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<Paper uid="C90-3003">
  <Title>Backwards Phonology</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Since Koskenniemi proposed using two-level phonology in computational morphological analysis in 1983, it has enjoyed considerable popularity \[Koskenniemi, 1983\]. It seems to be both expressiyely powerfid and computationaily tractable. Two-level phonological granntmars have been written for a dozen or more languages, and written in a form that is interpretable by a program. One question that arises fairly frequently however, at least in the context of discussion about two-level morphology, is roughly, &amp;quot;Why don't you use normal generative phonological rules?&amp;quot; i.e., rules of the type that are taught in elementary linguistics classes. A slightly more positive way to ask the question is, &amp;quot;In what way or ways does Koskenniemi's notion of two-level pholmlogical rule represent a theoretical advance?&amp;quot; This paper addresses that question by extending the notion of unilevel rule system to cope with tim same types of phenomena that two-level rule systems were designed to handle, and then contrasting the two different systems.</Paragraph>
    <Paragraph position="1"> At the annual meeting of the Linguistic Society of America (LSA) in 1981, Ron Kaplan and Martin Kay presented a paper describing results about equivalences between what they call a cascade of finite-state transducers and a set of normal, ordered phonological rules \[Kaplan and Kay, 1981\]. At the I, SA's 1987 annual meeting, Lauri Karttunen gave a paper attempting to show that, when viewed a certain way, Koskenniemi's two-level rules possess a certain elegance that cannot be ascribed to ordered sets of rules, namely their independence from order per se \[Karto tunen, 1986\].</Paragraph>
    <Paragraph position="2"> In spite of Karttunen's paper and Koskenniemi's, and perhaps to some extent because of Kaplan and Kay's paper, it is still not obvious to people who are interested in this field what, if anything, two-level phonology offers that cannot already be found in tile linguistic literature under the heading of generative phonology. Koskenniemi has made some claims about grammars of two-level rules being reversible whereas sets of ordered rules are not. However these claims are not backed up by solid argumentation, and the Kaplan and Kay paper seems to argue otherwise.</Paragraph>
    <Paragraph position="3"> From a linguistic point of view, there may be good reason to think that people use two different sets of rules or procedures for generation and recognition.</Paragraph>
    <Paragraph position="4"> From a computational point of view, however, it is interesting to ask, &amp;quot;What needs to be done in order to use the same grammar for generation and recognition; does a single reversible grammar lead to more or less work in terms of writing the grammar and in terms of run-time speed; and finally, does a reversible grammar lead to a more or less elegant presentation of the phenomena?&amp;quot; Another reason for asking about reversibility is to make a comparison of these two rule formalisms possible. The main novelty in Koskenniemi's system is the reversibility of the system, so we may well question what would be necessary to view unilevel rules as reversible.</Paragraph>
    <Paragraph position="5"> In short, there are very. good reasons for being interested in properties of reversibility, and these properties will serve as the basis tot this paper's comparison between the two different types of phonological rule formalisms mentioned above. The discussion here will focus more on concrete examples of generative capacity, and much less on issues of what is involved in building an acceptable linguistic theory. \[For more on global concerns of linguistic theory, see, for example, Ellasson, 1985\]. The questions addressed here will be, &amp;quot;What assumptions need to be made to use a grammar of unilevel generative rules to do recognition?&amp;quot;</Paragraph>
    <Paragraph position="7"> and &amp;quot;Ilow does tim resulting combination of grammar plus rules-of-interpretation compare with a two-level style grammar?&amp;quot;</Paragraph>
  </Section>
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