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<Paper uid="E93-1024">
  <Title>Restriction and Correspondence-based Translation</Title>
  <Section position="3" start_page="194" end_page="197" type="metho">
    <SectionTitle>
3. The restriction operator and
</SectionTitle>
    <Paragraph position="0"> structural misalignments A simple kind of syntax/semantics misalignment is exemplified by constructions involving light-verbs or complex predicates. These are  constructions formed by two or more verbs involving two or more semantic relations, but with the notable peculiarity that the complex behaves as a single, monoclausal syntactic unit according to standard tests of subcategorization and agreement. Butt et al. (1990) have argued persuasively that Urdu complex predicates are syntactically monoclausal and further, that the complex predicate cannot be formed in the lexicon. The details of the argument do not matter for present purposes, and we will simply accept their analysis of sentence (10a) whose English translation is given in (10b). The c-, f-, and semantic-structures, according to their analysis, are shown in Figure 3.</Paragraph>
    <Paragraph position="1">  (I0) (a) Anjum-ne diyaa Saddaf-koxat likhne. (b) Anjum let Saddafwrite a letter.</Paragraph>
    <Paragraph position="2">  The crucial feature of this analysis is that there is a single set of governed grammatical functions in the f-structure, and these are derived systematically from the normal subcategorization of the main predicate likhne 'write'. The governable functions of diyaa when it stands as an independent predicate (usually glossed as the ditransitive predicate 'give') are not represented in the f-structure. The second obvious feature is that the flat f-structure maps to the hierarchical semantic structure, where the outer predicate has the permissive reading conveyed by diyaa in its light-verb sense and the inner proposition contains the main predicate and its arguments. This analysis cannot be formulated using standard codescription, function-application, and equality because there is no separate level in the f-structure that the inner semantic proposition can correspond to and thus no way to describe its properties.</Paragraph>
    <Paragraph position="3"> While there may be a technical problem in finding a structure that the inner proposition can correspond to, there is a very clear intuition about what parts of the f-structure carry the information that constrains that piece of the semantic structure, namely, the sub-f-structure obtained by eliminating the SUBJ attribute and value. The following diagram depicts this intuition:</Paragraph>
    <Paragraph position="5"> In this arrangement the semantic correspondence o relates each level of the semantic structure to a unit in f-structure space, and that unit is the source of constraints on the properties of the corresponding element of the semantic structure.</Paragraph>
    <Paragraph position="6"> The ARG3 hierarchy in the semantic structure is not the image of an attribute embedding in the f-structure as is usually the case; rather, the semantic hierarchy here corresponds to a subsumption relation in the f-structure lattice.</Paragraph>
    <Paragraph position="7"> This organization of informational dependencies can be expressed by means of the restriction operator.</Paragraph>
    <Paragraph position="8"> Restriction is a new operator in the f-structure description language notated by \ and with the following (partial) definition:  (12) If f is an f-structure and a is an attribute:</Paragraph>
    <Paragraph position="10"> The restriction of a given f-structure f by a particular attribute a is the f-structure that results from deleting a and its value from f. If f is the f-structure in (13a), then the f-structure in  Restriction is a designator analogous to ordinary function-application in that it provides a way of referring to elements of f-structure space by virtue of their relations to other f-structures. If f and g are two f-structure designators and a denotes an attribute, then</Paragraph>
    <Paragraph position="12"> asserts that f and g both have an attribute a with exactly the same value; they may or may not have other attributes and values in common.</Paragraph>
    <Paragraph position="13"> fla=gla asserts that f and g have all attributes and values in common other than a; they may or may not have values for a and those values may or may not be identical.</Paragraph>
    <Paragraph position="14"> Thus, restriction and function-application can be used to impose complementary constraints on f-structure values. We note that restriction is associative and commutative in its second (attribute) argument, so that \[f\a\] \b = \[f\b\] \a = f\(ab}, and that for any f-structure f and attribute a it is always the case that f\a subsumes f (f\a V- f).</Paragraph>
    <Paragraph position="15"> Returning now to the Urdu example, we see that if the top-level f-structure (the one corresponding to the S node) is denoted by f, the subsidiary f-structure to which corresponds the inner proposition in (11) is the restriction off by SUBJ and can be referred to by the expression f\SUBJ. The restriction operator can be used in codescription statements so that exactly the configuration in (11) is assigned to the Urdu sentence. A lexical redundancy rule can be introduced to systematically modify the lexical entries for normal verbs like likhne to make them suitable for combination with a light-verb:</Paragraph>
    <Paragraph position="17"> This rule replaces all references to the grammatical function SUBJ with OBJ2, thus avoiding conflict with the SUBJ introduced by the light verb, and it replaces all occurrences of the term o 1' with the term o\[ 1' kSUBJ\]. This indicates that the main predicate provides constraints on the semantic structure corresponding to the subject-free f-structure. As a result of this rule, the usual equations for likhne in (16a) would give rise to the alternatives in (16b):</Paragraph>
    <Paragraph position="19"> The lexical rule would also make other minor adjustments to fill out the entry; the details do not concern us here.</Paragraph>
  </Section>
  <Section position="4" start_page="197" end_page="199" type="metho">
    <SectionTitle>
4. Restriction and adverbial
</SectionTitle>
