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<Paper uid="P94-1035">
  <Title>An Attributive Logic of Set Descriptions Set Operations</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Grammatical formalisms such as HPSG \[Pollard and Sag, 1987\] \[Pollard and Sag, 1992\] and LFG \[Kaplan and Bresnan, 1982\] employ feature descriptions \[Kasper and Rounds, 1986\] \[Smolka, 1992\] as the primary means for stating linguistic theories.</Paragraph>
    <Paragraph position="1"> However the descriptive machinery employed by these formalisms easily exceed the descriptive machinery available in feature logic \[Smolka, 1992\]. Furthermore the descriptive machinery employed by both HPSG and LFG is difficult (if not impossible) to state in feature based formalisms such as ALE \[Carpenter, 1993\], TFS \[Zajac, 1992\] and CUF \[D6rre and Dorna, 1993\] which augment feature logic with a type system.</Paragraph>
    <Paragraph position="2"> One such expressive device employed both within LFG \[Kaplan and Bresnan, 1982\] and HPSG but is unavailable in feature logic is that of set descriptions. Although various researchers have studied set descriptions (with different semantics) \[Rounds, 1988\] \[Pollard and Moshier, 1990\] two issues remain unaddressed. Firstly there has not been any work on consistency checking techniques for feature terms augmented with set descriptions. Secondly, for applications within grammatical theories such as the HPSG formalism, set descriptions alone are not enough since descriptions involving set union are also needed. Thus to adequately address the knowledge representation needs of current linguistic theories one needs to provide set descriptions as well as mechanisms to manipulate these.</Paragraph>
    <Paragraph position="3"> In the HPSG grammar formalism \[Pollard and Sag, 1987\], set descriptions are employed for the modelling of so called semantic indices (\[Pollard and Sag, 1987\] pp. 104). The attribute INDS in the example in (1) is a multi-valued attribute whose value models a set consisting of (at most) 2 objects.</Paragraph>
    <Paragraph position="4"> However multi-valued attributes cannot be described within feature logic \[Kasper and Rounds, 1986\] \[Smolka, 1992\].</Paragraph>
    <Paragraph position="5">  A further complication arises since to be able to deal with anaphoric dependencies we think that set memberships will be needed to resolve pronoun dependencies. Equally, set unions may be called for to incrementally construct discourse referents. Thus set-valued extension to feature logic is insufficient on its own.</Paragraph>
    <Paragraph position="6"> Similarly, set valued subcategorisation frames (see (2)) has been considered as a possibility within the HPSG formalism. (2) believes= IYNILOCISUBCAT~ \[\[SYN~LOOIHEADICAT v\] But once set valued subeategorisation frames are employed, a set valued analog of the HPSG subcategorisation principle too is needed. In section 2 we show that the set valued analog of the subcategorisation principle can be adequately described by employing a disjoint union operation over set descriptions as available within the logic described in this paper.</Paragraph>
  </Section>
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