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<Paper uid="C94-2137">
  <Title>Fr6d~rique Segond</Title>
  <Section position="2" start_page="853" end_page="854" type="metho">
    <SectionTitle>
2. Long-Distance Dependencies in CCG
</SectionTitle>
    <Paragraph position="0"> Consider, for example, the phrase Apples which Harry eats. This phrase contains three sets of binary dependences: 1) apples-eats, 2) which-eats, and 3) Harry-eats.</Paragraph>
    <Paragraph position="1"> The first two sets consist of discontinuous constituents.</Paragraph>
    <Paragraph position="2"> This is ml iastauce of file phenomenon called intersecting dependencies. Intersecting dependencies arise when one set of discontinuous constituents is intercalated by another set of discontinuous constituents in the surface expression. To find au adequate formed characterization of discontinuous constituents and intersecting dependencies is one of the cenla~d problems for categorial gr,'umnar, as lbr auy linguistic theory timt is concerned with linear representation of expressions. This problem induced some linguists to introduce new rules extending the tbnnalism of categori~d gramm~u'. Sleedman's Combiuatory Categorial Grammar (CCG) proposes file following ,-malysis of the phrase Apples which Harty eats (1987:415; presented hcrc in the AUG notation):  In (15), subject type raising (assigning OOtss to Harry) in coujuuction with composition is used to resolve tile difficulty caused by gapping involved ill the extraction of the direct object of the finite verb eats.</Paragraph>
    <Paragraph position="3"> Forward and backward composition ,are dclined as follows (ill terms of AUG): Under the rule of &amp;quot;compose forward&amp;quot;, A of type Oxy and B of type Oyz combine to yield the result (AB) of type Oxz. Under the rule of &amp;quot;compose backward&amp;quot;, A of type Oyz aud B of type Oxy comhinc to yield the result (AB) of type Oxz. (16) Type rai~ing is defiue(l as ,'m operation whereby an oper,'rod acquires a new type that turus it into ,'m operator over its operator. The general rule of type raising in tile AUG notation is:</Paragraph>
    <Paragraph position="5"> For exmnple, subject type raising is delined in lerms of AUG as follows: Subject type raising is a proccss by which a subject of type t acquires the type OOtss, which turns it into an opcmtor over the predicate (51 type Ots. (l 8) As ,'mothcr examplc of the ~m;dysis Ihat uses type raising, let us eonsidcr the scntcnce John loves Mary wiMly and Sue madly (Bouma, 1989: 25). Using typc raising and compositiou, the analysis of this sentence can be presenlcd as follows in |he AI. IG notation: John loves Mary wiMly and Sue nuMly</Paragraph>
    <Paragraph position="7"> in (19), to resolve the difficulty caused by gapping involved in the coordination operation, object type raisiug is used (assigning OP2Pl to Mary and Sue) ahmg with composition.</Paragraph>
    <Paragraph position="8"> l)oes lhe CCG machinery produce adequate syntactic and semaulic represenlations of the stn~cturc of a sentence? What is the semantic interpretation (51 type raising? It is ckfimed lhat Ilm nominative case moq)hology in laliguages like 1 ,atin delermines a noun-phrase argument like Balbus to be something that must combine with a predicate (Steedman, 1990: 22l). But case endings ~e not reliablc criteria for detc,'mining facts of syntax and selnalllics, lit Russiml and lnally oilier languages thc lIOlllinativc h~Ls no cndings. Scmantic~dly, predicate + subject is an attributivc conncclion just as adjectival modiJier + subject, lY=cdieate and a((jcctival modificr arc determining members, and sul)jcct is thcir determined member. Accordingly, wc get tile prolx)rtion: predicate : subject = adjectival modifier : subject (20) This means that if the synlactic categorial system is to confi)rm to the semantic catego,'ial system, predicates must be operators over subjects just as adjee|ives. Type raising transforming sut)jeets inlo operators over predicates conllicts with the scmmllie categorial system.</Paragraph>
    <Paragraph position="9"> Furthermore, if in (19) we have a correct analysis of e(~)rdination, we should bc able to deduce the two interpretations of the scntence John loves Mary wildly and Sue madly: &amp;quot;John loves Mary wildly, aud John loves Sue madly&amp;quot; mid &amp;quot;John loves Mmy wildly, and Sue loves M,-u'y madly.&amp;quot; This is a classic case of mnbiguity with co(n'dina~ tion (we do not know if the second conjunct is subject or object). Unfortunately CCG fails to distinguish I)ctween thc two interpretations.</Paragraph>
    <Paragraph position="10"> The other well-known prot)lem with type raising is spurious ambiguity. Spurious mnbiguity is multiple mmlyses of one sentence, Idl o1' them related to file s~unc seinautic interpretation. For instance, just by using subject and ol~icct type raising one obtains four different analyses ti)r a simple sentence: John loves Mary</Paragraph>
    <Paragraph position="12"> These lour a\[mlyses arc associated with just one motoring: ((loves Mary) John).</Paragraph>
