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<Paper uid="H91-1033">
  <Title>THE MAPPING UNIT APPROACH TO SUBCATEGORIZATION</Title>
  <Section position="4" start_page="185" end_page="185" type="metho">
    <SectionTitle>
THE &amp;quot;MAPPING UNIT&amp;quot; INFORMATION
STRUCTURES
</SectionTitle>
    <Paragraph position="0"> The central idea of the mapping unit approach is that there are several different types of subcategorization constraints, which ought to be represented as separate constraints, rather than enumerating the &amp;quot;cartesian product&amp;quot; of their possible combinations in fixed patterns. The basic building block is the &amp;quot;mapping unit&amp;quot;, a structure which represents the constraints on a particular phrasal argument and the contribution this argument makes to the semantics of the clause. Mapping units do not &amp;quot;know&amp;quot; whether they axe optional or not, or in what order they occur with respect to other mapping units; this information is instead represented in the grammar and in a larger structure called a &amp;quot;map&amp;quot;, of which the mapping unit is a component.</Paragraph>
    <Paragraph position="1"> The following is an example of a mapping unit:</Paragraph>
    <Paragraph position="3"> Each mapping unit has the four components shown here: a grammatical relation (SUBJECT, DIRECT-OBJECT, OTHER-PP ete), a syntactic pattern, a type requirement, and semantic role information.</Paragraph>
    <Paragraph position="4"> The syntactic pattern is a unification pattern, and thus retains all the advantages of being able to handle partial information that are associated with unification. The syntactic pattern (in the example just NP) also includes slots for semantic translation (&amp;quot;:trans&amp;quot;).</Paragraph>
    <Paragraph position="5"> The semantic type requirement (here &amp;quot;FLIGHT&amp;quot;) is also enforced by unification, but separately, so that a failure due to semantic type clash can be distinguished from one that violates syntactic constraints.</Paragraph>
    <Paragraph position="6"> In this way, ff the type requirement is not met, the mapping unit can be metonymically coerced, filling the semantic role not with the original complement translation but with an indefinite object related to it via a binary relation that resolves the clash. For example, the unit above could be coerced to accept an object of type AIRLINE via the binary relation FLIGHT-AIRLINE-OF, which maps flights to their airlines, thus handling the utterance &amp;quot;What airlines fly to Dallas&amp;quot;.</Paragraph>
    <Paragraph position="7"> A final separate representation is the contribution the semantics of the argument makes to the semantics of the clause, which is indicated by a semantic role constraint. The role is set (with the equality symbol &amp;quot;=&amp;quot;) in the case of ordinary complement arguments and restricted (with &amp;quot;&lt;&amp;quot;) in the ease of iterable temporal or locative adjunct moditiers (&amp;quot;in Harvard Square at Out of Town News next to the foreign magazine section&amp;quot;). A semantic role can only be set once in any given clause (which of course does not exclude it from being set to a conjunctive element), but can be rearicted arbitrarily many times.</Paragraph>
    <Paragraph position="8"> The mapping units are combined in a larger structure called a &amp;quot;map&amp;quot;, of which the following is a (much reduced) example for the verb &amp;quot;fly&amp;quot;:</Paragraph>
  </Section>
  <Section position="5" start_page="185" end_page="186" type="metho">
    <SectionTitle>
((FLY1 FLIGHT-OF FLIGHT
ORIG-CITY CITY
DEST-CITY CITY)
</SectionTitle>
    <Paragraph position="0"> Every map has four components: 1. a labeled-argument predicate with typed roles 2. a collection of &amp;quot;mapping units&amp;quot; 3. a completion condition 4. a translation rule for the labeled-argument predicate  The labeled-argument predicate--in the example 'FLY1 '--is the representation of the verb's &amp;quot;meaning&amp;quot;, and has an assigned set of typed semantic roles which can appear in any application of the predicate (but which are not necessarily required to appear in every application). The completion condition must be satisfied by any complete clause with the verb as head, and includes requirements on the instantiation of semantic roles. 1 In the example map, the FILLED completion predicate requires that the roles FLIGHT-OF and DEST-CITY be filled by a literal argument to the verb, while the FILLED-OR-ANAPHOR completion predicate allows the role ORIG-CITY to be be implicitly filled by a discourse entity. This condition allows &amp;quot;What flights fly *This rexluircment, in effect, implements the Functional Complcumcss f~ondition of I2G \[4\].</Paragraph>