    <Paragraph position="0"> modifiers Sentence with adverbial modifiers can also be characterized intuitively as having a fiat syntactic structure with hierarchical semantic relations, and restriction can also be used to describe the appropriate structural configurations. The adverbial examples above involve only single sentential adjuncts, but our analysis allows for any number of adverbs with all possible scope ambiguities, and it can easily be extended to handle VP modifiers as well. We start with a c-structure rule that assigns arbitrarily many adverbs to the set-value of the ADJ attribute, consistent with the original LFG account of adjuncts (Kaplan and Bresnan, 1982):</Paragraph>
    <Paragraph position="2"> The sentence (18a) will be assigned the f-structure (18b) by virtue of this rule. Our goal is to associate with this f-structure the  alternative semantic structures in (19). (18) (a) John obviously just fell.</Paragraph>
    <Paragraph position="3"> (b) pRED' fall&lt;\[John\]&gt;' \] JSUBJ ~RED 'John'\] }  Intuitively, the innermost proposition in both (19a) and (19b) is based on the f-structure information in (18b) ignoring the adjuncts; the middle proposition in (19a) is exactly what we would expect for a sentence that included just but not obviously, and the middle proposition in (19b) would be appropriate for a sentence containing only obviously. Thus the semantic structures again seem to correspond to subsets of f-structure information, and we begin by completing the definition of the restriction operator. In addition to restricting an f-structure by an attribute, as defined in (12), we also define the restriction of an f-structure by an element of an attribute's set-value: (20) If f is an f-structure and a is an attribute: f\&lt;ag&gt; = .f f\ a if (fa)-{g} = t f\ a U {'&lt;a, (f a)-{g} &gt; } otherwise The restriction of a given f-structure f by a particular member of an attribute a's set-value is the f-structure that results from deleting that member of the set and also deleting the attribute itself if the set would then be empty. The relationships in (21) exemplify the pattern: p RED 'fall&lt;\[John\]&gt;\] (21) f= ~UBJ ~RED 'John\] ~DJ { \[just\] } g = \[just\] = pR O 'f ll&lt;\[Joh.\]&gt;q f \&lt;ADJ g&gt; UBJ RED 'John\] \] We note that set-element restriction also has commutative and associative properties: (22) \[f~&lt;ag&gt;\]\&lt;ah&gt; =\[/~.&lt;ah&gt;\]\&lt;ag&gt; =t\&lt;agh&gt; The restriction operator can now be used to describe the semantic correspondences for adverbial sentences. If f designates the f-structure in (18b) and j and o designate the f-structures corresponding to the adverbs just and obviously, then the constraints (23a,b) describe the outermost REL and ARG1 configuration in  (19a) and (23c,d) describe the next level of semantic embedding: (23) (a) (OfREL)=(oo REL) (b) (of ARGI)----o\[f\&lt;CADJ o&gt;\] (c) (o~\&lt;ADJo&gt;\] REL)----(oj REL) (d) (o~\&lt;CADJ o&gt;\] ARG1) =o\[f\&lt; ADJ o j&gt; \]  = O~ADJ\] The innermost proposition can be described by interpreting (or redundantly rewriting) a T in the cedescription equations in the fall lexical entry as o\[ ~ ~kDJ\], that is, by interpreting the a specifications for all basic predicates as characterizing the semantics of an unmodified f-structure.</Paragraph>
    <Paragraph position="4"> The restriction constraints in (23) are sufficient to map f-structure subsumption relations into the desired hierarchical semantic structures, but the number of such constraints depends on the size of the initial adjunct set; indeed, (23d) suggests that the size of individual constraints used in this construction also grows in proportion to the number of modifiers.</Paragraph>
    <Paragraph position="5"> Constraints of this general form cannot be produced by the normal recursive analysis of the c-structure because the c-structure itself, by linguistic argumentation, does not have the degree of embedding that these constraints would require. The restriction operator can encode the intuitively desirable constraints, but an additional recursive process is needed to generate those constraints. This recursion can arise from an explicit traversal of the f-structure in the style of Halvorsen's (1983) semantic interpretation procedure. It can also come from lexical expressions of inside-out functional uncertainty; this formal device was introduced by Kaplan (1988) and has been applied to problems of quantifier scope (Halvorsen and Kaplan, 1988) and anaphoric dependencies (Dalrymple, 1993). Here we explore only the description-by-analysis  approach, using the following analysis rule to generate codescriptive assertions: (24) For fan f-structure, g ( (f ADJ), and g a sentence adverb, of = og and (of ARG1) = o\[fk&lt;ADJ g&gt;\] According to this rule, a single element is chosen (nondeterministically) from an adjunct set to contribute the relation for the semantic structure of the enclosing f-structure, and the semantic structure corresponding to the f-structure without the chosen element becomes that relation's argument. One application of the rule givesrise to additional structures to which the rule might also apply, and this recursion generates the appropriate set of constraints. For example, suppose fis the f-structure in (18b) and the obviously f-structure o is chosen as the instantiation of g in the rule. This produces the equations (23a,b) which define the configuration shown in (25). The rule then matches again against the lower f-structure, thereby completing the picture (26).</Paragraph>
    <Paragraph position="6">  The alternative in which just has wide scope (the semantic structure (19b)) results from nondeterministically choosing the j f-structure in the first rule instantiation. We note without discussion that the rule in (24) is appropriate for sentence adverbs, which take complete propositions as arguments, but a different semantic structure is required for adverbs that only modify the meaning of the basic relation, such as the manner adverb in (27a). The relational embedding in (27b) gives a better account of the meaning of this sentence.</Paragraph>
    <Paragraph position="7">  (27) (a) John walked slowly.</Paragraph>
    <Paragraph position="8"> (b) I. s,o, ly 11</Paragraph>
  </Section>
  <Section position="5" start_page="199" end_page="199" type="metho">
    <SectionTitle>
R61 EL ~EL walk~JJ
</SectionTitle>
    <Paragraph position="0"> LARGt John Assuming some suitable marking of the differences among adverbs, perhaps based on the semantic typing discussed by Wedekind and Kaplan (1993), this structure is defined by the additional description-by-analysis rule (28): (28) For fan f-structure, gE(f ADJ), and g a VP adverb,</Paragraph>
  </Section>
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