    <Paragraph position="13"> There m'e other difficulties with type raising. We see that in (19) (Mary wildly) and (Sue madly) m'e assigned type OP2Pl, which is associated with the accusative luucli(nL It is very dillicult to accept that (Mary wildly) or (Sue madly) are direct objects of low', or that they arc at all colnpatitsle. The correct analysis is: the adverbs wildly and mad@ me modifiers of the verb love, ,'rod the nouns Mary and Sue are direct objects of the verb love. (Mary wildly) and (Sue madly) arc phantom coustituenls Ihat (1o IIO1 correspoll(l I(1 ~uly synlaetic or SeluaulJc reality.</Paragraph>
    <Paragraph position="14"> Type raising corresponds to Ihe coml)inator C. and composithm correspond to combinator B. Both m'c powerful tools when properly used. One of tim conditions of Ilmir l)rope r use is respect for constituency. A(1G uses these combinators widely when their usc is justified.</Paragraph>
    <Paragraph position="15"> The main sin oi' CC(; is that it fails to recognize Ilmt synlaclic al|d semantic connections are non-associative. CC(; bmls liom linguistics Ilm norm~d non-~tssocialive constituency mmlysis based on the explicit or implicit rccognilion of the hierarchy of relative syntactic m~d semmdic clo~-IleSS of cOnlleCliOllS betwecll inunediate conslituents of a sentence.</Paragraph>
  </Section>
  <Section position="3" start_page="854" end_page="854" type="metho">
    <SectionTitle>
3. The AUG Theory of Type Superposition
</SectionTitle>
    <Paragraph position="0"> An altcrnativc method of parsing gapping consmlcthms is based on Ihc Thcory of Typc Superpositi(m. &amp;quot;1o explain our new method, wc need to outline this theory briclly.</Paragraph>
    <Paragraph position="1"> ( ;iron a synlactic unit, a secondary syntaclic type may bc supelposed on its inhercnl, primaxy syntactic tylx: so as to form a new bislralal, syncretic type. For exmnple, when the suflix -ing is used to change Ihe linite form of Ilm verb to itlslruct into a verbal noun- -the so-called gerundinstructing, wc have a ease of the supcrposition of type t on type OtOts. Thc verNd noun retains thc synlaetie rimelion of Ihe verb to inslruct: it can lake an ot'dcct in the accusative (on instructing him) and an adverb (He suggested our immediately instructing them). The s~unc is line of Ihe I~nglish or French inlinilives: they behave both like verbs and nouns. For exmnplc, ill tile Frellch senl~llec Life des livres est divertissant or in the English scntence &amp;quot;lb read books isfim the infinitivcs lake direct objccts likc finite verbs and simultaneously are subjects like nouns.</Paragraph>
    <Paragraph position="2"> The suflix -ing (or any olher similar device) we call a  superposer, and the finite form of the verb to instruct with respect to the suffix -ing we call the superponend of -ing.</Paragraph>
    <Paragraph position="3"> The suffix -ing superposes the syntactic type t on the syntactic type OtOts of the verb to instruct so as to combine them into a new syncretic syntactic type.</Paragraph>
    <Paragraph position="4"> We can formalize the notion ofsuperposition ,as follows: Let E be an expression of type x, and let E take on type y on type x. Then E shall be said to belong to type z such that z is stratified into y superposed onto x.</Paragraph>
    <Paragraph position="5"> Type z is represented by the formula:</Paragraph>
    <Paragraph position="7"> where the colon C) indicates the stratification of type z into y superposed on x enclosed into angle brackets. The right part of the formula indicates the primary type of E, and its left part indicates the secondary type of E.</Paragraph>
    <Paragraph position="8">  linguistic theory mid computational linguistics, the discussion of which is beyond the scope of the present paper. We will only focus on the topic of our paper--long-distance dependences. For the lack of space we must confine ourselves to some examples of our approach that conceru topicalization, relative clauses, and gapping (a detailed presentation of the theory of type superposition is given in Shaumyan and Segond, 1993).</Paragraph>
  </Section>
  <Section position="4" start_page="854" end_page="856" type="metho">
    <SectionTitle>
4. Long-Distance Dependencies in AUG
</SectionTitle>
    <Paragraph position="0"> We propose a new approach to parsing gapping sentences that allows us to dispense with the concept of type raising. AUG claims that gapping superposes secondary types on primary types of the adjacent syutactic units of a sentence, thereby establishing new relations betwecn them on top of the old ones preserved in superposition.</Paragraph>
    <Paragraph position="1"> Here is the AUG alternative analysis of the phrase in (15):  Under the characterization of superposition in the foregoing section, the obligatory absence of the adjacent direct object in apples which Harry eats is a contextual operator superposing type Ots on type OtOts of eats. Thc superposition yields the same result as the hypothetical application of eats to its absent direct object. That is, the secondary type of eats is equivalent to the type of the hypothetical combination eats' + direct object. Then, the application of eats to Harry results in Harry eats of type s. Following Benveniste's analysis of relative pronouns (1966: 208-224), we consider them operators having variable operands; hence, type OxOtt is assigned to which.</Paragraph>
