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<Paper uid="E93-1047">
  <Title>[ Type-Driven Semantic Interpretation of f-Structures \] ?.~,w),(njO)</Title>
  <Section position="2" start_page="0" end_page="405" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> In \[Kaplan and Bresnan, 1982\] Lexical Functional Grammar (LFG) was introduced as a grammatical formalism that assigns to a sentence entities of two different levels of representation: a c-structure representing information on the structure of the phrases of a sentence and an f-structure which represents its underlying predicate-argument structure. The structures are set in correspondence by a function from the c-structure nodes (constituents) into the sub-structures of the f-structure. The f-structure is identified with the smallest structure that satisfies the f-description, a description of the f-structure which is built up by instantiation of the annotations of the context-free rules and projected off the c-structure by the correspondence mapping.</Paragraph>
    <Paragraph position="1"> This architecture was then extended by Kaplan \[1987\] and Halvorsen \[1987\] to structures representing information on other levels of linguistic representation. These structures (called projections) are codescribed by the annotations of the context-free grammar and set in correspondence by additional projectors. Furthermore, Kaplan et ai. \[1989\] applied the general correspondence architecture to the problem of translation by projecting from the f-structure of a sentence of a given source language an additional f-structure of its translation into some target language.</Paragraph>
    <Paragraph position="2"> Within the domain of semantic interpretation, which is the topic here, the semantic structures are the range of the a-projector which maps substructures of the f-structure into corresponding substructures of the semantic structure. In figure 1, the S ........ rPaED 'arrive(SUB J)' 1 P VP &amp;quot;:/ su~Ja, \[PRED Jonn J N , --': t..- , \]J/ i-.. i /.j k N &amp;quot; .... Z:~ &amp;quot;/'~ PP~L~. arrive\] I &amp;quot;-. .J*'&amp;quot; / ~.. / John &amp;quot;&amp;quot;arrived L.~,.G1 3ohn J Figure 1 Structural correspondences between c-, f- and a-structure.</Paragraph>
    <Paragraph position="3"> semantic structure ((r-structure) and the structural correspondence between f- and a-structure for the sentence John arrived are codescribed by additional  annotations of the lexical entry for arrived in (1).</Paragraph>
    <Paragraph position="5"> Within the domain of translation, Wedekind \[1988\], and Sadler and Thompson \[1991\] recognized some problems of the correspondence approach which concern data of head.switching. These difficulties also arise in the domain of semantic interpretation. In the latter domain we find constructions where the syntactic head (the predicate) does not correspond to the semantic head as, e.g., in adverbially-modified sentences like (2) (2) John arrived late whose f- and a-structure are given in figure 2. In f: \]PRED 'arrive(SUB J)' P.EL lS ., \[P D 'john'\] ARG1 ARG\] Figure 2 Head-switching between fJand a-structure.</Paragraph>
    <Paragraph position="6"> arr'wl\] joh. JJ this diagram, the semantic-structure corresponding to the entire f-structure has the adverb &amp;quot;late&amp;quot; as its top-level relation, even though this does not correspond to the syntactic (f-structure) head &amp;quot;arrive&amp;quot;. Intuitively, the semantic argument (ArtG 1) of the adverb corresponds to the information coded in the partim f-structure (3), which comprises only the information concerning the subject and the predicate of the sentence.</Paragraph>
    <Paragraph position="8"> The formal difficulty is that this is not an isolated unit of the f-structure and hence cannot be in the domain of a. However, the f-structure description language can be extended by introducing a restriction operator which allows explicit reference to such smaller f-structures. The restriction operator &amp;quot;\&amp;quot; which is defined in (4) below 1 allows us then to refer to the partial structure (3) by the term f\(ADJ a).</Paragraph>
    <Paragraph position="9">  (4) The restriction operator is defined for an f-structure f and an attribute A by: (i) f\A = f\]Dom(f) - {A} if the value of(f A) is a structure, and (it) if g e (f A) (i.e. if (f A) is set-valued) by f\(A g) ff\A if (f A) -- {g} -- 0 = Lf\A U {(A,(f A) -- {g})} else.</Paragraph>
    <Paragraph position="10"> 1Cf. \[Kaplan and Wedekind, 1993\] for more details.  On the other hand, it becomes clear by examples with more than one adjunct that in addition a new source for recursion is needed, since it must in principle be possible to construct a multiple nesting for adjunct sets whose size is not bounded by any fixed finite upper bound. 2 In order to identify this additional recursive device and to test our extended description language for adequacy, we picked out Montague semantics as a well-known semantic theory and tried to specify the syntax-semantics interface by a rule-based semantic interpretation mechanism. Our goal is to derive the semantic representation by analyzing the f-structure recursively. We assume an interpretation mechanism that operates on f-structures (possibly extended by information on the linear precedence of the predicates) and can be stated by very general compositionality principles without relying on any kind of transformations. This is because an f-structure of a sentence represents its deep structure in terms of predicate-argument relations where all information relevant for the interpretation is locally available. Furthermore, we want to ensure the &amp;quot;completeness&amp;quot; of the interpretation and to specify conditions which allow us to control the &amp;quot;conservativity&amp;quot; of the extension (for those who require that a theory of grammar such as LFG be strong enough to ensure the (semantic) well-formedness of the strings accepted by a particular grammar). On the other hand, we want the semantic structure to be accessible from the f-structure by an explicit interpretation function (a-projector) in order to be able to formulate constraints, e.g. binding and scoping principles, which constrain the interpretation of the f-structures.</Paragraph>
    <Paragraph position="11"> In this paper, we give three different type-driven interpretation mechanisms which fulfill the requirements given above. The first one is a rather simple top-down algorithm that can be described by our extended description language but cannot be used for all type systems. The second algorithm is a more powerful bottom-up algorithm which can be used for all type systems but not formulated in our description language. The third one, finally, is a top-down simulation of the second algorithm which is again describable in our description language. The fact that the third algorithm can be described by our extended description language seems to confirm the adequacy of our extension by the restriction operator. Furthermore, this investigation indicates that an additional description-by-analysis mechanism is needed within a codescription approach in order to handle cases 2This situation, where the recursion given by the context-free rule system turns out not to be the adequate or at least desirable carrier for specific (recursive) description purposes, is not unusual. Functional uncertainty was e.g. introduced as a new recursive device operating on fstructures, since unbounded dependencies could be more adequately handled by this new mechanism than by exploiting the recursive phrase structure rule system alone.  where the interpretation recursion is completely independent of the recursion given by the context-free grammar (cf. \[Kaplan and Wedekind, 1993\]).</Paragraph>
  </Section>
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