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<Paper uid="P98-1057">
  <Title>Group Theory and Linguistic Processing*</Title>
  <Section position="5" start_page="349" end_page="350" type="evalu">
    <SectionTitle>
4 Generation
</SectionTitle>
    <Paragraph position="0"> Applying directly, as we have just done, the definition of a group computation structure in order to obtain public results can be somewhat unintuitive. It is often easier to use the preorder --+. If, for a, b, c 6 F(V), abc is a relator, then abc --+ 1, and therefore b --+ a-lc -1. Taking this remark into account, it is possible to write the relators of our G-grammar as the &amp;quot;rewriting rules&amp;quot; of Fig. 2; we use the notation ----&amp;quot; instead of --+ to distinguish these rules from the parsing rules which will be introduced in the next section.</Paragraph>
    <Paragraph position="1"> The rules of Fig. 2 have a systematic structure. The left-hand side of each rule consists of a single logical form, taken from the corresponding relator in the Ggrammar; the right-hand side is obtained by &amp;quot;moving&amp;quot; all the renmining elements in the relator to the right of the arrow.</Paragraph>
    <Paragraph position="2"> Because the rules of Fig. 2 privilege the rewriting of a logical form into an expression of F(V), they are called generation-oriented rules associated with the Ggrammar. null Using these rules, and the fact that the preorder is compatible with the product of F(V), the fact that s ( j, 1 ) louise-lsaw-ljohn - 1 is a public result can be obtained in a simpler way than previously. We have:</Paragraph>
    <Paragraph position="4"> by the seventh, first and second rules (properly instanciated), and therefore, by transitivity and compatibility of the preorder: s(j,1) ~ j saw 1 john saw 1 ~ john saw louise which .proves that s (j, 1 ) ---~john saw louise, which Is equivalent to saying that s(j, 1) louise- 1 saw- l john- 1 is a public result. Some other generation examples are given in Fig. 3. The first example is straightforward and works similarly to the one we have just seen: from the logical form 5. ( s ( j, 1 ), p) one can derive the phonological string john saw louise in paris.</Paragraph>
    <Paragraph position="6"> _.x j saw 1 in p --~ john saw 1 in p john saw louise in p john saw louise in paris  ev(m,x,sm(w,y, s (x,y) ) ) --~ ct -I every m x -I c~ sm(w,y,s(x,y)) 0 -1 every m x -1 o~ 19 -1 some w y-1 /3 s (x,y) ---, cr -~ every man x -1 a /3-1 some woman y-1 /3 x saw y a -1 every man x -1 a x saw some woman (by taking/3 = saw -1 x -1) __x every man saw some woman (by taking a = 1) sm(w,y,ev(m,x, s (x,y) ) ) ._~ /3-i some w y-1 /3 ev(m,x,s(x,y))) /3 -I some w y-1 /9 ce-1 ever)' m x -1 ce s(x,y) --~ /3 -1 some woman y-1 fl c~ -1 ever), man x -1 ce x saw y /3 -1 some woman y-1 /3 every man saw y (by taking a = 1) .--, every man saw some woman (by taking/3 = saw -1 man -a every -1)  merit, quantified noun phrases can move to whatever place is assigned to them after the expansion of their &amp;quot;scope&amp;quot; predicate, a place which was unpredictable at the time of the expansion of the quantified logical form. The identifiers act as &amp;quot;target markers&amp;quot; for the quantified noun phrase: the only way to &amp;quot;get rid&amp;quot; of an identifier x is by moving z -1, and therefore with it the corresponding quantified noun phrase, to a place where it can cancel with z.</Paragraph>
  </Section>
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