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<Paper uid="J82-1001">
  <Title>Phrase Structure Trees Bear More Fruit</Title>
  <Section position="2" start_page="0" end_page="0" type="abstr">
    <SectionTitle>
1. Introduction
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    <Paragraph position="0"> There is renewed interest in examining the descriptive as well as generative power of phrase structure grammars. The primary motivation for this interest has come from the recent investigations in alternatives to transformational grammars (e.g., Bresnan 1978; Kaplan and Bresnan 1979; Gazdar 1978, 1979a, 1979b; Peters 1980; Karttunen 1980). 2 Some of these approaches require amendments to phrase structure grammars (especially Gazdar 1978, 1979a, 1979b; Peters 1980; Karttunen 1980) that increase their descriptive power without increasing their generative power. Gazdar wants to restrict the power to that of context-free languages. Others are not coml This work was partially supported by NSF grant MCS 7908401 and MCS 81-07290.</Paragraph>
    <Paragraph position="1"> This paper is a revised and expanded version of a paper presented at the 18th Annual Meeting of the Association for Computation Linguistics, University of Pennsylvania, Philadelphia, June 1980.</Paragraph>
    <Paragraph position="2"> Thanks are extended to the two referees of this paper and to Michael McCord for their valuable comments, which helped in the improvement of both the content and the presentation of the material herein.</Paragraph>
    <Paragraph position="3"> pletely precise on this aspect. Berwick has shown that the Kaplan-Bresnan system is nearly equivalent to the 2 Since this paper was submitted for publication, a number of papers have appeared that should be of interest to its readers. &amp;quot;Phrase Linking Grammars&amp;quot; by S. Peters and R.W. Ritchie describes their system (Technical Report, Department of Linguistics, University of Texas at Austin, 1982). Strong adequacy of context-free grammars has been discussed by J. Bresnan, R.M. Kaplan, S. Peters, and A. Zaenan in &amp;quot;Cross-Serial Dependencies in Dutch&amp;quot; (to appear in Linguistic Inquiry in 1982). This paper shows that context-free grammars are not strongly adequate (i.e., they are unable to provide the appropriate structural descriptions) to characterize cross-serial dependencies in Dutch. In a recent paper (&amp;quot;How much context-sensitivity is needed to provide reasonable structural descriptions: A tree adjoining system for generating phrase structure trees,&amp;quot; presented at the Parsing Workshop, Ohio State University, May 1982; also Technical Report, Department of Computer and Information Science, University of Pennsylvania, 1982), A.</Paragraph>
    <Paragraph position="4"> Joshi discusses weak and strong adequacy of grammars and proposes a tree adjoining grammar (TAG) that appears to be strongly adequate and has only slightly more power than context-free grammars. Joshi has also given a rough characterization of a class of context-sensitive language (MCSL) that appears to be suitable to characterize natural languages. Languages of TAG belong to MCSL, and languages of PLG's of Peters and Ritchie also belong to this class. (TAG's use a linking device similar to that in the PLG's.) Copyright 1982 by the Association for Computational Linguistics. Permission to copy without fee all or part of this material is granted provided that the copies are not made for direct commercial advantage and the Journal 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/82/010001-11501.00 American Journal of Computational Linguistics, Volume 8, Number 1, January-March 1982 1 Aravind K. Joshi and Leon S. Levy Phrase Structure Trees Bear More Fruit so-called indexed grammars. The power of the phrase linking grammars of Peters and Ritchie is not completely known at this time.</Paragraph>
    <Paragraph position="5"> The notion of node admissibility plays an important role in these formulations. The earliest reference to node admissibility appears in Chomsky 1965 (p.</Paragraph>
    <Paragraph position="6"> 215); he suggests the possibility of constructing a rewriting system where the rewriting of a symbol is determined not only by the symbol being rewritten but also by the dominating category symbol. In his analysis of the base component of a transformation grammar, McCawley 1968 suggested that the appropriate role of context-sensitive rules in the base component of a transformational grammar can be viewed as node admissibility conditions on the base trees. The base component is thus a set of labeled trees satisfying certain conditions. Peters and Ritchie 1969 made this notion precise and proved an important result, which roughly states that the weak generative power of a context-sensitive grammar is that of a context-free grammar, if the rules are used as node admissibility conditions. Later Joshi and Levy 1977 made a substantial extension of this result and showed that, if the node admissibility conditions include Boolean combinations of proper analysis predicates and domination predicates, the weak generative capacity is still that of a context-free grammar.</Paragraph>
    <Paragraph position="7"> Besides the notion of node admissibility, Gazdar introduces two other notions in his framework (Generalized Phrase Structure Grammars, GPSG).</Paragraph>
    <Paragraph position="8"> These are (1) categories with holes and an associated set of derived rules and linking rules, and (2) meta-rules for deriving rules from one another. The categories with holes and the associated rules do not increase the weak generative power beyond that of context-free grammars. The metarules, unless constrained in some fashion, will increase the generative power, because, for example, a metarule can generate an infinite set of context-free rules that can generate a strictly context-sensitive language. (The language {anbncn/n&gt;l} can be generated in this way.) The metarules in the actual grammars written in the GPSG framework so far are constrained enough so that they do not increase the generative power.</Paragraph>
    <Paragraph position="9"> Besides node admissibility conditions, Peters 1980 introduces a device for &amp;quot;linking&amp;quot; nodes (see also Karttunen 1980). A lower node can be &amp;quot;linked&amp;quot; to a node higher in the tree and becomes &amp;quot;visible&amp;quot; while the semantic interpretation is carried out at the lower node. The idea here is to let the context-free grammar overgenerate and the semantic interpretation weed out ill-formed structures. Karttunen 1980 has developed a parser using this idea.</Paragraph>
    <Paragraph position="10"> Kaplan and Bresnan 1979 have proposed an intermediate level of representation called functional structure. This level serves to filter structures generated by a phrase structure grammar. Categories with holes are not used in their framework. In this paper we will not be concerned with the Kaplan-Bresnan system.</Paragraph>
    <Paragraph position="11"> In Section 2 we briefly review Gazdar's proposal, especially his notion of categories with holes. We give a short historical review of this notion.</Paragraph>
    <Paragraph position="12"> In Section 3 we briefly describe our work on local constraints on structural descriptions (Joshi and Levy 1977; Joshi, Levy, and Yueh 1980). We give an intuitive explanation of these results.</Paragraph>
    <Paragraph position="13"> In Section 4 we propose some extensions of our results and discuss them in the context of some long distance rules. We also describe Peters's 1980 approach and present some suggestions for &amp;quot;contextsensitive&amp;quot; compositional semantics.</Paragraph>
    <Paragraph position="14"> In Section 5 we briefly present the framework of Peters and Karttunen and compare it with that of Gazdar and of ourselves.</Paragraph>
    <Paragraph position="15"> In Section 6 we briefly discuss our results concerning a characterization of structural descriptions entirely in terms of trees without labels.</Paragraph>
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