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<Paper uid="C86-1156">
  <Title>Discourse, anaphora and parsing</Title>
  <Section position="4" start_page="670" end_page="672" type="metho">
    <SectionTitle>
3. Discourse Representation Theory
</SectionTitle>
    <Paragraph position="0"> The naive model presented in the last section ignored all syntactic and lexical interactions with the &amp;quot;left-to-right&amp;quot; nature of anaphoric dependency. The fatal flaw of this account is that is fails to explain the anaphoric propeties of universally quantified NPs. The data which shows this is well known, and some illustrative cases are given in (5) to (7).</Paragraph>
    <Paragraph position="1">  (5) a. A woman i went home. She. was tired 1 b. Every woman i went home. She i was tired.</Paragraph>
    <Paragraph position="2"> (6) a. Every man i thought he i was ill.</Paragraph>
    <Paragraph position="3"> b. Lee gave every woman i her t prize.</Paragraph>
    <Paragraph position="4"> (7) a. Every man saw a woman t. She i was going home.</Paragraph>
    <Paragraph position="5"> b. Every woman who klssed a man I loved him 1.</Paragraph>
    <Paragraph position="6"> (5) shows that a universal NP does not normally act as an  antecedent for pronouns in a following sentence. 4 According to the variable-binding paradigm of anaphora, this follows because a universal can only enter into an anaphorie relation with pronouns that are in its scope. For our current purposes, it is not important whether scope is determined in terms of a tree-geometrical notion like e-command (Reinhart 1983), or in terms of function-argument structure, as proposed by (Ladusaw 1980) and (Bach and Partee 1980); in either case, it is clear that the scope of the universal in (5) is that portion of the first sentence that we have italicised. Examples (6) illustrate cases where a universal does enter into an anaphoric relation with a pronoun in its scope (again indicated by italieisation). (7) is intended to indicate the interaction between indefinites and universals. In (7a), the indefinite has narrower scope than the universal, and it is thereby incapable of acting as an antecedent for a pronoun such as the following she which is outsid the scope of the universal. By contrast, when both the indefinite and the pronoun fall within the scope of a universal, as in (7b), an anaphorie link is permissible. Note that (7b) is a so-called 'donkey' sentence.</Paragraph>
    <Paragraph position="7"> The study of these syntactic and lexieal effects has been a central theme of modern theoretical linguistics, but most work within this paradigm has concentrated almost exclusively on intra-sentential anaphora. However, recently (Kamp 1981), (Helm 1982) and (Haik 1984) have developed theories capable of providing a unified account of the main properties of intraand inter-sentential anaphora. We will base our account on Kamp's Discourse Representation Theory, and in this section, we briefly outline those aspects of Kemp's model which are of most relevance to us.</Paragraph>
    <Paragraph position="8"> DRT is intended to explicitly capture the distinctions in anaphoric potential exhibited by (ga) and (gb), while simultaneously providing a basis for truth-conditional semantic interpretation. Thus (ga) would be associated with a DRS of the form  4 Sentences like (i) are exceptions to this generalization: (i) Every man will like this car. He'll certainly want to drive it.</Paragraph>
    <Paragraph position="9">  Rather than abandoning the generalization altogether, it seems more fruitful to adopt the hypothesis that such discourses involve 'modal subordination' (Roberts 1986) of the second sentence to the first. However, we do not understand the precise mechanics of this process.</Paragraph>
    <Paragraph position="10"> A discourse representation has two parts: a 'universe' consisting of set of discourse markers (in this case a singleton set) and set of conditions. The sentenee A woman went home licences the introduction of the reference marker f into the universe of the DRS, and this marker is also entered as the argument of tile predicate went-home. When She was tired is analyzed, the pronoun can be interpreted as anaphorie on a preceding NPs if the marker licensed by that NP is 'aecessio bit'; i.e. if tile marker belongs to the universe of the immediately enclosing DR or a superordinate one. Since f is accessible, the prouoan her can be identified with it to yield the condition tired(f).</Paragraph>
    <Paragraph position="11"> Before turning to sentences involving universal NPs, it will be useful to consider in a little more detail the procedure for constructing a Dlt like (8) proposed by (Kamp 1981/. Karnp's rules pivot on the noun phrases in a sentence, and depend particularly on any determiners in the noun phrases. It is usedeg ful to think of every determiner as having a semantic restrictor and a semantic scope. The determiner will bind an argument position in each of these. Thus, in a simple intransitive sentence like tlu~ first sentence of (5), the restrictor of a is woman(), while its scope is went home(), where the empty parentheses indicate an open argument position. Given an existing (possibly empty) DRS K, a sentence of the form \[\[a Res\] Scope\] is &amp;quot;processed&amp;quot; in the following manner: (i) add a new reference marker x to the universe of K; (ii) fill the argument slot in Res by x, and add the resulting clause to the conditions of K; and (iii) fill the argument slot in Scope by x, and recursively call any applicable construction rules to process the resulting string.</Paragraph>
    <Paragraph position="12"> Let us turn now to sentences involving universals. The DR associated with (5b) is illustrated in (9).</Paragraph>
