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<Paper uid="J87-1001">
  <Title>RESTRICTING LOGIC GRAMMARS WITH GOVERNMENT-BINDING THEORY</Title>
  <Section position="12" start_page="0" end_page="0" type="concl">
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NOTES
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    <Paragraph position="0"> 1. I am indebted to Janet Dean Fodor, Fernando Pereira, and Yuriy Tarnawsky for helpful discussions of this material. Discussions after a presentation of parts of this material at the University of Toronto in March 1986 also inspired some significant improvements, as did the comments of an anonymous referee. Richard O'Keefe provided valuable advice on aspects of the design of the prolog implementations.</Paragraph>
    <Paragraph position="1"> 2. Tffe qualification &amp;quot;in their most straightforward use&amp;quot; really is / necessary. As noted below, DCGs with tests or with grammatical predicates that have more than two arguments have the full universal power of prolog. It is no surprise, then, that DCGs can be used to define bottom-up parsers, as Pereira (1985) points out.</Paragraph>
    <Paragraph position="2"> The DCG notation is actually a convenient one for the definition of all sorts of parsers. They provide a convenient representation of the string to be parsed, as we will see.</Paragraph>
    <Paragraph position="3"> 3. Chomsky (1981, p.33) points this out as well: &amp;quot;It is immaterial ... whether Move-a is regarded as a rule forming s-structure from d-structure, or whether it is regarded as a property of s-structures that are 'base-generated'.... It is in fact far from clear that there is a distinction apart from terminology between these two formulations.&amp;quot; null 4. Parasitic gaps complicate the story here - hence the parenthetical qualification &amp;quot;in most cases&amp;quot;, above. In certain cases a single moved constituent can have two gaps, as in Which articles did Dana file \[t\] without reading It\]?. Gazdar et al. (1985) in fact proposes an analysis according to which any gap can be passed to both the NP and the VP under an S node. Consequently, their grammar accepts some strange things like Which authors did reviewers of\[t\] always detest \[t\]?. In a practical system, one wants to avoid getting parses that are as unlikely to occur as these. A more restrictive Chomskian analysis of parasitic gaps has been proposed and looks like it may be usable in parsing with methods for leftward movement like those described below. Roughly, when the &amp;quot;real&amp;quot; trace is found, the trick is to put another special operator in the extraposition list that allows a subjacent parasitic gap but doesn't require one (Berwick and Weinberg 1985). (I do not mean to claim that a restrictive GPSG analysis of parasitic gaps could not be formulated - Gazdar et al. (1985) is just an example of a relatively unrestricted analysis.) 5. This sort of rule may be useful for other constructions as well.</Paragraph>
    <Paragraph position="4"> Pollard (1984) argues that, even just in English, a similar &amp;quot;wrapping&amp;quot; analysis is appropriate for many constructions: the phrase take to task seems to wrap around its object in take Kim to task; the phrase much taller than Sandy seems wrapped into the adjective phrase in Kim is a much taller person than Sandy; and a similar wrap analysis is proposed to relate Kim is very easy to please and Kim is a very easy person to please.</Paragraph>
    <Paragraph position="5"> 6. Actually, Marcus (1980) used a special subject-auxiliary inversion rule, and Berwick (1982) noted that the effect of Marcus's rule can be achieved with a very simple &amp;quot;switch&amp;quot; mechanism that can be assumed to be one of a small set of primitive parser operations.</Paragraph>
    <Paragraph position="6"> 7. The &amp;quot;lookahead&amp;quot; technique used here for switch rules is described in a slightly more general form in Stabler (1983).</Paragraph>
    <Paragraph position="7"> 8. Notice that we need different symbols for traces of different categories, since our trace handling mechanism does not check the identity of the node dominating a trace It\].</Paragraph>
    <Paragraph position="8"> 9. The principles actually proposed in Chomsky (1981) are a little more complex, but the versions formulated here suffice for illustrating the basic approach which can be applied to the more sophisticated formulations. In spite of the simplification, the versions presented here provide the desired simplification of the grammar rules.</Paragraph>
    <Paragraph position="9"> 10. In any case in which the moved element was not the first sibling under the dominating branching node, a different sort of rule would have to be used. We allow the three place predicate '&lt;&lt;&lt;'(Nt,Trace,N), where Nt can have at most M daughters and N E \[1,2,...,M-I\]. These rules introduce the Trace into the extraposition list after the Nth daughter of Nt. Since '&lt;&lt;&lt;'(Nt,Trace,1) is the most common case in English, we give it the short form 'Nt&lt;&lt;&lt;Trace'.</Paragraph>
    <Paragraph position="10"> Computational Linguistics, Volume 13, Numbers 1-2, January-June 1987 9 Edward P. Stabler, Jr. Restricting Logic Grammars with Government-Binding Theory 11. One other common construction with crossing bindings that Fodor (1983) mentions is illustrated with examples like Who didyou ask 1 j trace whether PRO to blame yourselfi? As indicated the subject of , J J ' the embedded clause in this construction is not a trace produced by a movement but another type of empty category: a base-generated pronominal element which is controlled by the higher subject. A movement analysis would be inappropriate for these constructions (Chomsky 1981; Manzini 1983).</Paragraph>
    <Paragraph position="11"> 12. A compiler that will do this is under construction, together with a proof of its correctness. A complete account is beyond the scope of this paper, but the idea is easy to see. Basically, on the first pass we construct a CFG corresponding to.the RLG being processed, a CFG that would generate the same derivations as the RLG except that it is not restricted by the requirements about the presence of appropriate elements in the extraposition list for the expansion of np or of a wh phrase to a trace. We then compute the nodes that can dominate traces in this CFG, working backwards from the right hand sides of the rules. In specifiable cases (which will typically hold), this set will be exactly the set of nodes that can in fact dominate the traces in RLG derivations; otherwise, it is a superset of the set of nodes that can dominate the traces in RLG derivations (though this superset will typically still be a proper subset of the set of nonterminals, and hence useful).</Paragraph>
    <Paragraph position="12"> 13. Notice that the XG rules that were shown as examples are comparable in complexity to the RLG rules shown, but the XG rules were incorrect in the crucial respects that were pointed out! The XG rules shown allowed ungrammatical sentences (viz., violations of the subjacency and c-command constraints) that the RLG rules properly rejected. The XG rules that properly rule out these cases would be considerably more complex.</Paragraph>
    <Paragraph position="13"> 14. These rules for rightward movement are oversimplified. Most linguists in the Government-Binding tradition follow Baltin (1981 ) and others in assuming that phrases extraposed from inside a vp are attached inside of that vp, whereas phrases extraposed from subject position are attached at the end of the sentence (in roughly the position we have ~narked adjunct). Baltin (1981) points out that this special constraint on rightward movement seems to hold in other languages as well, and that we can capture it by counting vp as a bounding category for rightward movement. This approach could easily be managed in the framework we have set up here, though we do not currently have it implemented. Notice that although rightward movement is not structure-preserving on this linguistic approach, the parser rules for this movement are structure-preserving in the trivial sense that they supply the category adjunct just to accommodate these movements.</Paragraph>
    <Paragraph position="14"> 15. Colmerauer's (1978) MGs, Dahl's (1984) GGs, and other systems are very powerful, and they sometimes allow fairly elegant rules for natural language constructions, but they are not designed to automatically enforce constraints: that burden is left to the grammar writer, and it is not a trivial burden.</Paragraph>
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