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<Paper uid="J89-3003">
  <Title>NON-SINGULAR CONCEPTS IN NATURAL LANGUAGE DISCOURSE</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
2 COMPUTING INTERSENTENTIAL DEPENDENCIES IN
DISCOURSE
</SectionTitle>
    <Paragraph position="0"> A first step toward automating the process of discourse understanding is to grasp the meaning contents of the discourse message, at least the literal meaning. A discourse normally consists of more than a single utterance, and although every utterance may be assumed to contribul:e something to the discourse meaning as a whole, this latter can only rarely be regarded as a simple sum of meanings of component utterances. Utterances, or sentences, making up a discourse are usually involved in complicated mutual dependencies, that often go beyond the text itself. A careful study of these extrasentential and intersentential dependencies in discourse is necessary before a more successful attempt to design an automated discourse understanding system can be undertaken.</Paragraph>
    <Paragraph position="1"> In Strzalkowski (1986) and Strzalkowski and Cercone (1986) we introduced a rigorous method for handling certain cases of extrasentential dependencies in discourse, within a general framework, which we call the Stratified Model. The Stratified Model comprises a collection of disambiguating transformations that are applied to a discourse fragment before it can be assigned a final representation. These transformations include morphological analysis, lexical disambiguation, syntactic parsing, computing extrasentential dependencies, and pragmatic evaluation in discourse context. In order to compute anaphoric, and other, dependencies between sentences in a discourse fragment, we first translate each sentence in the fragment into an intermediate, formal representation language. We call these translations literal or &amp;quot;context-less&amp;quot; because they are derived based solely on sentences' syntactic structure. In fact, this transformation is done Montague-style (Montague 1974d) except for the intermediate representation, which, in the Stratified Model, is a A-categorial language A, rather than an intensional logic. For this presentation it is enough to say that A is a typed predicate-calculus language: with A-operator. A formal definition of A is given in Strzalkowski and Cercone (1986). Next, we 172 Computational Linguistics, Volume 15, Number 3, September 1989 Tomek Strzalkowski and Nick Cercone Non-Singular Concepts in Natural Language Discourse proceed to compute various contextual dependencies of sentences, including extrasentential anaphoric links.</Paragraph>
    <Paragraph position="2"> Let L be a language of parse structures obtained in some grammar of a fragment of English. For the purpose of this presentation, L is identified with the set of phrase markers that can be generated from English sentences with a categorial grammar CAT similar to that of Montague (1974). Although some other syntactic system may be more suitable in practical application, we select CAT here for its relative simplicity and elegance. We concentrate on the translation of some example expressions, sentences, and paragraphs of L into a representation in a A-categorial language A that would capture both a sentence's logical form and its cohesive links to the surrounding discourse. In particular, we shall look closely at the cohesive links created by inter-sentential anaphoric references appearing in different contextual situations.</Paragraph>
    <Paragraph position="3"> A possesses adequate expressive power to represent the meaning of a considerable spectrum of linguistic constructs found in a natural language discourse. What is of a particular interest to us, A provides a natural and uniform means for computing and representing extra-sentential dependencies. As we shall see in the next section, a meaning representation language so-defined is still inadequate for capturing some more difficult cases, which we call remote co-references.</Paragraph>
    <Paragraph position="4"> Our present effort is to describe a transformation ISD such that ISD _C L x A, and whenever a source expression in L consists of more than one sentence, a class of intersentential dependencies within this fragment is identified and resolved, if possible. It must be noted here that ISD represents a semantic process that is entirely independent, of any pragmatic or domain related factors. As a result a substantial amount of domain oriented ambiguity may be left unresolved. In any practical application, this transformation must be accompanied by a pragmatic process, as described in Strzalkowski (1986). ISD consists of a collection of translation rules {R1, R2 .... }, such that each rule is responsible for translating a specific type of dependency. Actually, only Rule 1 works directly on expressions of L, translating them into literal representations in A, independent of one another. Rules numbered 2 and up will take these literal translations and try to relate them pairwise looking, among other things, for unresolved anaphoric references. Most of these rules can be written in terms of two distinguished expressions of A, S 1 and S 2, which we call the context-setting sentence and the current sentence, respectively. Expression S 1 is a A-representation of the linguistic context in which the sentence with translation S 2 is to be evaluated. Neither $1 nor S 2 must correspond to surface sentences, though.</Paragraph>
    <Paragraph position="5"> S~ may represent a larger part of discourse, perhaps an entire paragraph; on the other hand, S 2 may constitute only a subclause of S l in which case we would talk of intra-sentential dependency. It should be noted here that the potentially explosive number of possibilities will be in fact limited by the actual structure of the discourse under consideration (see, among others, Grosz and Sidner 1985), as well as by the pragmatic and domain related information, not discussed here.</Paragraph>
    <Paragraph position="6"> Let us now consider a two sentence paragraph given below: $1: John interviewed a candidate.</Paragraph>
    <Paragraph position="7"> $2: The guy had impressive references.</Paragraph>
    <Paragraph position="8"> In the most natural reading of this paragraph, the anaphor of &amp;quot;the guy&amp;quot; is resolved against &amp;quot;a candidate&amp;quot; in the first sentence, so that the second sentence actually means: &amp;quot;the guy whom John interviewed had impressive references.&amp;quot; When considered separately from one another, $1 and S 2 obtain the following translations into A.</Paragraph>