    <Paragraph position="14"> The universal quantifier every triggers the introduction of two subordinate DRSs, linked by the relation =&gt;; this corresponds roughly to implication in first order logic. When we come to analyze the second sentence of the discourse, She was tired the reference marker licensed by every woman is trapped in the subordinate DRS; it is not accessible at the top level of the discourse. Consequently, the only option is to treat the pronoun she as non-anaphorie, which we have indicated here by associating it with a distinct reference marker. When we consider sentence-internal anapbora, the antecedent-introducing potential of every and a converge. For example, in both of the following sentences, he can be anaphoric to the subject NP: (6a) t?,very man i thought he i was ill.</Paragraph>
    <Paragraph position="15"> (10) A man i thought he i was ill.</Paragraph>
    <Paragraph position="16"> Although it may not be obvious from the examples given so far, DR theory correctly predicts that the reference markers associated with an indefinite or universal NP in subject position will be anaphorically accessible to pronouns that it ccommands. 5 To see why, we need to consider in a little more 5 It might be argued that DR theory fails to provide an adequate semantic distinction between a 'c-command binding' relation and a 'discourse anaphora' relation, as proposed for example by (Rcinhart 1983) in order to account for the strict/sloppy ambiguity in VP ellipsis. Whether this criticism is justified or not depends in large part on the appropriate analysis of such ellipsis phenomena in the DR framework.</Paragraph>
    <Paragraph position="17"> For some discussion, see (van Eijck 1985), (Klein 1985), (Roberts 1984).</Paragraph>
    <Paragraph position="18"> detail tile way in which DR's are coustructcd on g~amp's approach.</Paragraph>
    <Paragraph position="19"> Construction rules apply to sentences on a top-down, left-too right basis. Given a sentence like (6a) or (10), the first constituent to be processed is tile subject NP. We either stay in the current DR, if tile determiner is a, or 'push down' to an embedded DR if the determiner is every. (This embedded DR is, therefore, the antecedent box of tile conditional like that displayed in (9).) A discourse marker x i is introduced into the universe of whatever is now the current DR, and x i also becomes the argument of the subject nominal (e.g.</Paragraph>
    <Paragraph position="20"> man(rot)) and the first argument of the predicate VP (e.g. m t thought he was ill). When tile VP is processed, there are again two cases, depending on whether tile subject determiner was a or every. In tile first ,:;ase, we enter tile new conditions licensed by the VP into the current DR. Ill the second case, we close off the current (antecedent) DR, and open a new embedded DR which forms the conseqent box of the conditional. Kamp claims that the reference markers accessible as antecedents to a given pronoun occurrence consist of those reference markers which are present in the universe of either the current DR or of any DR.'s which are superordinate to the current DR. Of two DR's K 1 and K2, K 1 is superordinate to I{ 2 if: (i) K 2 is embedded in K1, or (ii) if K 1 is the anteeedeut of a conditional of which K 2 is tile consequent, or (iii) if there is some K~ such that K 1 is superordiaate to K 3 and K 3 is I;uperordmate to K 2.</Paragraph>
    <Paragraph position="21"> This is illustrated in (11) diagram below, where tile lightly shaded boxes arc all superordinate to the darkly shaded box.</Paragraph>
    <Paragraph position="23"> Consider now what follows when we come to process the NP he in either (6a) or (10). It can be anaphorically linked to any reference marker which is accessible to it, and this will of course include the marker x i introduced by the subject NP.</Paragraph>
    <Paragraph position="24"> Let us now attempt to summarise the salient features of DRT.</Paragraph>
    <Paragraph position="25"> Note, first, that every noun phrase is associated with a 'space '6 in a Discourse Representation. Referential terms which we take to include definite and indefinite descriptions, proper names, and definite pronouns - are entered into an existing space. By contrast, universally quantified NPs induce a new subspace~ Second, the space associated with an NP represents both the quantificational scope of the NP and its anaphoric domain.</Paragraph>
    <Paragraph position="26"> Third, the boundaries of these spaces are not coterminous with clause or sentence boundaries. A clause containing universal NPs will induce a number of subspaces; conversely, the space associated with a referential NP can encompass indefinitely many sentences of a given discourse.</Paragraph>
    <Paragraph position="27"> Fourth, the space of an indefinite NP which occurs within the scope of a uniw~rsal NP is the same as the space of the universal. null 4. The flow of anaphorlc Information In the last section we showed how DRT is able to simultaneously describe both the semantics of quantification and tile anaphorie 'range' of referential noun phrases in terms of a single discourse representatkm. The standard version of DRT depends crucially on processing notions in order to explain the failure of anaphora in examples like (12).</Paragraph>
    <Paragraph position="28">  (12) He i liked a boy i.</Paragraph>
    <Paragraph position="29"> Since the reference marker for a boy is not introduced into the DR until after the pronoun he is introduced, it is unavailable as a possible antecedent. That is, the failure of anaphora is explained by assuming that the pronoun's antecedent is assigned at the time at which it is introduced into the DRS, and that the reference marker for the noun phrase is introduced after the pronoun was introduced.</Paragraph>
    <Paragraph position="30"> In a declarative framework, an explanation in terms of processing order is impermissible hence we represent left-to-right dependencies by explicit equations. Although these equations are in principle non-directional, it can be helpful to think of them as providing a means for transmitting information from one node in the syntactic structure to another.</Paragraph>
