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<Paper uid="E93-1018">
  <Title>A unification-based approach to multiple VP Ellipsis resolution*</Title>
  <Section position="9" start_page="145" end_page="146" type="evalu">
    <SectionTitle>
7 Problems and further research
</SectionTitle>
    <Paragraph position="0"> A first problem concerns the propagation of anaphoric information throughout the discourse tree.</Paragraph>
    <Paragraph position="1"> To see what the problem is, consider the discourse in (14).</Paragraph>
    <Paragraph position="2"> (14) Jon won't dance unless Mary does.</Paragraph>
    <Paragraph position="3"> In the absence of any additional context, the antecedent of the VPE in the second clause is the VP of the first clause i.e dance. Now let us examine again the discourse rule for unless sketched in section 3. For this rule, the distribution of anaphoric information can be pictured as follows: \[11, I2~O1, 02\] Note that anaphoric information is only shared between mother and daughters, not between sisters. This means that the rule sketched in section 3.3 will fail to resolve the VPE in example (14) because in this case, resolution can only obtain if O1 - I2 i.e. if anaphoric information is shared between sisters. An obvious fix would be to modify the unless rule so that Is unifies not only with the IN value of the rightmost daughter but also with the OUT value of the leftmost daughter. The modified rule would then be:  However, although this would solve the problem raised by example (14), it would still fail to account for cases such as (15).</Paragraph>
    <Paragraph position="4">  (15) (a) Jon won't \[1 dance\] unless (b) Mary does 01 and (c) Bob won't \[2 come\] unless (d) Sarah  does 02.</Paragraph>
    <Paragraph position="5"> Here the problem is that the new unless rule requires the IN value of (d) to unify both with the OUT value of (b) i.e. dance and with the OUT value of (c) i.e. come. Clearly unification fails and thus example (15), although perfectly well-formed, is rejected by the grammar.</Paragraph>
    <Paragraph position="6"> In more general terms, the problem is that anaphoric information can come to be instantiated both in a top-down and in a bottom-up fashion (i.e. through sharing of information between mother and daughter or through sharing of information between sisters) 11. When the two types of information conflict, unification fails and a perfectly well formed discourse may be rejected by the grammar. In other words, the grammar will undergenerate.</Paragraph>
    <Paragraph position="7"> There are several possible solutions to this problem. A first one would be to privilege one source of information over the other, say by means of priority union. In this way, one anaphoric flow would overwrite the other. But apart form the computational problems involved in using such rewrite operations at run time, it is also unclear which information should be privileged. Thus although in (15), bottom-up (or local) information seems to prevail, example  (16) shows that in some cases, top-down information may be strongest: (16) (a) Jon won't go to Manchester unless (b) he  opens his mail and (c) Bob won't go to Paris unless (d) he does.</Paragraph>
    <Paragraph position="8"> alThe first type of anaphoric flow is top-down in that anaphoric information on the mother may be required to unify with the anaphoric information of some other node higher up in the discourse tree, whereas the second type is bottom-up because the anaphoric information specified on the sisters may in turn be required to unify with the anaphoric information carried by some other node lower down in the discourse tree.</Paragraph>
    <Paragraph position="9">  Here, there is at least one reading where the ellipsis in (d) resolves to the parallel element (b) (i.e. opens his mail) rather than to the immediately preceding VP (i.e. go to Paris). Furthermore it is easy to find cases where the overall discourse is ambiguous between a &amp;quot;top-down reading&amp;quot; and a &amp;quot;bottomup&amp;quot; one. Thus perhaps a better solution would be to always allow both possibilities and to let the various modules of the grammar decide which reading is actually available. The details and the adequacy of such an approach, I leave here as an open research question.</Paragraph>
    <Paragraph position="10"> A second problem concerning the present paper concerns the definition of discourse relations and of equivalence classes over discourse relations. Here it is perhaps worth stressing that although logical connectives have been used throughout the paper to represent discourse relations, these are definitely not a sufficient means of characterization. As a simple case in point, consider a natural language discourse of the form P so Q. In section 3.2, such a discourse is translated as p A q (where p and q represent the propositional content of the natural language discourses P and Q respectively). Clearly this translation does not exhaust the meaning of the discourse connective so: for instance, the causal link between p and q is not accounted for. More generally, it is clear that much work remains to be done on the semantics of discourse relations before the present analysis of multiple VPE resolution can be adequately tested.</Paragraph>
    <Paragraph position="11"> Finally, a third question involves the interaction of discourse grammar with anaphora resolution in general. As already mentioned, the resolution of most types of anaphora can be argued to be influenced by discourse structure. It would be interesting to investigate in how far the various mechanisms developed to express this constraint are compatible. More specifically, it would be interesting to see whether the discourse grammar sketched in section 2 could be made to account for the complex interaction of VPE with other anaphoric phenomena such as strict/sloppy identity, pronominal and temporal anaphora.</Paragraph>
  </Section>
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