Indexing And A Referential Dependencies Within Binding Theory: Computational Framework

This work is concerned with the development of instruments for GB parsing. An alternative to the well known indexation system of (Chomsky, 1981) will be proposed and then used to formalize the view of Binding Theory in terms of the generation of constraints on the referential properties of the NPs of a sentence. Finally the problems of verification and satisfiability of BT will be addressed within the proposed framework. 1 I n t r o d u c t i o n This work is concerned with the development of instruments for GB parsing (see Barton, (1984); Berwick (1987); Kolb & Tiersch, (1990)); in particular, our attention will be focused on the Binding Theory (henceforth, BT) a module of the theory of Government and Binding (henceforth, GB; see Chomsky (1981; 1986)). It has been pointed out (eg. in Kolb & Tiersch, (1990)) that the lack of a complete and coherent formalization of a linguistic theory like GB can be a major obstacle in addressing the issue of principle-based parsing; this is true of BT too, in particular with respect to the indexing system of Chomsky (1981), the shortcomings of which have often been pointed out in the literature. A formalism for the treatment of the referential relationships among the NPs of a sentence will be presented that is more expressive than indexation and more effective as a computational tool. In Section 2 the indexing system and the role it plays within BT will be discussed; in Section 3, an alternative will be developed that overcomes some of the shortcomings of indexing. Such a system will, then, be used to formalize the view of BT as a device that generates (syntactic) constraints on reference. In Section 4, it will be shown how our proposal could be applied to some computational problems, i.e. the problems of verification and satisfiability within BT. 2 P r e l i m i n a r i e s Since Chomsky (1981), it has become commonplace to denote the interpretative relations among the NPs of a sentence by means of indices, i.e. integers attached to NPs in such a way that elements bearing the same index are taken to denote the same object(s), while different indices correspond to different denotations; most of the statements of BT have been |aid down in terms of this system (Chomsky, 1981, 1986). In a number of works (see Chomsky (1981), Higginbotham (1983) and Lasnik & Uriagereka (1988)), however, it has been pointed out that the indexing device is not adequate to capture certain referential relations; this is true for the relation between pronouns and split antecedents, i.e. antecedents composed of two or more arguments bearing different thematic roles, l Furthermore, indices blur the distinction between coindexing under c-command and coindexing without c-command, thereby making it difficult to capture the dependence of an element, behaving like a variable, upon its antecedent (see Reinhart, (1983)). 2 The replacement of indices with index sets has been proposed as a way to address the first problem (see Higginbotham, (1983)): an ordinary index is substituted by a singleton; when there are pluralities, e.g. when an NP is coindexed with a split antecedent, it is annotated with the (set) union of the index sets of each component of the plurality; therefore, coindexing amounts to equating index sets. In this view, the ordinary conditions on disjoint reference (Principles B and C of BT) must be extended to avoid not only identical reference but, more generally, reference intersection. It has also been argued (Higginbotham, 1983) that indices should be abandoned and substituted by the non symmetric relation of linking; when the antecedent is split, a plurality of links should be used. This way, however, two different situations are collapsed together: the one in which an item is coindexed with a plurality of elements all of which share the same index, and the case of true split antecedents, where the elements composing the antecedent do not have the same index. Furthermore, the asymmetric behaviour of linking has no clear correlate at the structural level; it will be suggested below that c-command should continue to play a role here. Computational works about BT have been mainly concerned with providing lists of possible or impossible antecedents for the NPs of a sentence (see Correa (1988); Ingria & Stallard (1989)); additional procedures select actual antecedents 1 R-expressions can take split antecedents too, at least in certain cases (epithets); however, we will not explicitly address this point here. Anaphors, instead, can never take ~lit antecedents. There is a full range of phenomena for which such a distinction seems crucial, eg. weak crossover and sloppy reading of pronouns (Reinhart, 1983); donkey sentences and the so called indirect binding (Ha'de, 1984; Reinhart, 1987). However, only few of them will be addressed here.