    <Paragraph position="1">  to Denver from Boston?&amp;quot;, &amp;quot;What flights fly from Boston to Denver&amp;quot; and &amp;quot;What flights fly to Denver?&amp;quot; but forbids &amp;quot;What flights fly?&amp;quot;. Other completion predicates include FILLED-OR-DEFAULT, which specifies a defanlt value for a role, FILLED-OR-EXISTS, which generates an existential quantification over the range type ff the role is unfilled, and GRAMMAR-REL-FILLED, which requires that a particular grammatical relation have been assigned. The unqualified optionality of a semantic role is indicated simply by leaving it out of the completion conditions. 2 The fourth map component, the translation rule, converts labeled-argument predicate applications into ordinary logic expressions based on the roles they instantiate. Its separation from the rest of the map avoids duplicate specification of the details of logical form construetion. null This last point is important because a map can have multiple units on the same semantic role to represent multiple syntactic realizations of it. For example, the utterance &amp;quot;fly DENVER to Boston&amp;quot; (meaning &amp;quot;fly FROM DENVER to Boston&amp;quot;) can be aecomodated simply by adding the following unit to the map above:</Paragraph>
    <Paragraph position="3"> and the function of the translation rule is exactly the same.</Paragraph>
    <Paragraph position="4"> Any semantic role can be frilled only once, so that overgeneration from multiple mapping units assigning the same role (&amp;quot;fly Boston from Denver&amp;quot;, &amp;quot;fly Denver from Denver&amp;quot;) is prevented. 3 Certain grammatical relations can also be assigned only once in the derivation of any clause. These are the &amp;quot;major&amp;quot; grammatical relations ---SUBJECT, DIRECT-OBJECT, INDIRECT-OBJECT. The OTHER-(eat) relations can be assigned arbitrarily many times, sub-ject only to the constraint that semantic roles be filled only once.</Paragraph>
    <Paragraph position="5"> Multiple mapping units that assign the same major grammatical relation are also allowed, subject only to the above constraint and of course to the constraint on the unique assignment of semantic roles.</Paragraph>
    <Paragraph position="6"> This is useful for handling certain types of polysemy---specifically, the semantic overloading of syntactic argument positions.</Paragraph>
    <Paragraph position="7"> For modifiers which are normally treated as adjuncts, such as temporal or locative modifiers, our framework provides a notion of &amp;quot;free&amp;quot; mapping units associated with distinguished roles (such as TIME-OF-DAY, etc.). Such units do not have to be included in the map for individual lexical items whose labeled-argument predicate translation includes the role. In the example map above, TIME-OF-DAY is such a &amp;quot;free&amp;quot; mapping unit.</Paragraph>
    <Paragraph position="8"> Finally, we should point out that while the map information structures can handle a considerable degree of variation, it is not necessary  of LFG \[4\]. This requirement and the requirement that completion predicates be satisfied, in effect, implements the Theta Criterion of GB theory \[5\]. for any one map to handle all the possible variations associated with a verb. A verb can have multiple maps in the case of conventional lexieal ambiguity, just as it can have multiple subeategorization frames in other approaches.</Paragraph>
  </Section>
  <Section position="6" start_page="186" end_page="187" type="metho">
    <SectionTitle>
USE OF MAPPING UNITS IN GRAMMAR AND
SEMANTIC INTERPRETATION
</SectionTitle>
    <Paragraph position="0"> Standard phrase structure rules augmented with features \[11\] are in our approach further augmented with the non-constituent predicates AVAILABLE, VP-BIND, and COMPLETE-WFF, along with the selector CONST1T. The following is an example of the grammar nile that assigns DIRECT-OBJECT, reduced to include only features of interest (non-constituent predicates appear in curly brackets):</Paragraph>
    <Paragraph position="2"> The predicate AVAILABLE takes a grammatical relation, a map, and a bindings li~, which is a list pairing mapping units with role fillers. It is satisfied if there is a unit in the map with that grammatical relation such that the semantic role of that unit is not set in the bindings list, and the grammatical relation is not assigned in the bindings list (if it is a &amp;quot;major&amp;quot; grammatical relation).</Paragraph>
