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<Paper uid="P90-1014">
  <Title>Free Indexation: Combinatorial Analysis and A Compositional Algorithm*</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> In the principles-and-parameters model of language, the principle known as 'free indexation' plays an important part in the process of determining the referential properties of elements such as anaphors and pronominals. This paper addresses two issues. (1) We investigate the combinatorics of free indexation. By relating the problem to the n-set partitioning problem, we show that free indexation must produce an exponential number of referentially distinct phrase structures given a structure with n (independent) noun phrases. (2) We introduce an algorithm for free indexation that is defined compositionally on phrase structures. We show how the compositional nature of the algorithm makes it possible to incrementally interleave the computation of free indexation with phrase structure construction. Additionally, we prove the algorithm to be an 'optimal' procedure for free indexation. More precisely, by relating the compositional structure of the formulation to the combinatorial analysis, we show that the algorithm enumerates precisely all possible indexings, without duplicates.</Paragraph>
  </Section>
class="xml-element"></Paper>