    <Paragraph position="2"> Type superposition is a strictly fonn,-d concept reflecting observable formal processes of language. There are observable strictly formal criteria for defining superposition. A derived syntactic unit with a syncretic type is always more complex than the initial one; it consists of two parts: initial syntactic unit + superposer. So read-ing, where -ing is a superposcr, is more complex than read.</Paragraph>
    <Paragraph position="3"> But where are formal markers of superposition in (25)? The answer is that superposers, as all other language items, ,are signs, and a sign is not necessarily a sequence of sounds. It may be a change of stress, an alternation, a change of word order, a change of grammatical context, etc. (ShaumymL 1987: 3-5). In (25) the syntactic configuration of the phrase apples which Harry eats contains observable contextual signs of superposition. To do justice to this fact we have to use an adequate formalism.</Paragraph>
    <Paragraph position="4"> AUG includes two principles to describe superposition: the Principle of Elimination of Empty Constituents and the Principle of Syntactic Assimilation.</Paragraph>
    <Paragraph position="5"> Principle of Elimination of Empty Constituents': Given a syntactic group of an operator A of type Oxy and its operand B of type x, either A or B may be empty: 1) if B is empty, empty B serves as a contextual sign superposiug type y on type Oxy of A, so that A is assigned the syncretic type &lt;y:Oxy~; and 2) ifA is empty, empty A serves as a contextual sign superposing type y on type x of B, so that B is assigned the syncretic type &lt;y:x~. (26) The Principle of the Elimination of Empty Constituents eharactcrizes natural syntactic connectivity. When in the group operator:operand file empty operand is eliminated, the operator represents the whole group and is assigned the type of the whole group. Conversely, when in the group operator:operand the empty operator is eliminated, the operand represents the whole group and is assigncd thc type of the whole group.</Paragraph>
    <Paragraph position="6"> Lct us turn to the senteuce John loves Mary wildly and Sue madly in (19). As was said above, this sentence is ,'unbiguous: Sue may bc a subject or ,an object. A correct syntactic analysis of this sentence must reflect this semantic ambiguity. Dcpending on two possible iutcrpretations of this sentence, we discover two different gappings here: &amp;quot;John loves Mary wildly, and \[loves\] Sue madly&amp;quot; and &amp;quot;John loves Mary wildly, and Sue \[loves Mary\] madly&amp;quot;. In the light of the lhiuciple of Elimination of Empty Constituents, AUG proposes the following two mmlyses of the sentence to reflect two different gappings:  Given two phrases A and B belonging to types incompatible under the Rule of Phrase Application, one of these phrases can change its type by superposition so that the types of the two phrases become compatible, if tile relation A:B is analogous to some relation X:Y between phrases of compatible types. (29) Consider the sentence Apples Harry eats. qtfis sentence is an exmnple of long-distance dependency because the sub-ject intervenes between the direct object and the predicate. ! Iere is tile AUG analysis:  We observe that in (30) Apples is the topic and Harry eats is tile comment. Since the proportion topic : comment = subject : predicate holds, type Ots is supcrposed on type s of ttarry eats.</Paragraph>
    <Paragraph position="7"> The Principle of Syntactic Assimilation is completely general: it concerns both long-distance and immediate dependencies. Consider the phrase gold watch. Both words have type t. Therefore, they belong to incompatible types. But since the proportion gold : watch = goMen : watch holds, type Ott is superposed on type t of goM.</Paragraph>
    <Paragraph position="8"> The phenomenon of superposition must not be coufused with polymorphism. Polymorphism is a situation when a word is assigned several types, having equal syntactic weight. For example, an English adverb can be assigned at least three types having equal syntactic weight: OPlPl , Op2P2 or OP.~3, depending whether it modifies an intransitive, transitive or ditransitive verb. Iiere we have an equality between the types. But in the above example the noun gold remains a noun even though it modifies another noun. To describe polymorphism in a compact way, Fr6d6rique Segond has introduced the concept of type variable. &amp;quot;Ilms, the above and other types that can be assigned to an adverb are coded by the formula Oxx (Segond, 1990a: 131-132). Other cases of polymorphism are exhibited by the conjunction and, which can combine two sentences, two nouns or any units belonging to identical types; ~md by the relative pronoun which of type OxOtt, mentioned in (25). Depending on different cases of polymorphism, we introduce various type variables.</Paragraph>
  </Section>
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