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<Paper uid="P84-1027">
  <Title>The Semantics of Grammar Formalisms Seen as Computer Languages</Title>
  <Section position="6" start_page="126" end_page="127" type="evalu">
    <SectionTitle>
6. Applications
</SectionTitle>
    <Paragraph position="0"> We have used the techniques discussed here to analyze the feature systems of GPSG \[15\], LFG \[2\] and PATR-II \[17\]. All of them turn out to be specializations of our domain D of descriptions. Figure 1 provides a summary of two of the most critical formal properties of context-free-based grammar formalisms, the domains of their feature systems (full F~ finite elements of F, or elements of F based on nonrecursive domain equations) and whether the context-free skeletons of grammars are constrained to be off-line paraeable \[13\] thereby guaranteeing decidability.</Paragraph>
    <Paragraph position="1">  aDCGs based on Prolog-lI which allows cyclic terms.</Paragraph>
    <Paragraph position="2"> bHPSG, the current Hewlett-Packard implementation derived from GPSG, would come more accurately under the PATR-II  Though notational differences and some grammatical devices are glossed over here, the comparison is useful as a first step in unifying the various formalisms under one semantic umbrella. Furthermore, this analysis elicits the need to distinguish carefully between the domain of feature structures F and that of descriptions. This distinction is not clear in the published accounts of GPSG and LFG, which imprecision is responsible for a number of uncertainties in the interpretation of operators and conventions in those formalisms.</Paragraph>
    <Paragraph position="3"> In addition to formal insights, linguistic insights have also been gleaned from this work. First of all, we note 'that while the systems make crucial use of unification, generalization is also a well-defined notion therein and might indeed be quite useful. In fact, it was this availability of the generalization operation that suggested a simplified account of coordination facts in English now being used in GPSG \[15\] and in an extension of PATR-II \[8\]. Though the issues of coordination and agreement are discussed in greater detail in these two works, we present here a simplified view of the use of generalization in a GPSG coordination analysis.</Paragraph>
    <Paragraph position="4"> Circa 1982 GPSG \[6\] analyzed coordination by using a special principle, the conjunct realization principle (CRP), to achieve partial instantiation of head features {including agreement} on the parent category. This principle, together with the head feature convention (HFC) and control agreement principle {CAP), guaranteed agreement between the head noun of a subject and the head verb of a predicate in English sentences. The HFC, in particular, can be stated in our notation as (0 head) = (n head) for n the head of 0.</Paragraph>
    <Paragraph position="5"> A more recent analysis \[4,15\] replaced the conjunct realization principle with a modified head feature convention that required a head to be more instantiated than the parent, that is: (0 head) E (n head) for all constituents n which are heads of 0. Making coordinates heads of their parent achieved the effect of the CRP. Unfortunately, since the HFC no longer forced identity of agreement, a new principle--the nominal completeness principle (NCP), which required that NP's be fully instantiated--was required to guarantee that the appropriate agreements were maintained.</Paragraph>
    <Paragraph position="6"> Making use of the order structure of the domains we have just built, we can achieve straightforwardly the effect of the CRP and the old HFC without any notion of the NCP. Our final version of the HFC merely requires that the parent's head features be the generalization of the head features of the head children. Formally, we have: (0 head) ---- \[7 (i head) i~heads of 0 In the case of parents with one head child, this final HFC reduces to the old HFC requiring identity; it reduces to the newer one, however, in cases {like coordinate structures} where there are several head constituents.</Paragraph>
    <Paragraph position="7"> Furthermore, by utilizing an order structure on the domain of constants C, it may be possible to model that troublesome coordination phenomenon, number agreement in coordinated noun phrases \[8,15\].</Paragraph>
  </Section>
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