<?xml version="1.0" standalone="yes"?>
<Paper uid="J87-1003">
  <Title>SIMULTANEOUS-DISTRIBUTIVE COORDINATION AND CONTEXT-FREENESS</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
INTRODUCTION
</SectionTitle>
    <Paragraph position="0"> Pullum and Gazdar (1982) systematically review and critique a large number of arguments for trans-context-freeness of natural languages, t finding each one defective conceptually, empirically, or mathematically. Among these are various ones (e.g., that of Bar-Hillel and Shamir  (1960) 2 ) appealing to the existence in English of sentences like (1) John and Bill dated Mary and Alice respectively.  Pullum (1984) cites a number of more recent arguments, involving languages other than English, which do appear to establish their trans-context-freeness and remarks (p. 117), in connection with a suggestion regarding Swedish gender agreement, that if this type of agreement can be shown to be a purely syntactic matter, then sentences analogous to English instances of the schema The N, N, ... and N are respectively A, A ... and A r, might provide the basis of an argument for trans-context-freeness of the language (or of any other with similar facts). In this paper, we shall produce a rigorous argument along comparable lines to show that English is trans-context-free (trans-CF), though we shall rely on facts regarding grammatical number rather than gender.</Paragraph>
    <Paragraph position="1"> The relevance of a strictly negative result such as the one we have obtained is not restricted to the narrow question of where natural languages do (or don't) place in the Chomsky hierarchy. Given that proving the trans-Copyright 1987 by the Association for Computational Linguistics. Permission to copy without fee all or part of this material is granted provided that the copies arc not made for direct commercial advantage and the CL reference and this copyright notice are included on the first page. To copy otherwise, or to republish, requires a fee and/or specific permission. 0362-613X/87/010025-30503.00 Computational Linguistics, Volume 13, Numbers 1-2, January-June 1987 25 Michael B. Kac, Alexis Manaster-Ramer, William C. Rounds Simultaneous-Distributive Coordination and Context-Freeness context-freeness of particular natural languages has turned out to be considerably more difficult than anyone had expected it to be, and that solutions to difficult problems are likely to bear fruit outside the parochial confines of the original problem area and to call attention to hitherto unnoticed facts, an exercise such as this goes well beyond lily gilding or dead horse beating. To develop our argument, for example, we shall turn the spotlight on the linguistics phenomenon of arbitrary number, something which is rarely mentioned in standard treatment of grammatical phenomena (in vivid contrast to arbitrary gender), but which turns out to be more than a mere curiosity.</Paragraph>
    <Paragraph position="2"> The mathematical approach that we employ is also noteworthy in making crucial use of the Interchange Lemma for CFLs (Ogden et al. 1985) and of a &amp;quot;separation&amp;quot; technique that allows trans-context-freeness to be demonstrated by showing that certain strings are included in a language while others are excluded.</Paragraph>
    <Paragraph position="3"> Neither of these has, to our knowledge, been used in a natural language context before. The interest of the separation method in particular lies in the way in which it simplifies the following problem. Since natural languages are large, complex, and (most important) lacking in antecedent definitions, the only practical way to argue about their mathematical properties is to examine sublanguages.</Paragraph>
    <Paragraph position="4"> If one is not careful, however, one runs the risk of committing the &amp;quot;trickle-up&amp;quot; fallacy, which consists in showing that a certain set S has a property P and then attributing P to some proper superset of S. The usual way of circumventing this difficulty is to capitalize on closure properties of languages under intersection with a regular set; the separation technique provides an alternative in cases where appeal to such closure properties is not sufficient (or at least not obviously so).</Paragraph>
    <Paragraph position="5"> Partly in the interest of a terminology free of English bias, we call constructions like (1) simultaneous-distributive (SD) coordinations. This label reflects the fact that a sentence such as (1) can be &amp;quot;unpacked&amp;quot; to yield, salva veritate, a coordination of noncoordinate sentences by means of the following procedure: * first, put a copy of the verb directly before each NP in the second coordinate phrase that is not already immediately preceded by a verb, thus creating a coordination of VPs; * then &amp;quot;distribute&amp;quot; the NPs in the first coordinate phrase among the VPs by simultaneously associating a copy of each of the former with exactly one of the latter, namely the one in the corresponding positions; * finally, suppress the first coordinate phrase, the first and and respectively.</Paragraph>
  </Section>
class="xml-element"></Paper>