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<Paper uid="C90-2025">
  <Title>Funetor-Driven Natural Language Generation with Categorial-Unification Grammars</Title>
  <Section position="2" start_page="0" end_page="0" type="metho">
    <SectionTitle>
2. The Grammar Formalism: Catego-
</SectionTitle>
    <Paragraph position="0"> rim Unification Grammar The grammatical formalism that we adopt for categorial unification grammar is similar to that proposed in Uszkoreit (1986). Following the schema for syntactic rules developed for PATR-style grammars, we formulate the ca tegorial grammar rule of functional application by the rule schema in fig. 1. The  zl node (i.e. the node at the end of the path (zl}) represents a functor category that combines with an argument at x2 to yield as a result the category at x0. The rule also specifies that the semantic translation (trans) of the result category x0 is inherited from the functor xl. As is characteristic of categorial grammars, our syntactic rules are highly schematic, with most of the grammatical information encoded in the categorial lexicon. For example, constraints on word order are encoded in lexical representations of functor categories, rather than in the syntactic rules themselves. To this end we adopt an attribute phon (for: phonology) which is used to encode linear order for syntactic strings. The values for p~taon are structured as difference lists. The use of this data structure, inherited from PROLOG, allows us to concatenate functor categories with their arguments either to the left or to the right. It also allows us to state syntactic rules without having to make reference to constituent order.* The graphs in fig. 2 display partial lexical entries for the intransitive verb smiles, 1In this respect, our representation is more compact than other categorial-unitlcation grammar formalisms which state order constraints in the categorial lexicon and in each syntactic rule. In particular, we don't need to distinguish between forward application and backward application</Paragraph>
    <Paragraph position="2"> for the proper name Tom and for the sentence Tom smiles. The phon attribute for argument categories such as proper names is encoded as a singleton list which contains the argument string in question, e.g.</Paragraph>
    <Paragraph position="3"> Tom. The phon attribute for functor categories is designed to combine the string for the functor category with the phon feature structure of its argument categories. In the case of the intransitive verb smiles, the morpheme smiles appears as the first element in a list that is appended to the difference list for its subject argument. When the phonology attributes for Ibm and smiles are combined by function application, the resulting sentence exhibits the correct word order, as fig. 2c shows. For the sake of con&gt; pleteness, we also include the representation of the preposition from as an example of a forward functor in fig. 2d.</Paragraph>
    <Paragraph position="4"> For the remainder of this paper we will concentrate on the interplay between syntax and semantics for the purposes of language generation. We will assume that information about word order propagates from the lexicon in the manner we just outlined by example.</Paragraph>
  </Section>
  <Section position="3" start_page="0" end_page="0" type="metho">
    <SectionTitle>
3. Natural Language Generation with
Categorial-Unification Grammars
</SectionTitle>
    <Paragraph position="0"> In this section we describe our functor-driven approach to natural language generation which pairs logical forms (represented in first-order predicate logic) with syntactically well-formed expressions of English. For example, given a first-order fornmla such as</Paragraph>
    <Paragraph position="2"> we want to generate a sentence such as Everyone smiles.</Paragraph>
    <Paragraph position="3"> Ill order to produce the appropriate sentence, the generator is supplied with a start Dag as in fig. 3.  The first order formula (1) is represented in fig. 3 under the attribute trans (for: logical form translation). The value for the attribute cat specifies that the translation corresponds to a syntactic expression of category s (for: sentence). Unlike functional categories which take other syntactic categories as arguments, s is a basic category, i.e. a category which does not take an argument.</Paragraph>
    <Paragraph position="4"> The task of the generator is to further instantiate start Dags such as that in fig. 3 so that appropriate syntactic expressions are generated in the most efficient manner possible.</Paragraph>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
3.1 A Functor-Driven Generation Algorithm
</SectionTitle>
      <Paragraph position="0"> One advantage of the use of categorial grammars is that efficient generation can be effected by a completely general principle: at each step in the derivation of a syntactic expression, constituents tha.t correspond to functor categories are to be generated before the generation of constituents that correspond to the functor's argument categories. The strategy underlying this principle is that in any grammatical construction, functor categories always provide more syntactic and semantic information than any of the argument categories. By generating the fnnctor cat- null .::gory first, the choice of argnmenI~ categories will be :~e.verely con~-trained, which sigJ:ificantly prunes the ;;earch space in whieh the algorithm has t.o operate.</Paragraph>
