<?xml version="1.0" standalone="yes"?>
<Paper uid="C90-3022">
  <Title>A Computational Approach to Binding Theory*</Title>
  <Section position="6" start_page="0" end_page="0" type="concl">
    <SectionTitle>
5 Discussion
</SectionTitle>
    <Paragraph position="0"> By fixing an upper bound, it has been shown that the computational complexity of the recognition problem of a language that encodes Principles A and B of BT is in p.~S These results are similar to those obtained by all authors who have studied BT from a computational point of view (Correa, 1988; Ingria and Sta\[lard, 1989; Berwick and Weinberg, 1984; Berwick, 1989).</Paragraph>
    <Paragraph position="1"> Nevertheless, with respect to such works we have both taken a rather different perspective and paid more attention to the subtleties of the linguistic theory.</Paragraph>
    <Paragraph position="2"> Previous works were mainly concerned with providing actual referents (actual indexations) for the NPs of a sentence. We claim, on the contrary, that Principles A, B and C per se are not sufficient for this puq~ose, since BT only restricls the search space for indices selection, and does not actually provide them. For instance, Correa (1988) proposes an algorithm that builds lists of antecedents for pronouns and anaphors, and complements it with a Binding Rule, that selects, for each item, an indexation from such lists. However, the selection of an antecedent for a certain item could affect the indexation of other nodes, leading to violations of Principle B. 16 In tb.is framework, a related problem arises considering split antecedents for pronouns; in fact, a pronoun can be coindexed with a set of items, provided that each of them has a different thematic roleJ 7 This point has never been explicitely addressed in computational works; nevertheless, if the purpose is to output actual indexations, it seems to us that the only possibility, in order to consider split antecedents, would be to compute lists of possible antecedents for pronouns and then to consider their power set; this way, however, the search space becomes exponentially large.</Paragraph>
    <Paragraph position="3"> Furthermore, the interactions of the referential properties 15C/o denotes the class of languages recognizable in polynomial time by a deterministic Turing machine.</Paragraph>
    <Paragraph position="4"> 16Consider, for instance, the following sentence: (i) Mary says that she saw her in this case both embedded pronouns can take Mary as an antecedent, according to Correa's Binding Rule, leading to a violation of Principle B. In our opinion, to avoid this incorrect result, it is necessary to put together the constraints that have been separately computed for each item according to Principles A and B (and C); this way we can account for the interactions between coindexations and disjointness. A possible way to do it, is to pose the problem of BT verification, i.e. whether a given index assignment for the NPs of a sentence complies with the restrictions of BT. See Giorgi, Pianesi, Satta (1989b).</Paragraph>
    <Paragraph position="5"> 17For instance, in Mary tom John that they should go home the pronoun they can refer to the complex antecedent constituted by Mary plus John.</Paragraph>
    <Paragraph position="6"> of a split antecedent with those of other items (,possibly other split antecedents) would thereby hardly be addressable. TM Finally, given the referential properties of pronouns, it seems that there is no point in trying to use the grammatical knowledge of BT to hypothesise intrasentential antecedenks, t9 Another crucial aspect concerns the treatment of local domains, whose importance has often been misconsidered in computational works on BT. Such a notion has been mainly seen as a static one, whereas, in our interpretation, the value of the actual domain depends on the interaction of structural and lexical properties of at least two different positions in the derivation tree. For example, in Ingria and Stallard (1989), an S node is taken to be the binding domain for every node it dominates. Consider, however, the cases in which government of the specifier position of a maximal projection is obtained through an external head; this situation arises, for instance, in exceptional case marking examples, as in John believed him to be intelligent. Ingria and Stallard's static definition of local domain would lead to the conclusion that the pronoun, being dominated by an S type node (the embedded sentence), is free in that category and, thus, could be coindexed outside, for instance with the R-expression John. But this is ungrammatical; according to the definition adopted here, the domain of binding for him is the matrix clause, so that the pronoun must, correctly, be free in it, i.e, disjoint from John. Our approach also improves on Ingria and Smllard's treatment of NP as a binding domain. If a node NP containes a possessive then they consider it a binding domain for all the nodes it dominates, except the possessive itself. There are at least two problems, though. First, they do not predict that a pronoun subcategorized for by the head cannot be bound in the domain of the NP; second the well-known not complementary distribution of pronouns and anaphors in the specifier position of an NP cannot be accounted for. The definition of binding domain adopted in (5) and the way it is computezt allow our algorithms to avoid these problems; see Giorgi, Pianesi, Satta (1989a).</Paragraph>
    <Paragraph position="7"> As a final remark, note that in this work the interaction with A-chains has been explicitely considered. This problem is particularly important in Italian which, being a pro-drop language, admits sentences like (8) and (10): (10) Giannii ha detto che proj arriver~t \[la propriai madre\]j lit.: Gianni told that will arrive self's mother Gianni told that his mother will arrive 18Also the so called weak crossover phenomena may raise some problems. Roughly, pronouns cannot be coindexed with non c-commanding quantified expressions, as in *His imother loves \[every boY\]i , where the embedded pronoun cannot be taken to refer to the quantified expression. But this fact raises some problems for both Correa's and Ingria's approach.</Paragraph>
    <Paragraph position="8"> 19pronouns can refer intersententially or deictically; note that this property is shared with certain R-expressions, like the epithets, which obey Principle C (see Ha'ik, 1984).</Paragraph>
    <Paragraph position="9"> 124 5 in (8) the postverbal slibject pronoun is coindexed with the expletive pro, but a procedure looking for disjoint elements would output a list containing pro (it lies in the local domain of the pronoun) thereby giving rise to a contradiction: the pronoun is coindexed with the expletive pro but must be disjoint fi'om it. In (10), we must avoid the anaphoric possessive proprio being coindexed with the c-commanding expletive pro, in order to rule out circular interpretations. The circularity and identity checks, discussed in Section 3.2, explicitly take care of these cases.</Paragraph>
  </Section>
class="xml-element"></Paper>