    <Paragraph position="3"> The predicate VP-BIND takes a grammatical relation, a map, an entire constituent (retrieved by the function CONSTIT as seen above) an input bindings list and an output bindings list. If it succeeds, it preduees a new bindings list containing an additional pair of unit and filler. It will succeed ff it finds a free unit in the map that can be matched with the passed-in constituent both syntactically and semantically. VP-BIND will have more than one solution ff it finds multiple units with these properties, in which case there are multiple parses. (Note that the AVAILABLE predicate is really only necessary to prevent the parser from looking for a constituent that would only wind up not being attachable to the VP.) The pair of map and bindings effectively constitutes the meaning of the VP, and can be likened to a an application of lambda-expression (the map) to arguments (the bindings). The difference is that while the arguments to a regular lambda-expression can either be bound all at once or in some fixed order (e.g. through currying) the arguments to a map are referred to by label, and can be applied in any order we plea.</Paragraph>
    <Paragraph position="4"> Currently, the maps only provide optionality information, while the relative order of complements is enforced by the grammar via grammatical relmions. This has the advantage that certain ordering constraints need only be stated once, as opposed to over and over again in map entries. An example of a rule imposing ordering constraints is the ditransitive VP rule, which handles &amp;quot;Show me the flights&amp;quot;:</Paragraph>
    <Paragraph position="6"> The constraint that the subject precedes post-venal complements is expressed by the clause-level S rule, which assigns the relation SUBJECT:</Paragraph>
    <Paragraph position="8"> The completion conditions for the clause are enforced by the rule for the top-most node, START. This rule contains a predicate COMPLETE-WFF that takes a map, bindings list, and delivers an output formula:</Paragraph>
    <Paragraph position="10"> COMPLETE-WFF enforces the completion conditions of the map and reduces the map and bindings combination to a formula ff these conditions are satisfied.</Paragraph>
    <Paragraph position="11"> The formula to be generated is specified by the translation rule component of the map. This translation rule can really be regarded as a kind of meaning postulate for the predicate that is associated with it directly. It consists of an ordinary logic expression containing references to the argument labels of the predicate. Repeated below is the translation for the predicate 'FLY1 ':  To generate the formula, the fillers of the argument roles are substituted for these references. The P-AND is a meta-conjunction operator with the property that ff any of the role references of one of its eonjuncts are unfilled, that conjunct is left out of the final formula. In this way we are not required to generate an existential quantification for a missing argument place (as for example the departure time of the flight).</Paragraph>
    <Paragraph position="12"> There are certain instances in which an existential quantification is generated, however. If a semantic role has merely been restricted instead of fired, a narrow-scope existential quantification is generated and the variable of this quantification substituted for the role reference in the translation rule. Thus for &amp;quot;Flight 1 flies before 3 pm&amp;quot; we would have: (exists t (precede t (time 3 0 pm))</Paragraph>
    <Paragraph position="14"> Another case in which narrow-scope existentials are generated is the case of predicative metonomy, in which the semantic role in question has been type-coerced to accept an argument of a type different from its restriction. In this type of metonymy, the referent of this argument does not change. Instead a relation is established between it and an indefinite, existentially quantified object of the proper type.</Paragraph>
    <Paragraph position="15"> Thus for &amp;quot;Delta Airlines flies from Boston to Baltimore&amp;quot; we would have: (exists x flight (airline-of x Delta) (and (orig-clty x boston) (dest-city x baltimore))) The distinction between referential and predicative metonymy only becomes visible when the actual referents of NPs are sought, as in: What airlines fly to Boston? What wide-body jets serve dinner? In the first, it is implausible that &amp;quot;airlines&amp;quot; is being used to refer to some set of flights, since every flight is on some airline and there is no constraint. In the second, &amp;quot;wide-body jets&amp;quot; is far more likely to refer to some set of flights, since not every flight is on a wide-body jet.</Paragraph>
