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<Paper uid="C96-1092">
  <Title>Applying Lexical Rules Under Subsumption</Title>
  <Section position="3" start_page="0" end_page="543" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Current linguistic theories place an increasing amount of grammatical information in the lexicon and employ a variety of mechanisms to express generalizations across lexical entries: templates (Flickinger 1987, Shieber 1986), inheritance hierarchies (Flickinger 1987, Pollard and Sag 11994), and lexical rules (Bresnan 1982, I)owty 1982, Gazdaret al. 1985, Pollard and Sag 1994). Lexical rules (henceibrth: LRs) have been subjected to particularly close s&lt;:rutiny. 'Fhis research has tbcused on two important issues: 1. how the use of LRs affects the generative power of grammar formalisms and the computational complexity of parsing algorithms (Uszkoreit and Peters 1986, Carpenter 1991), and 2. how to provide a denotational semantics for LRs (Calcagno and PoP lard 1995, Meurers 1995). In this paper we address neither of these two issues. Instead we will concentrate on a question that we c&lt;msider to be of equal importance, but that has received surprisingly little attention: Under what conditions should an I,R be applicable to a given lexical entry (henceforth: LE)? For gramrnar formalisms that employ the notion of unitication of attribute-value structures, two criteria for applicability naturally suggest themselves: 1. llypolhcsis A: A lexical rule applies to a lexical entry ifr the lexi&lt;:al entry unifies with the left-hand side of t;he lexical rule.</Paragraph>
    <Paragraph position="1"> 2. Hypothesis B: A lexical rule applies to a lexical entry iff the lexical entry is subsumed by the left-hand side of the lexical rule) Without much argument, it is cotnmonly assume&lt;t that llypothesis A is correct (el. Pollard and Sag 1994, (\]alcagno and Pollar&lt;t :1995, and Meurers 1995). This paper argues that 11ypothesis A should be rejected on empirical grounds. We discuss a number of Ll{s that have been used in IIPSG analyses of German (tlinri&lt;:hs and Nakazawa 1994) and show that the grammar will either vastly overgenerate and accept ungrammatical sentences or introduce spurious structural ambiguity for grammatical sentences, if ltypothesis A is adopted. Itowever, no such problems ofovergeueration or spurious ambiguity arise, if one adopts llypothesis B, instead.</Paragraph>
    <Paragraph position="2"> It would go beyond tim scope of this paper to present a flJly worked-out proposal on how to i&gt;ro cess LRs in a coml)utational system for IIPSG.</Paragraph>
    <Paragraph position="3"> Itowever, as discussed in section 6, it is worth noting that the subsumption test for I,l{ application &lt;'.an be integrated straightforwardly into two recent proposals by van Noord and Bouma (:1994) and by Meurers and Minnen (1995) of how to implement lab in a processing system for HPSG.</Paragraph>
    <Paragraph position="4"> l'Fhis paper will not provide a formal definition of subsumption or nnificiation for typed feature structures. Instead, we refer the reader to the standard definitions of Kasper and Rounds (1986) and Carpentel: (1992), among many &lt;)tilers. Informally speaking, two feature structures are unifiable itf they do not contab incompatible information. One feature structure subsumes another iff the intormation contained in the former is less specific than in the latter.</Paragraph>
  </Section>
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