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<Paper uid="W04-0712">
  <Title>Ellipsis Resolution by Controlled Default Unification for Multi-modal and Speech Dialog Systems</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
2 Default unification
</SectionTitle>
    <Paragraph position="0"> Default unification is a method to inherit defeasible (in our case old) information which does not contradict strict (in our case new) information. As already mentioned, the consistency criterion is to weak, but the basic approach is useful. There are two forms of default unification: credulous and skeptical default unification. Credulous default unification tries to maintain as much old information as possible. Due to structure sharing, there are often different alternatives for achieving a maximal amount of old information. Skeptical default unification takes only the information that is common to all credulous solutions. We are interested in getting every maximal solution, which correspond to the strict, sloppy or mixed readings of ellipsis. By mixed readings we mean readings that contain a strict reading in one part, and a sloppy reading in another.</Paragraph>
    <Paragraph position="1"> We follow the definition of credulous default unification provided by Carpenter (Carpenter, 1992). But we take the most general type as the top element of the type lattice, while Carpenter takes it as the bottom element.</Paragraph>
    <Paragraph position="2"> If O is the old, defeasible information and N is new, strict information, then the credulous default unification of O and N is the unification of O' with N, where O' is a minimal structure that subsumes O such that O' and N unify: O &gt;uc N = fO0uNjO0 w O minimal s.t. O0uN 6= ?g The following example, shows how default unification can be used in ellipsis resolution.</Paragraph>
    <Paragraph position="3">  The analysis of these utterances is slightly simplified. John would get a more complicated presentation with john being the value of the NAME feature of the type person. The verb do is considered as being the most general verb with an agent. We use here event-agentive as a supertype of activities. null In this example the types of the top nodes are on a comparable &amp;quot;level&amp;quot;. By being on a comparable level we mean that the top node of the one item is a supertype of the top node type of the other item.</Paragraph>
    <Paragraph position="4"> Notice that due to the well-typing condition, types and features may not be mixed arbitrarily . For instance, the most general type of the type hierarchy (and many others too), cannot be combined with the feature agent. Otherwise our level condition would be meaningless.</Paragraph>
    <Paragraph position="5"> We find two minimal upper bounds of (1.) that unify with (2.).</Paragraph>
    <Paragraph position="6">  We get by unifying (1') with (2) the strict reading (2'), while we get the sloppy reading (2&amp;quot;) by using</Paragraph>
  </Section>
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