    <Paragraph position="16"> Predicative metonymy is an essentially local phenomenon, while referential metonymy is an essentially global one. Our present implementation assumes predicative metonymy only and allows only a limited set of binary relations. Processing is such as to prefer attachments that do not require metonymy, by assigning a lower probability at parse-time to parses which do require it \[2\]. This is necessary to exclude an unreasonable parse of: Show flights to Denver on wide-body jets serving dinner.</Paragraph>
  </Section>
  <Section position="7" start_page="187" end_page="188" type="metho">
    <SectionTitle>
OTHER BENEFITS
</SectionTitle>
    <Paragraph position="0"> The combination of labeled-argument predicate mad translation rule offers several benefits not yet mentioned. One is that a given predicate can be shared between different lexical entries which provide different syntactic realizations of it. For example, in the ATIS domain the verbs &amp;quot;depart&amp;quot; and &amp;quot;originate&amp;quot; have very similar core meanings, yet have semantic roles realized by different prepositions: The flight departs from Boston.</Paragraph>
    <Paragraph position="1"> The flight originates in Boston.</Paragraph>
    <Paragraph position="2"> *The flight departs in Boston.</Paragraph>
    <Paragraph position="3">  The words are not synonyms in the normal sense that one can be substituted for the other in such a way as to preserve grammatieality. But their common semantic content can be represented.</Paragraph>
    <Paragraph position="4"> Another advantage is that a denotational semantics with optionality is implemented without requiring Davidsonian-style event quantifications \[7\]. While event objects make sense in some contexts, having an existontial quantification over events for every verb is frequently inconvienent in further processing. Certainly it is so in the ATIS domain, where the chief semantic outcome of clauses seems to be a set of predications on attributes of flight-individuals and there really are no &amp;quot;events&amp;quot; as such at all. Event quanfifieations are not precluded, however--they could be produced with a different translation rale schema.</Paragraph>
  </Section>
  <Section position="8" start_page="188" end_page="188" type="metho">
    <SectionTitle>
COMPARISON WITH OTHER WORK
</SectionTitle>
    <Paragraph position="0"> Our treatment of the syntactic aspects of subeategofization is most like that of PATR-II \[13\]. Both PATR-II and the mapping units approach use recursive VPs, with each level of VP structure, in effect, &amp;quot;peeling off&amp;quot; a single constituent of the head verb's complement list. 4 A major difference between the two approaches is that the PATR-II system of subcategofization is essentially limited to popping constituents off the subcategorization list, in fixed order, requiring a separate subeategorizatlon list for each variation in order. Our approach allows complements to be found in whatever order the grammar will allow them. In this respect, it is more like the UD system \[8\], which has an operator for &amp;quot;non-deterministic extraction from arbitrary list positions&amp;quot;. 5 However, our system does not literally remove units from the map, but rather simply marks them as no longer available for binding. Moreover, the mechanism of allowing multiple syntactic realizations for a given semantic relation in a single representation of complement structure is, to our knowledge, unique.</Paragraph>
    <Paragraph position="1"> Related work on the semantic aspects of argument optionality has been reported by Palmer \[10\], \[6\]. Our work differs from this mainly in the tighter coupling of syntax and semantics during processing and the use of recursive VP structures, which Potentially allows for an elegant solution of cases of nun-consituent conjunction, not addressed in the other work. Our system also has a finer grained treatment of optionality; whereas \[10\] and \[6\] divide argument roles into OBLIG-ATORY, ESSENTIAL, and NON-ESSENTIAL roles, we provide a richer set of possibilities. The dccoupling of syntactic realizations of a role in a mapping unit from the semantic typing constraints on that role, to allow for different types of metonymie extension is also a distinction. On the other hand, the use of named thematic or semantic roles which cut across particular predicates in \[10\] and \[6\] might provide a more compact form for capturing linguistic generalizations, to the extent that such a theory of thematic relations is well-motivated.</Paragraph>
  </Section>
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