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<Paper uid="C00-1067">
  <Title>On Underspecified Processing of Dynamic Semantics</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> A particularly appealing aspect of lmdersl)ecification (van Deemter and Peters, 1996; Reyle, 1993; Muskens, 1995; Pinkal, 1996; Bos, 1996) is that it can in principle deal very efficiently with local ambiguities - ambiguities which are only due to lack of inibrmation at an intermediate stage of processing and go away by the end of the analysis. An example for this effect is (1): The scope ambiguity that is perceived alter processing the first sentence is no longer present after the second one. This effect can be explained in a framework of dynamic selnantics (Groelmndijk and Stokhof, 1991; Kamp and Reyle, 1993) by the fact that a wide-scope universal quantifier would make the indefinite inaccessible for anaphoric reference from the second sei/tence.</Paragraph>
    <Paragraph position="1"> (1) Every man loves a woman.</Paragraph>
    <Paragraph position="2"> Her nanle is Mary.</Paragraph>
    <Paragraph position="3"> In this paper, we show how this particular type of local ambiguity can be processed efficiently. The approach we propose employs deterministic inference rules that can exclude the readings which violate anaphoric accessibility conditions without enlnnerating them. These rules operate directly on underspecified descriptions and fully maintain underspecifiedness. We also show how this behaviour Call be captured by constraint propagation in an existing implementation of tree descriptions using finite set constraints (Duchier and Niehren, 2000; Keller and Niehren, 2000; Duchier and Gardent, 1999).</Paragraph>
    <Paragraph position="4"> More specifically, we introduce DPL structuT&amp;quot;cs~ extended trce structures that encode formulas of dynamic predicate logic (DPL) in much the same way as Egg et al.'s (1998) lambda structnres encode A-terms. Then we define a constraint language tbr the description of DPL structures, called CL(DPL), in analogy to Egg et al.'s constraint langague for lambda structures (CLLS). We characterize those DPL structures in which all restrictions oil anaphoric accessibility are obeyed by talking directly about the syntactic structure of a DPL formula. This is ill contrast to the standard procedure in dynanfic semantics, where the dynamic behaviour is produced by the semantics of the logic; we do not need to (and do not) talk about interpretation of DPL structures and model accessibility by purely &amp;quot;static&amp;quot; means.</Paragraph>
    <Paragraph position="5"> The paper is structured as follows. In Section 2, we introduce DPL structures and tree descrit)tions in the language CL(DPL). In Section 3, we add syntactic restrictions on admissible variable bindings to DPL structures and present axioms that characterize these restrictions. In Section 4:, we turn these axioms into deterministic infhrence rules and combine them with deterministic inference rules known from an existing ilfference algorithm for dominance constraints. We obtain a procedure that can do the kind of underspccified reasoning described above without enmncrating readings. In Section 5, we sketch all imtflelnentation of our inf'erence system based on finite set constraint progralnming. This implementation can be obtained by adapting an existing ilnI)lelnentation of a solver for dominance constraints. Finally, we conclude and point to further work in Section 6.</Paragraph>
  </Section>
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