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<Paper uid="P80-1012">
  <Title>PHRASE STRUCTURE TREES BEAR MORE FRUIT THAN YOU WOULD HAVE THOUGHT*</Title>
  <Section position="1" start_page="0" end_page="0" type="metho">
    <SectionTitle>
PHRASE STRUCTURE TREES BEAR MORE FRUIT THAN YOU WOULD HAVE THOUGHT*
</SectionTitle>
    <Paragraph position="0"/>
  </Section>
  <Section position="2" start_page="0" end_page="41" type="metho">
    <SectionTitle>
EXTENDED ABSTRACT**
</SectionTitle>
    <Paragraph position="0"> There is renewed interest in examining the descriptive as well as generative power of phrase s~-~uctur~ grammars. The primary motivation has come from the recent investigations in alternatives to t-~ansfor~ational gremmmrs \[e.g., i, 2, 3, 4\]. We will present several results and ideas related to phrase structure trees which have significant relevance to computational linguistics. null We %~_nT to accomplish several objectives in this paper. I. We will give a hrief survey of some recent results and approaches by various investigators including, of course, our own work~ indicating their interr~laticn- ships. Here we will review the work related to the notion of node admissibility starring with Chomsky) followed by the work by McCawley, Peters and Ritchie, Joshi and Levy, a~d more recent work of Gazdar.</Paragraph>
    <Paragraph position="1"> We will also discuss other amendments to context-free grammars which increase the descriptive power but not the generative power. In particular, we will discuss the notion of categories with holes as recently introduced by Gazdam \[3\]. There is an interesting history behind this notion. Sage~'s parser explieitly exploits such a convention and, in fact, uses it to do some co-ordinate st-ructnK-a computation. We suspect that some other parsers have this feature also, perhaps ~plicitly. We will discuss this matter, which obviously is of great interes~ to computational linguists.</Paragraph>
    <Paragraph position="2"> 2. Our work on local constraints on st-r~/cin/ral descriptions, \[5, 6\], which is ccmputationally relevant both to linguistics and programming language theory, has art-~'acted some attention recently; however, the demonsrration of these results has re~.ained somewhat inaccessible to many due to the technicalities of the tree automata theory. Recently, we have found a way of providing an intuitive explanation of these results in terms of intel&amp;quot;acting finite state machines (of the , usual kind). Besides providing an intuitive and a more transparent explanation of our results, this approach is computationally more interesting and allows us to formulate an interesting question: How large a variable set (i.e., the set of nonterminals) is required for a phrase slx~cture grammar or how much information does a nontermdmal encode? We will present this new approach.</Paragraph>
    <Paragraph position="3">  3. We will present some new results which extend the &amp;quot;po~er&amp;quot; of local constraints without affecting the chax~ acter of earlier results. In particular, we will show That local constraints can include, besides the pmope~ analysis (PA) predicates and domination (~) pmadicates, * This work was partially supported by NSF grant MCS7908401. null ** Full paper will be available at the time of the meeting.</Paragraph>
    <Paragraph position="4"> mor~ complex predicates of the following form.</Paragraph>
    <Paragraph position="5"> (1) (PRED N 1 N 2 ... Nn)  where N I, N2, ... N n are nonterminals mentioned in the PA and/or ~ constraint of the rule in which (i) appears and PR~ is a predicate which, r~ughly speaking, checks fo~ certain domination or left-of (or right-of) rela-Tionships among its arguments. Two examples of inTer~ est are as follows.</Paragraph>
    <Paragraph position="6">  (2) (CCOFMAND A B C) CC0~LND holds if B immediately dominates A and B dominates C, not necessarily ~iately. Usually the B node is an S node.</Paragraph>
    <Paragraph position="7"> (3) (LEFTMOSTSISTER A B)  LEFTMOSTSISTER holds if A is the leftmost sister of B. We will show that introduction of predicates of the type (I) do not change the character of our result on local cons~-raints. This extension of our earlier work has relevance to the forTm~ation of some long distance rules without %-mansformations (as well as without the use of The categories with holes as suggested by Gazdar).</Paragraph>
    <Paragraph position="8"> We will discuss some of the processing as well as linguistic relevance of these results.</Paragraph>
    <Paragraph position="9"> 4. We will tr~y to compare (at least along two dimensions) the local const-raint approach to that of Gazdar's (specifically his use of categories with holes) and to that of Peters' use of linked nodes (as presented orally at Stanford recently).</Paragraph>
    <Paragraph position="10"> The dimensions for cc~ison would be (a) economy of representation, (b) proliferation of categories, by and large semantically vacuous, and (c) computational relevance of (a) and (b) above.</Paragraph>
    <Paragraph position="11"> 5. Co~positional semantics \[8\] is usually context-free, i.e., if nodes B and C are immediate descendants of node A, then the semantics of A is a composition (defined appropriately) of the semantics of B and semantics of C. Semantics of A depends only on nodes B and C and not on any other part of the st-ruerural description in which A may appear. Our method of local constraints (and to sQme extent Peters' use of linked nodes) opens the possibility of defining the semantics of A not only in terms of the semantics of B and C, but also in terms of sc~e parts of the sZ~-uc~ description in which A appears. In this sense, the semantics will be contex-tsensitive. We have achieved some success with This aFpLuaeh to the semantics of progr~g languages. We will discuss some of ou~ preliminary ideas for extending this approach to natural language, in particular, in specifying scopes for variable binding.</Paragraph>
    <Paragraph position="12">  6. While developing our theory of local constrains and some other related work, we have discovered that it is  possible to characterize structural descriptions (for phrase sl-r~crure gz%m~mars) entirely in terms of trees without any labels, i.e., trees which capture the grouping structure wi~hou~ the syntactic categories (which is the same as the constitn/ent st-r~cture without the node labels \[7\]. This is a surprising result. This result  provides a way of deter~ how much &amp;quot;~&amp;quot; ~zerm/nels (syntactic cazeEories) encode and therefore clearly, it has ca~aticnal si~icance.</Paragraph>
    <Paragraph position="13"> Moreover, ~o The extent That The cla/m ~ha~ natural languages ere conzex~-bree is valid, this result has significant z~levancs to leamabili~y ~\]~eories, because our result suEges~s that it might be possible to &amp;quot;infer&amp;quot; a phrase s~ruc'~r,e ~ L,-,, jus~ the grouping s~ruc~ure of ~he input (i.e., j us~ phrase boundaries). Pur~her, the set of descrip~iuns wit.bout labels are directly rela~ed to the ~ descz'ip~ic~s of a context-free Eramn~z-; hence, we may be able to specify '~aTural&amp;quot; syntactic categories.</Paragraph>
    <Paragraph position="14"> In summery, we will prese~1: a selectian of mathematical resul:s which have sisnifj~lnt z~l.evancs to m=~y aspec~ of con~tional lin~is~ics.</Paragraph>
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