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<Paper uid="E91-1008">
  <Title>INDEXING AND REFERENTIAL DEPENDENCIES WITHIN BINDING COMPUTATIONAL FRAMEWORK</Title>
  <Section position="7" start_page="0" end_page="0" type="concl">
    <SectionTitle>
5 Conclusions
</SectionTitle>
    <Paragraph position="0"> BT is concerned with the relationships among the references of NPs. Indices, however, tend to collapse together situations in which more subtle distinctions seem to be needed or blur the distinctions between symmetrical relationships (coreference) and asymmetrical ones (binding).</Paragraph>
    <Paragraph position="1"> A formalism has been provided that does not suffer the shortcomings of indexation. It permits a relevant number of phenomena to be addressed in a rather natural way and provides a richer and less ambiguous input to the semantic routines. The overall architecture can be depicted as follows: given a sentence, w, and a phrase structure tree representation &amp;quot;rw, a set ~w is built which, essentially, is a partial encoding of Principles A, B and C of BT as applied to z~,. ~w, together with general BT compatibility conditions (see Theorem 1), constrains the form and content of any well 12Generalizing, it is easy to see how the empty set is a BT compatible indexation set whenever anaphors are not involved.</Paragraph>
    <Paragraph position="2"> - 43 formed indexation set, ~w. As far as the version of BT considered here (essentially, that of Chomsky, (1986)) is concerned, the work of syntax ends with $,v; any further computation is semantic.</Paragraph>
    <Paragraph position="3"> The formalism could be extended to other phenomena. Consider, for instance, the ban against circular reference; statements (ii) and (iii) of Theorem 1 account for the particular cases in which an item a is bound by itself or contributes to the reference of another element while being coindexed with it. More general cases were addressed by the so called i-within-i condition of Chomsky (1981) and, more recently, by the condition on circular chains of Hoeksema and Napoli (1990). The latter forbids circular chains, where a chain is a sequence of elements al ..... an such that either ai is coindexed with ai+l or a/contains ai+l. This condition could be captured within the framework proposed here by explicitly introducing dominance, say, by means of a relation symbol sl and, then, by requiring that no circular paths are in ~w such that their strings are in the language (siLl) +. If this approach is tenable, then a parallelism emerges between the s and the s~ relations, since both are involved in statements forbidding some kind of circularity (for s, the relevant statement is (iii) of Theorem 1) and both can be seen as estabilishing some sort of referential dependency between two items. The relevant dependency for s is set inclusion while for sl it is some kind of functional dependency, under the assumption that the reference of a constituent is a function of the references of its subconstituents. This observation accounts for the fact that disjoint reference constraints affect items in the s relation (see point (vi) of Theorem 1) but not those in sl.</Paragraph>
    <Paragraph position="4"> This work has been developed as part of a larger system that uses GB as the reference syntactic theory. Currently, we are studying two applications of the formalism presented here: 1) on-line algorithms for the satisfiability problem addressed in Section 4.2 in an off-line fashion; the interleaving of the computation of satisfiability with structure building would provide a way to rule out ungrammatical analysis of the input string at an early stage, i.e. as soon aS their incapability of satisfing BT can be detected; 2) algorithms for the exhaustive generation of all index sets that are BT compatible w.r.t, a given zw,.</Paragraph>
    <Paragraph position="5"> ACKNOWLEDGMENTS. The author would like to acknowledge the continuous and fruitful discussions with Alessandra Giorgi and Giorgio Satta; many of the ideas in this paper have arisen during them. Of course, the responsability for any error is author's one.</Paragraph>
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