      <Paragraph position="1"> We will illustrate our approach by discussing the funetor-driven order of processing for the generation of the sentence Ever'gone &lt;&lt;-rsz'i, les. First the generator will make a top-down prediction by unifying the e.',bart Dag in fig..3 with the m0 node of the functional ;xpplication rule shown in fig. 1. The resulting Dag is shown in fig. 4.</Paragraph>
      <Paragraph position="2"> The predicted Dag in fig. 4 then becomes sub.}eel; to the principle of generating functor categories !'h-st. Identification of a functor eategory in a rule of categoriab.unitication grammar is straightforward: Ihe functor category is represented by the subdag whose wflue for the attribute c~tt is a Dag with ato i;,'ibut.es art and reszUt a.nd whose 'ce.~zlt are is reen!rant with the value of the subdag rooted in ):0.</Paragraph>
      <Paragraph position="3"> Thus, in the case of fig. 4, the functor category is zl. 2 At this point there is enough information on the zl node to uniquely det, ermine the choice of a functor category, whereas the choice of an argument category would be eompletciy unconst.raired. When the !exical entry for eve,&amp;quot;;t/cne (fig. 5a.) unifies with the a:l node, the result is the Dag in fig. oh. ~ Then, at this point, the z2 node is fully enough instantiated to uniquely determine the choice of .~miles (fig. 5e) hom the lexicon.</Paragraph>
    </Section>
    <Section position="2" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
3.2 Non-minimally Type Raised Functors
</SectionTitle>
      <Paragraph position="0"> Now consider w\]',at, happens when non-quantified NPs like To~Tz are type-raised as in ~'\[ontague (1974).</Paragraph>
      <Paragraph position="1"> That is, suppose that the lexical entry for Torn is the Dag ill fig. 6a rather than the lower type in fig. 6b.</Paragraph>
      <Paragraph position="2"> It turns out that if the type raised NP is used, it will not be possible to constrain the choice of funcfor in generation. For example, fig. 7a shows the rule of flmction application (fig. 1) in which the z0 node has been unified with a start \])ag appropriate.</Paragraph>
      <Paragraph position="3"> to generate Tom ~miles. In fig. 7b, the zl node has unified with a type-raised entry for Hatred, show-.</Paragraph>
      <Paragraph position="4"> ing that the start Dag has done nothing to constrain the choice of functor. Thus, apart fl-om introducing spurious ambiguity into the grammar (see Wittenburg 1987 for detailed discussion), the operation of type-raising, when used unconstrained, can also lead to considerable inefficiency in generation. In order 2Alternatively, one could could simply take C/1. to always be the functor since, given our use of the phon attribute, the order of xl and x2 no longer corresponds to linear order.</Paragraph>
      <Paragraph position="5"> aA problem that arises here is that the ~1 node in fig. 4 will also unify with the lexieal entry for s~r~iles (fig. 5c) giving a nonsensical translation. Clearly, what needs to be done is to modify the semantic representations so that quantified expressions will not unify with non-quantified expressions. One line that could be investigated would be to have a type system which distinguishes quantified and non-quantified signs as in</Paragraph>
      <Paragraph position="7"> to constrain rite use of type-raising, we adopt the principle of minimal type a.,sigament suggesl;ed on independent grounds by Partee and Rooth (1(.)83).</Paragraph>
      <Paragraph position="8"> Part:ee and Rooth argued for t, he principle of minireal type assigament, tto account fox&amp;quot; seopal properties of NPs in a variety of coordinate structures. Among the examples they discuss is tthe contrast between sentences sud~ as (2) a,,d (3).</Paragraph>
      <Paragraph position="9">  (2) Every student failed or got' a D.</Paragraph>
      <Paragraph position="10"> (3) Every student failed or every student got a D. (2) and (3) have different truth  true if some students failed and while others got a D and did not would be false in that situat,ion.</Paragraph>
      <Paragraph position="11"> point out that appropriate truth conditions. (2) is did not get a D, fail. (3), however,  can only obtained if intransitive verbs are given a non-Wpe-raised intterpretation and if their conjunction is represented by the k-abstract in (4). When (4) is combined with the translation for every student, the desired reduced formula in (5) is obtained. (4:) Aa\[fail'(a:)V goLa_D'(z)\] (5) Vm\[student'(z) .... \[failed'(ac) v got,_~LD'(~;)\]l  The use of conjoined type-raised predicates as in (6), however, would incorrectly yield the formula in (7), which is appropriate for (3) but not for (2).</Paragraph>
      <Paragraph position="13"> On the other hand, Partee and Rooth point' out that for the interprc't,ation of senttences such as (8): intransitive verbs do ha.ve to be Wpe-raised, since (9)  is a paraphrase of (8).</Paragraph>
      <Paragraph position="14"> (8) A tropical storm was expected to form off t.lle coast of Florida and did form there within a few days of the forecast.</Paragraph>
