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<Paper uid="P98-1072">
  <Title>Semantic-Head Based Resolution of Scopal Ambiguities*</Title>
  <Section position="4" start_page="433" end_page="434" type="metho">
    <SectionTitle>
2 Underspecified Semantics: USR
</SectionTitle>
    <Paragraph position="0"> The representation we will use, USR, is a tertiary term containing the following pieces of semantic information: a top label, a set of labeled conditions, and a set of constraints. The conditions represent ordinary predicates, quantifiers, pronouns, operators, etc., all being uniquely labeled, making it easier to refer to a particular condition. Scope (appearing in quantifiers and operators) is represented in an underspecified way by variables (&amp;quot;holes&amp;quot;) ranging over labels. Labels are written as ln, holes as hn, and variables over individuals as in. The labelling allows us to state meta-level constraints on the relations between conditions. A constraint l &lt; h is a relation between a label and a hole: 1 is either equal to or subordinated to h (the labeled condition is within the scope denoted by the hole).</Paragraph>
    <Paragraph position="2"> Fig. 1 shows the USR for (1). The top label 11 introduces the entire structure and points to the declarative sentence mood operator, outscoping all other elements. The pronoun 'das' is pron, marking unresolved anaphora. 'auch' and 'nicht' are handled as operators. The verb condition (passen) and its pronoun subject are in the same scope unit, represented by a grouping.</Paragraph>
    <Paragraph position="3"> The first three constraints state that neither the verb, nor the two particles outscope the mood operator. The last two put the verb information in the scope of the particles. (NB: no restrictions are placed on the particles' relative scope.) Fig. 2 shows the subordination relations.</Paragraph>
    <Paragraph position="4">  A USR is interpreted with respect to a &amp;quot;plugging&amp;quot;, a mapping from holes to labels (Bos, 1996). The number of readings the USR encodes equals the number of possible pluggings. Here, two pluggings do not violate the _&lt; constraints: /3/ }h I = 14, h2 = 15, h3 = 18 t ls, h2=le, hs 14 The plugging in (3) resembles the reading where 'auch' outscopes 'nicht': the label for 'nicht', 15, is taken to &amp;quot;plug&amp;quot; the hole for 'auch', h2, while 'auch' (14) is plugging the top hole of the sentence, hi. In contrast, the plugging in (4) gives the reading where the negation has wide scope.</Paragraph>
    <Paragraph position="5">  With a plugging, a USR can be translated to a Discourse Representation Structure, DRS (Kamp and Reyle, 1993): a pron condition introduces a discourse marker which should be linked to an antecedent, group is a merge between DRSs, passen a one place predicate, etc.</Paragraph>
  </Section>
  <Section position="5" start_page="434" end_page="434" type="metho">
    <SectionTitle>
3 Construction of USRs
</SectionTitle>
    <Paragraph position="0"> In addition to underspecification, we let two other principles guide the semantic construction: lexicalization (keep as much as possible of the semantics lexicalized) and compositionality (a phrase's interpretation is a function of its subphrases' interpretations). The grammar rules allow for addition of already manifest information (e.g., from the lexicon) and three ways of passing non-manifest information (e.g., about complements sought): trivial composition, functor-argument and modifier-argument application.</Paragraph>
    <Paragraph position="1"> Trivial composition occurs in grammar rules which are semantically unary branching, i.e., the semantics of at the most one of the daughter (right-hand side) nodes need to influence the interpretation of the mother (left-hand side) node.</Paragraph>
    <Paragraph position="2"> The application type rules appear on semantically binary branching rules: In functor-argument application the bulk of the semantic information is passed between the mother node and the functor (semantic head). In modifier-argument application the argument is the semantic head, so most information is passed up from that. (Most notably, the label identifying the entire structure will be the one of the head daughter. We will refer to it as the main label.) The difference between the two application types pertains to the (semantic) subcategorization schemes: In functor-argument application (5), the functor subcategorizes for the argument, the argument may optionally subcategorize for the functor, and the mother's subcategorization list is the functor's, minus the argument:</Paragraph>
  </Section>
  <Section position="6" start_page="434" end_page="436" type="metho">
    <SectionTitle>
4 A Resolution Algorithm
</SectionTitle>
    <Paragraph position="0"> Previous approaches to scopal resolution have mainly been treating the scopal constraints separately from the rest of the semantic structure and argued that contextual information must be taken into account for correct resolution. However, the SRI Core Language Engine used a straight-forward approach (Moran and Pereira, 1992). Variables for the unresolved scoped were asserted at the lexical level together with some constraints on the resolution. Constraints could also be added in grammar rules, albeit in a somewhat ad hoc manner. Most of the scopal resolution constraints were, though, provided by a separate knowledge-base specifying the inter-relation of different scope-bearing operators. The constraints were applied in a process subsequent to the semantic construction.</Paragraph>
    <Section position="1" start_page="434" end_page="435" type="sub_section">
      <SectionTitle>