    <Paragraph position="10"> In the translation of S 2, C is a free predicate variable that needs to be bound by the sentence's context. The context variable is introduced into the translation of a definite noun phrase containing a definite article, such as &amp;quot;the,&amp;quot; by Rule 1 (Strzalkowski 1986, Strzalkowski and Cercone 1986). This rule generates literal translations of sentences without considering their context, and does so in PTQ-style, that is, by assigning to each syntactic operation in CAT a formula formatting operation in A (Montague 1974a). The next step is to resolve context references; we must find a binding for C occurring in S 2 in the context provided by $1 in order to obtain the final translation of the former. This intersentential dependency is captured by the translation Rule 2, which operates on the literal translations of both sentences delivered by Rule 1 (Strzalkowski and Cercone 1986). In the example above, the second sentence obtains the desired translation as shown below.</Paragraph>
    <Paragraph position="12"> If the context-setting sentence S 1 has a referential interpretation in the form</Paragraph>
    <Paragraph position="14"> and the current sentence S 2 contains an unresolved definite anaphor, that is,</Paragraph>
    <Paragraph position="16"> then this anaphor can be resolved against S~, and the resulting translation of S 2 is obtained as AC\[S2\](Au\[P(u) &amp; F(u)\]).</Paragraph>
    <Paragraph position="17"> A somewhat different problem arises when we consider a fragment with a possible non-referential interpretation, as in</Paragraph>
    <Paragraph position="19"> Computational Linguistics, Volume 15, Number 3, September 1989 Tomek Strzalkowski and Nick Cercone Nou-Singular Concepts in Natural Language Discourse John wants to marry a princess. The girl must be rich and pretty.</Paragraph>
    <Paragraph position="20"> Now, Rule 2 can compute the anaphoric link between &amp;quot;the girl&amp;quot; and &amp;quot;a princess&amp;quot; only if both sentences receive their referential interpretations. In a case where both sentences are understood non-referentially, we have to use Rule 3, given below. No other combinations are possible.</Paragraph>
    <Paragraph position="21"> Rule 3 (Imperfect-Context Translation Rule): If the context-setting sentence S I has a non-referential interpretation in the form imp (3u \[P(u) &amp; F(u)\]), where imp is an imperfect operator, and the current sentence S 2, also in a non-referential interpretation, contains a definite anaphor which occurs in scope of an imperfect operator imp1 i.e.,</Paragraph>
    <Paragraph position="23"> then this anaphor can be resolved against St, with the resulting translation of S e derived as AC\[S2\](Au\[P(u ) &amp; F(u)\]).</Paragraph>
    <Paragraph position="24"> Rule 3 encompasses a large class of non-referential contexts, which we call imperfect contexts, and which involve constructs including propositional attitudes (want, try, wish), intensional verbs (seek, conceive, think about), other complement-taking verbs (go, come), modal verbs (must, can, will), as well as progressive tense forms. In Rule 3, all this is reduced to the formula with the imp operator which translates compound phrases, such as &amp;quot;John wants,&amp;quot; or &amp;quot;John will.&amp;quot; Thus, in the example given above, Rule 3 is applicable when both sentences contain a wide scope imp operator. In this case, the second sentence of the fragment obtains the full translation with the following formula:</Paragraph>
    <Paragraph position="26"> Other studied cases of intersentential anaphora (see Strzalkowski 1986a-c, Strzalkowski and Cercone 1986) include non-referential interpretation of discourse fragments involving attitude report verbs (believe, know, disagree). These cannot be translated with Rule 3, and a new rule, Rule 4, is developed to compute anaphoric links in texts similar to the one given below.</Paragraph>
    <Paragraph position="27"> John believes that a unicorn lives in the park.</Paragraph>
    <Paragraph position="28"> He thinks the creature has a long horn.</Paragraph>
    <Paragraph position="29"> Rules 5, 6, and 7 account for the pronominal anaphora, Rule 10 deals with certain instances of attributive use of definite noun phrases. Rules 8 and 9 are used when the antecedent of an anaphor is a proper name rather than a description. This is the situation where an interesting type of referential ambiguity occurs whose resolution may have far reaching consequences on the process of discourse understanding.</Paragraph>
    <Paragraph position="30"> Rule 9 (Names as Ultimate Referents): If the context-setting sentence S 1 has the form of FI(N) where N is an individual constant denoting a name, and the current sentence S 2 contains a definite anaphor, so that its literal translation has the form</Paragraph>
    <Paragraph position="32"> then the anaphor can be resolved against N as its ultimate referent with the following derivation: xplp( N) \]( Xx\[ :tC\[ S2\]( Xs\[ R(s) \]) \]) where \]V is the predicative use of name N.</Paragraph>
    <Paragraph position="33"> In the following fragment, Sylvester tries to catch a bird. The cat is clumsy. there are two possible ways of linking &amp;quot;the cat&amp;quot; with &amp;quot;Sylvester.&amp;quot; In one reading, not very different from those processed with Rule 2, the definite anaphor refers primarily to the entity that can be described as &amp;quot;the one who tries to catch a bird,&amp;quot; and only contingently to its name. In this case we acquire some new information about Sylvester, namely that it is a cat. In the other possible reading, the anaphor refers to the name only, and thu,; may draw on some context that is different from the first sentence in the fragment. This latter situation is handled by Rule 9. In the above fragment, Rule 9 would produce the following translation for &amp;quot;the cat is clumsy&amp;quot; (S is an individual constant denoting the individual named Sylvester, and Syl(x) means that x's</Paragraph>
    <Paragraph position="35"> Syl(x)} 3 (x=S)\] There are more aspects of ISD transformation that merit attention. These include rules for dealing with other kinds of anaphora not discussed here, elliptical constructions, enumerably singular (plural) terms, intrasentential anaphora, and non-anaphoric dependencies, as well as indirect and forward reference cases where access to the speaker/hearer knowledge base may be required. We also have to deal with the changing reference level.</Paragraph>
  </Section>
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