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<Paper uid="C96-2160">
  <Title>Computing Phrasal-signs in HPSG prior to Parsing</Title>
  <Section position="3" start_page="0" end_page="949" type="intro">
    <SectionTitle>
2 Rule Sch(:nmta and Definite
Claus(; l)rograms
</SectionTitle>
    <Paragraph position="0"> Our fonmdism has only one type of compolmnt g-tS llOll-10xic&amp;l (;ollll)Ollellt,q of ~rallllnar, i.e., rule schemata. I An example is showll in Figure 1. A ruh' s(:henl;~ consists of the following two items.</Paragraph>
    <Paragraph position="1"> Ihl ()Ill' cilrr(!ilt, sysLeil/~ rill(', s(;h(2mltt~ ~l'('. goltc.ri~t('.(1 froul principh,.s and rewriting rules ~m(:ording (;c) ;L SlmCifical, ion given by ~ progr~mmter.</Paragraph>
    <Paragraph position="2">  rule(R) a rewriting rule without specific syntactic categories; fs(R) a feature structure.</Paragraph>
    <Paragraph position="3"> A characteristic of HPSG is in the flexibility of principles which demands complex operations, such as append or subtraction of list-value feature structures. In our formalism, those operations are treated by a Definite Clause Program. A DCP can be seen as a logic program language whose arguments are feature structures. An auxiliary term, a query to a DCP augmenting a rule schema, is embedded in a feature structure of a rule schema as the value of goals. The rule schema in the exampie has an auxiliary term, append(\[1\], \[2\], \[3\] ). The bottom-up application of the rule schema R is carried out as follows. First, two daughter signs are substituted to the HEAD-DTP~ position and NOR-HEAD-DTI~ position of the rewriting rule rule(R). Then, the signs are unified with the head-dtr value and the non-head-dtr value of the feature structure of the schema, fs(R). Finally, the auxiliary term for DCPs given in the schema is evaluated* Our definition of a DCP has a more operational flavor than that given by Carpenter(Carpenter, 1992)* The definition is crucial to capture the correctness of our method. 2 Definition 1 (DCP) A definite clause program (DCP) is a finite set of feature structures, each of which has the following form.</Paragraph>
    <Paragraph position="4"> goals (HI 1-13) J next-steps \[ goaSs (1~o, B1 ,''', ~, \[1\] ) \] a where 0 &lt;_ n and H, Bo,&amp;quot; * *, B,~ are feature structures. null A feature structure of the above form corresponds to a clause in Prolog. H, B0,...,B~ corresponds to literals in Prolog. H is the head and Bo,&amp;quot;', B,~ are literals in the body of a clause. Definition 2 (Execution of DCP) Execution of a DCP P for the query, C2~e~y = \[ go~Ss (qo, q~,'&amp;quot; qz) \] is a sequence of unification, Query U rl U r2 U ... Urn where ri = \[ (next-steps) i-1 Ci \], C, C/ P or Ci = \[ goals 0 \]. /f the execution is terminated, C~ must be unifiable with\[ goals () \]. In this case, we call the sequence (rl,'&amp;quot;,r,~} a resolution sequence.</Paragraph>
    <Paragraph position="5"> 2Though, through the rest of the paper, we treat the definition as if it were used in an actual implementation, the actual implementation uses a more efficient method whose output is equivalent with the result obtained by the defiifition.</Paragraph>
    <Paragraph position="6"> a (H0,.-', H~, \[1\]) is an abbreviation of</Paragraph>
    <Paragraph position="8"> (next-steps) i-1 \[goals of QueryHrl Hr2 H. * * H ri represents the goals which are to be solved in the steps following the i-th step. The goals are instantiated by the steps fi'om the first one to i-th one, through structure sharings. The result of execution in a Prolog-like sense appears in the query, Figure 2 is an example of execution for the query append(\[a\], \[b\] ,X) , whose definition is based on a standard definition of append in Prolog.</Paragraph>
    <Paragraph position="9"> Given this definition of DCPs, an application of a rule schema to two (laughter signs D1 and D2 can be expressed in the following form, where @1, r2,.&amp;quot;, r,~} is a resolution sequence: M= \[ head-dtrnon_head_dtr D~D2 \]Ufs(R)U','tUr.2U...Ur,~</Paragraph>
  </Section>
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