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<Paper uid="P97-1053">
  <Title>A Uniform Approach to Underspecification and Parallelism</Title>
  <Section position="2" start_page="0" end_page="410" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Traditional model-theoretic semantics of natural languages (Montague, 1974) has assumed that semantic information, processed by composition and reasoning processes, is available in a completely specified form. During the last few years, the phenomenon of semantic underspecification, i.e. the incomplete availability of semantic information in processing, has received increasing attention. Several aspects of underspecification have been focussed upon, motivated mainly by computational considerations: the ambiguity and openness of lexical meaning (Pustejovsky, 1995; Copestake and Briscoe, 1995), referential underspecification (Asher, 1993), structural semantic underspecification caused by syntactic ambiguities (Egg and Lebeth, 1995), and by the underdetermination of scope relations (Alshawi and Crouch, 1992; Reyte, 1993). In addition, external factors such as insufficient coverage  ported by the SFB 378 at the UniversitS.t des Saarlandes and the Esprit Working Group CCL II (EP 22457).</Paragraph>
    <Paragraph position="1"> of the grammar, time-constraints for parsing, and most importantly the kind of incompleteness, uncertainty, and inconsistency, coming with spoken input are coming more into the focus of semantic processing (Bos et al., 1996; Pinkal, 1995).</Paragraph>
    <Paragraph position="2"> The aim of semantic underspecification is to produce compact representations of the set of possible readings of a discourse. While the readings of a discourse may be only partially known, the interpretations of its components are often strongly correlated. In this paper, we are concerned with a uniform treatment of underspecification and of phenomena of discourse-semantic parallelism. Some typical parallelism phenomena are ellipsis, corrections, and variations. We illustrate them here by some examples (focus-bearing phrases are underlined):  (1) John speaks Chinese. Bill too.</Paragraph>
    <Paragraph position="3"> (2) John speaks Japanese. - No, he speaks Chinese.</Paragraph>
    <Paragraph position="4"> (3) ??? - Bill speaks Chinese, too.</Paragraph>
    <Paragraph position="5">  Parallelism guides the interpretation process for the above discourses. This is most obvious in the case of ellipsis interpretation (1), but is also evident for the resolution of the anaphor in the correction in (2), and in the variation case (3) where the context is unknown and has to be inferred.</Paragraph>
    <Paragraph position="6"> The challenge is to integrate a treatment of parallelism with underspecification, such as in cases of the interaction of scope and ellipsis. Problematic examples like (4) have been brought to attention by (Hirschbuehler, 1982). The example demonstrated that earlier treatments of ellipsis based on copying of the content of constituents are insufficient for such kinds of parallelism.</Paragraph>
    <Paragraph position="7"> (4) Two European languages are spoken by many linguists, and two Asian ones (are spoken by many linguists), too.</Paragraph>
    <Paragraph position="8">  The first clause of (4) is scope-ambiguous between two readings. The second, elliptic one, is too. Its interpretation is indicated by the part in parentheses. The parallelism imposed by ellipsis requires the scope of the quantifiers in the elliptical clause to be analogous to the scope of the quantifiers in the antecedent clause. Thus, the conjunction of both clauses has only two readings: Either the interpretation is the wide scope existential one in both cases (two specific European languages as well as two specific Asian languages are widely known among linguists), or it is the narrow scope existential one (many linguists speak two European languages, and many linguists speak two Asian languages).</Paragraph>
    <Paragraph position="9"> A natural approach for describing underspecified semantic information is to use an appropriate constraint language. We use constraints interpreted over finite trees. A tree itself represents a formula of some semantic representation language. This approach is very flexible in allowing various choices for the particular semantic representation language, such as first-order logic, intensional logic (Dowty, Wall, and Peters, 1981), or Discourse Representation Theory, DRT, (Kamp and Reyle, 1993). The constraint approach contrasts with theories such as Reyles UDRT (1993) which stresses the integration of the levels of semantic representation language and underspecified descriptions.</Paragraph>
    <Paragraph position="10"> For a description language we propose the use of context constraints over finite trees which have been investigated in (Niehren, Pinkal, and Ruhrberg, 1997). This constraint language can express equality and subtree relations between finite trees. More generally it can express the &amp;quot;equality up-to&amp;quot; relation over trees, which captures (non-local) parallelism between trees. The general case of equality up-to constraints cannot be handled by a system using subtree plus equality constraints only. The problem of solving context constraints is known as context unification, which is a subcase of linear second-order unification (L~vy, 1996; Pinkal, 1995). There is a complete and correct semi-decision procedure for solving context constraints.</Paragraph>
    <Paragraph position="11"> Context unification allows to treat the interaction of scope and ellipsis. Note that in example (4) the trees representing the semantics of the source and target clause must be equal up to the positions corresponding to the contrasting elements (two European languages / two Asian languages). Thus, this is a case where the additional expressive power of context constraints is crucial. In this paper, we elaborate on the example of scope and ellipsis interaction. The framework appears to extend, however, to all kinds of cases where structural underspecification and discourse-semantic parallelism interact.</Paragraph>
    <Paragraph position="12"> In Section 2, we will describe context unification, and present some results about its formal properties and its relation to other formalisms. Section 3 demonstrates the application to scope underspecification, to ellipsis, and to the combined cases. In Section 4, the proposed treatment is compared to related approaches in computational semantics. Section 5 gives an outlook on future work.</Paragraph>
  </Section>
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