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<Paper uid="C00-1037">
  <Title>Formal Syntax and Semantics of Case Stacking Languages</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Case stacking is a phenomenom that occurs in many Australian languages (such as Warlt)iri and Kayardild) and e.g. Old Georgian. Case stacking is known to pose t)roblems for the treatment of case in many fi)rmal ti'ameworks today 1. In (Nordlinger, 1997) the problem was attacked by extending the fl'amework of LFG.</Paragraph>
    <Paragraph position="1"> Nordlinger claims that case morphology can construct grammatical reb~tions and larger syntactic contexts.</Paragraph>
    <Paragraph position="2"> In Section 2 we will introduce an ideal languge, which exhibits perfect marking. This language captures Nordlinger's idea of case as constructors of grammatical relations, but is independent of any syntactic framework. We will prove of this language that the case stacks provide all the intbrmation needed tbr reconstructing the flsnctor-argument relations and tim syntactic context a word appears in. Additionally, since structure lies encoded in these case stacks there is no need to assume any phrase structure lsee (Nordlinger, 1997) and (Malouf, 1999) for a discussion on LFG and HPSG respectively.</Paragraph>
    <Paragraph position="3"> or restriction on word order. At the end of this section we consider tile computational complexity of our language and draw some conclusions about grammar formalisms that are able to generate it.</Paragraph>
    <Paragraph position="4"> In Section 3 we propose a compositional semantics tbr our case stacking languages. Unlike Montague semantics, where the management of variables is not made explicit, we will use rethrent systems to kee t) track of variables and to make semantic composition eflicently computable 2. Tile proposal will be applied to our tbrmal language and to an example t'rom Warlpiri.</Paragraph>
  </Section>
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