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<Paper uid="J82-3004">
  <Title>Coping with Syntactic Ambiguity or How to Put the Block in the Box on the Table 1</Title>
  <Section position="11" start_page="5" end_page="5" type="concl">
    <SectionTitle>
10. Conclusion
</SectionTitle>
    <Paragraph position="0"> We began our discussion with the observation that certain grammars are &amp;quot;every way ambiguous&amp;quot; and suggested that this observation could lead to improved parsing performance. Catalan grammars were then introduced to remedy the situation so that the processor can delay attachment decisions until it discovers some more useful constraints. Until such time, the processor can do little more than note that the input sentence is &amp;quot;every way ambiguous.&amp;quot; We suggested that a table lookup scheme might be an effective method to implement such a processor.</Paragraph>
    <Paragraph position="1"> We then introduced rules for combining primitive grammars, such as Catalan grammars, into composite grammars. This linear systems view &amp;quot;bundles up&amp;quot; all the parse trees into a single concise description capable of telling us everything we might want to know about the parses (including how much it might cost to ask a particular question). This abstract view of ambiguity enables us to ask questions in the most convenient order, and to delay asking until it is clear that the pay-off will exceed the cost. This abstraction was very strongly influenced by the notion of delayed binding.</Paragraph>
    <Paragraph position="2"> We have presented combination rules in three different representation systems: power series, ATNs, and context-free grammars, each of which contributed its own insights. Power series are convenient for defining the algebraic operations, ATNs are most suited for discussing implementation issues, and context-free grammars enable the shortest derivations. Perhaps the following quotation best summarizes our motivation for alternating among these three representation systems: null A thing or idea seems meaningful only when we have several different ways to represent it - different perspectives and different associations. Then you can turn it around in your mind, so to speak; however, it seems at the moment you can see it another way; you never come to a full stop. (Minsky 1981, p. 19) In each of these representation schemes, we have introduced five primitive grammars: Catalan, Unit Step, 1, and 0, and terminals; and four composition rules: addition, subtraction, multiplication, and division. We have seen that it is often possible to employ these analytic tools in order to re-organize (compile) the grammar into a form more suitable for processing efficiently. We have identified certain situations where the ambiguity is combinatoric, and have sketched a few modifications to the grammar that enable processing to proceed in a more efficient manner.</Paragraph>
    <Paragraph position="3"> In particular, we have observed it to be important for the grammar to avoid referencing quantities that are not easily determined, such as the dividing point between a noun phrase and a prepositional phrase as in (55) Put the block in the box on the table in the kitchen ...</Paragraph>
    <Paragraph position="4"> We have seen that the desired re-organization can be achieved by taking advantage of the fact that the auto-convolution of a Catalan series produces another Catalan series. This reduced processing time from O(n 3) to almost linear time. Similar analyses have been discussed for a number of lexically and structurally ambiguous constructions, culminating with the example in section 9, where we transformed a grammar into a form that could be parsed by a single left-to-right pass over the terminal elements. Currently, these grammar reformulations have to be performed by hand. It ought to be possible to automate this process so that the reformulations could be performed by a grammar compiler. We leave this project open for future research. null</Paragraph>
  </Section>
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