      <Paragraph position="15"> (9) A tropical st'orm was expected to form off the  cc, ast of Florida and A tropical storm did form there within a few day's of the forecast'. In order to reconcile this conflict, Partee and Rooth propose that extensionM intransitive verbs such as formed should be assigned t,o the lowest possible type and be type-raised only when t,hey are conjoined with an intensional verb such as be ezpected. Given the principle of minimal type assignment, the entry for smile3 fig. 5c will now be the main functor in generating the sentence To~n s~..iles. It. can be seen that smiles (and no other non-type-raised cat.egory) will unify with the zl node of fig. 7a. The resulting prediction is shown in fig. 7c. At this point the x2 node is constrained to unify with the minimal, non-type-raised entry fox: Torn (fig. 6by. Thus, the principle of minimal type assignment turns out to be crucial tor constructing efficient generation algorithms for categorial-unification grammars.</Paragraph>
    </Section>
    <Section position="3" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
3.,3 Allowing Type-Raising as Needed
</SectionTitle>
      <Paragraph position="0"> As seen in the previous section, efficient generation requires the use of basic (non-type-raised) NPs, whenever possible. However, this is not' t,o suggest'  that the operation of type-raising can be eliminated from the grammar altogether. For example, t,yperaising needs to apply in the case of conjoined NP's such as Tom and every boy. If we assume, as in Wittenburg (1986), that and is assigned the category in (10), 4 then to parse or generate a conjoined NP like Tom and every boy the category for Torn will have to be raised so that its type will match that of every boy.</Paragraph>
      <Paragraph position="1"> (10) (XIX)iX What is needed then is sonle operation that will convert the non-type-raised entry for \[/bm in fig. 6b to its raised counterpart in fig. 6a. One way of incorporating the necessary operation into the grammar would be via the type-raising rule in fig. 8a, in which the non-type-raised entry unifies with the xl node to yield the type-raised result at z0 '5 ttowever, the problem with the rule in fig. 8a is that it will allow type-raising not just as needed but also anywhere else. So the problem of spurious predictions like that. in fig. 7b reemerges.</Paragraph>
      <Paragraph position="2"> Clearly, what is needed is some way of allowing type-raising only in those cases where it is needed. Partee and Rooth suggest that type raising should be constrained by some kind of processing strategy, 6 withou~ indicating how such a processing strategy 4We use a non-directional calculus here, since word order is encoded into lexical items. The domain is to the right of tt~e bar and the range is to the left. The capital Xs represent a variable over categories. This is just a schematic representation of a considerably more complicated category. SNote again thai., since phonology is encoded into lexical items, we can get by with a single rule of type-raising whereas most formalisms would require two. The phonological counterpart of type-raising would be: * 4/ ~Partee and Rooth were actually more interested in psyeholinguisC/ic processing strategies. Still their ideas carry over straightforwardly to computational linguistics.</Paragraph>
      <Paragraph position="3"> can be implemented. It turns out that the processing strategy that Partee and Rooth suggest can be stated declarativcly as part of the grammar, if the operation of type-raising is incorporated into a supercombinator (in the sense of Wittenburg 1987,89) that combines type-raising and functional application into a single operation.</Paragraph>
      <Paragraph position="4"> Wittenburg himself was interested in constraining type-raising in order to eliminate the spurious ambiguity problem of eombinatory categorial grammars.</Paragraph>
      <Paragraph position="5"> He noted that in some of Steedman's (1985,1988) grammars type-raising was needed just in those cases where an NP needed to compose with an adjacent functor, tie, therefore, proposed that the type-raising rule be included into the function composition rule. The use of type-raising in coordinate structures that we have considered in this paper, is quite similar: We want type-raising to be licensed, just in case an NP is adjacent to a funetor that is locking for a type-raised argument. We, therefore, incorporate type-raising into the function application rule as seen in fig. 8b. Now, the old type-raising rule in fig. 8a is no longer needed, and spurious type-raising will no longer be a problem.</Paragraph>
      <Paragraph position="6"> The type-raising supereombinator schema in fig. 8b is, for example, used in the generation of cool dinate structures such as Tom and every boy. Space will not allow us to fully present an analysis of such an NP here, but. the important point is that a non-type-raised lexical entry such as that in fig. 6b will be able to unify with the x2 node, and when it. does so, the subdag at the end of the path (zl cat art) will become identical to the type-raised entry for Tom in fig. 6a.</Paragraph>
    </Section>
  </Section>
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