every x man(x) saw(x,&lt;a y picture(y,z)&gt;)) Application of &lt;a y picture(y,x)&gt; would now lead to &amp;quot;x&amp;quot; being free. H&amp;S prevent this by stipulating that a complex term is applicable only if all free variables in the term are also free in the containing formula. \[Pereira 1989\] calls this 'The Free; Variable Constraint' and complains of an appeal to logical syntax.</Paragraph>
    <Paragraph position="1"> Our own methodology avoids this. First, note that 6) is supposed l;o be a purely syntactic structure. The occurrence of &amp;quot;x&amp;quot; in &amp;quot;picture(y,x)&amp;quot; represents the pronoun &amp;quot;himself&amp;quot;, and the fact that &amp;quot;x&amp;quot; also occurs in &amp;quot;&lt;every x man(x)&gt;&amp;quot; represents the grammatical relation holding bef~ween &amp;quot;&lt;every x man(x)&gt;&amp;quot; and &amp;quot;himselP'. Coindexing is used here just to indicate certain grammatical relations. ~ Tile following notation is clearer.</Paragraph>
    <Paragraph position="3"> Now, we alter our quantification rule so that if C is an environment containing &lt;q x r(x)&gt;, our new term is constructed from &amp;quot;q&amp;quot;, &amp;quot;x&amp;quot;, and recursions on &amp;quot;r(x)&amp;quot; and C where &lt;q x r(z)&gt; and all embedded coindexed reflexives are replaced by &amp;quot;x&amp;quot;.</Paragraph>
    <Paragraph position="4"> ~;uppose vce choose to apply ~This is one area where H&amp;S'e analysis is d\]fflcult to follow - wh~t is the role of variables in the input and intermediate forms ? &lt;a y picture(y,himself-x)&gt; first to 6). Then we construct our result from &amp;quot;a', &amp;quot;y&amp;quot; and recursions on both &amp;quot;saw(&lt;every x man(x)&gt;,y)&amp;quot; and &amp;quot;picture(y,himself-x)&amp;quot; ;the final recursion cannot proceed however, for we have no rule to interpret a reflexive in this position. There is no appeal to logical syntax, only English syntax.</Paragraph>
    <Paragraph position="5"> The same holds true of non-reflexives as in 7. Every man saw a friend of his where &amp;quot;every man&amp;quot; and &amp;quot;his&amp;quot; are co-indexed. 6</Paragraph>
  </Section>
class="xml-element"></Paper>