4.1 Lexical entries
</SectionTitle>
      <Paragraph position="0"> In contrast, we want to be able to capture the constraints already given by the function-argument structure of an utterance and provide a possible resolution of the scopal ambiguities.</Paragraph>
      <Paragraph position="1"> This resolution should be built up during the construction of (the rest of) the semantic representation. Thus we introduce a set of features (called holeinfo) on each grammatical category.</Paragraph>
      <Paragraph position="2"> On terminals, the features in this set will normally have the values shown in (7), indicating that the category does not contain a hole (isahole has the value no), i.e., it is a nonscope-bearing element, sb-label, the semantic-head based resolution label, is the label of the element of the substructure below it having widest scope.</Paragraph>
      <Paragraph position="3"> In the lexicon, it is the entry's own main label.</Paragraph>
      <Paragraph position="4"> (7) holeinfo isa-hole no hole no Scope-bearing categories (quantifiers, particles, etc.) introduce holes and get the feature setting of (8). The feature hole points to the hole introduced. (Finite verbs are also treated this way: they are assumed to introduce a hole for the scope of the sentence mood operator.)  (8) holeinfo isa-hole yes hole Hole</Paragraph>
    </Section>
    <Section position="2" start_page="435" end_page="435" type="sub_section">
      <SectionTitle>
4.2 Grammar rules
</SectionTitle>
      <Paragraph position="0"> When the holeinfo information is built up in the analysis tree, the sbdeglabels are passed up as the main labels (i.e., from the semantic head daughter to the mother node), unless the nonhead daughter of a binary branching node contains a hole. In that case, the hole is plugged with the sb-label of the head daughter and the sb-label of the mother node is that of the nonhead daughter. The effect being that a scope-bearing nonhead daughter is given scope over the head daughter. On the top-most level of the grammar, the hole of the sentence mood operator is plugged with the sb-label of the full structure.</Paragraph>
      <Paragraph position="1"> Concretely, grammar rules of both application types pass holeinfo as follows. If the nonhead daughter does not contain a hole, holeinfo is unchanged from head daughter to mother node:  However, if the nonhead daughter does contain a hole, it is plugged with the sb-label of the head daughter and the mother node gets its sb-label from the nonhead daughter. The rest of the holeinfo still come from the head daughter:  The hole to be plugged is here identified by the hole feature of the nonhead daughter. To show the preferred scopal resolution, a relation 'Hole =sb HeadLabel', a semantic-head based plugging, is introduced into the USR.</Paragraph>
    </Section>
    <Section position="3" start_page="435" end_page="435" type="sub_section">
      <SectionTitle>
4.3 Resolution Example
</SectionTitle>
      <Paragraph position="0"> We will illustrate the rules with an example.</Paragraph>
      <Paragraph position="1"> The utterance (1) 'das paPSt auch nicht' has the semantic argument structure shown in Fig. 3, where Node\[L, HI stands for the node Node having an sb-label L and hole feature value H.</Paragraph>
      <Paragraph position="2"> The verb passen is first applied to the subject 'alas'. The sb-label of 'passen' is its main label (the grouping label 16). Its hole feature points to hi, the mood operator's scope unit. The pronoun contains no hole (is nonscope-bearing), so we have the first case above, rule (9), in which the mother node's holeinfo is identical to that of the head daughter, as indicated in the figure.</Paragraph>
      <Paragraph position="4"> Next, the modifier 'nicht' is applied to the verbal structure, giving the case with the nonhead daughter containing a hole, rule (10). For this hole we add a 'h3 =sb 16' to the USR: The label plugging the hole is the sb-label of the head daughter. The sb-label of the resulting structure is 15, the sb-label of the modifier. The process is repeated for 'auch' so that its hole, h2, is plugged with 15, the label of its argument. We have reached the end of the analysis and hi, the remaining hole of the entire structure is plugged by the structure's sb-label, which is now 14. In total, three semantic-head based plugging constraints are added to the USR in Fig. 1: (11) hi =sb 14, h2 =sb 15, 53 &amp;quot;=sb 16 Giving a scope preference corresponding to the plugging (3), the reading with auch outscoping nicht, resulting in the correct interpretation.</Paragraph>
    </Section>
    <Section position="4" start_page="435" end_page="436" type="sub_section">
      <SectionTitle>
4.4 Coordination
</SectionTitle>
      <Paragraph position="0"> Sentence coordinations, discourse relation adverbs, and the like add a special case. These categories force the scopal elements of their sentential complements to be resolved locally, or in other words, introduce a new hole which should be above the top holes of both complements.</Paragraph>
      <Paragraph position="1"> They get the lexical setting (12) holeinfo isa-hole island hole Hole So, isa-hole indicates which type of hole a structure contains. The values are no, yes, and island, island is used to override the argument structure to produce a plugging where  the top holes of the sentential complements get plugged with their own sb-labels. This complicates the implementation of rules (9) and (10) a bit; they must also account for the fact that a daughter node may carry an island type hole.</Paragraph>
    </Section>
  </Section>
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