    <Paragraph position="31"> Bottom-up information flow is central to syntax-drlven compositional semantles of the familiar sort: semantic values are associated with the leaves of the syntax tree, and the semantic value of a complex constituent is determined as a function of the semantic values of the constituents daughters. The diagram in (13) shows this direction of information flow.</Paragraph>
    <Paragraph position="33"> Although this approach has proven to be extremely powerful, it is awkward and intuitively unsatisfactory as a means for dealing with anaphorie dependencies. Even if much semantic information is indeed composed on a bottom-up regime, it seems highly plausible that anaphorie information - that is, information about the set of available antecedents - flows in a left-to-right direction. We have already seen that a simple left-to-rlght model of this information flow can be constructed by regarding meaning as a relation between contexts, but we have also seen that such a model is inadequate for dealing with the facts of bound anaphora. A more satisfactory model can be constructed by reflecting on the principles involved in constructing Discourse Representations. As we pointed out in the previous section, Kamp's construction rules centre on the determiners a and every, since they trigger the introduction of reference markers, the binding of argument positions, and the introduction of sub-spaces. What we shall suggest, therefore, is that information about possible antecedents flows from a determiner to the determiner's restrietor, and from the restrietot to the determiner's scope. The following diagram (14) illustrates how this top-down, left-to-right flow is integrated with the orthodox phrase marker of a girl kissed a boy.</Paragraph>
    <Paragraph position="35"> s This term is intended to be reminiscent of work by Fauconnier (1985) on mental spaces, and by Reichman-Adar (1984) on context spaces, though considerable work needs to be done in showing that these ideas are in fact compatible.</Paragraph>
    <Paragraph position="36">  The light, incoming lines on the left-hand side of a node indicate incoming information about the set of possible antecedents. This set will be encoded in something we call the &amp;quot;in-list&amp;quot;. The light lines on the right-hand side of a node indicate outgoing ~ information about antecedents, encoded in the form of an &amp;quot;out-list&amp;quot;. In general, the out-list of any node will be its in-list plus any additional information added by that node. Circled nodes mark constituents that supplement their in-list with new reference markers. The in-list and the out-list together form a difference list, in that the content added by any item is the difference between its in-list and out-list.</Paragraph>
    <Paragraph position="37"> Alternatively, one can view the in-lists and the out-lists of nodes as streams along which information about antecedents flows: this anaphoric information is threaded through the syntactic tree structure. Notice that we assume the sentence as a whole will be fed an in-list which is supplied by the preceding discourse. Moreover, the sentence as a whole will also a produce an out-list, which will provide potential antecedents for following discourse.</Paragraph>
    <Paragraph position="38"> The next diagram (15) illustrates the flow of information for every girl kissed a boy.</Paragraph>
    <Paragraph position="40"> By contrast with (14), the out-list from the VP, containing reference markers for gtrl and boy, is &amp;quot;trapped&amp;quot; at that level rather than percolating up to the S node. The out-list for the sentence as a whole is just the sentence's in-list. This captures the idea from binding theory that the scope of a quantifier is normally limited to its e-command domain (Reinhart 1981, Reinhart 1983); In terms of DRT, it corresponds to the closed subspace that is associated with universal NPs.</Paragraph>
    <Paragraph position="41"> Let us summarize our claims so far. We have suggested that there is a contrast between the bottom-up information flow of compositional semantics, on the one hand, and the top-down flow that is naturally associated with anaphoric information.</Paragraph>
    <Paragraph position="42"> We have also suggested that top-down flow is largely determined, according to the principles of DRT, by the lexical properties of determiners and their structural position in the sentence. null One possible implementation of this analysis would be to factor out anaphoric, contextual information from the rest of semantics, and to use two distinct mechanisms for building the two kinds of representation. However, such an approach fails to explain why the spaces in a DR, and the list of contextually-divan antecedents always covary; that is, when a new DR subspace is opened, a new context list begins, and when a DR subspace is closed, a context list is simply &amp;quot;dropped&amp;quot;, ie. it does not serve as the in-list to any other expression. Indeed, the fact that a DRS in Kamp's theory consists of a universe, corresponding to our context list, and a set of conditions, corresponding roughly to compositional semantic information, suggests that it out to be possible to enrich the notion of a context from being just a list of antecedents to being a whole DR structure.</Paragraph>
    <Paragraph position="43"> In our analysis, then, we thread a list through the syntactic structure which contains both conventional semantic information and information about available antecedents, so that an expression mapping an incoming context into an outgoing context does more than incrementing the set of possible antecedents: it also adds conditions to the context that correspond to its truth-conditional semantics.</Paragraph>
    <Paragraph position="44"> It is necessary that the context be structured, rather than a simple list, as it was in the naive model, and as discussed above. This is because we need to be able to incorporate the semantic structures associated with all expressions, even those that are anaphorically opaque to following anaphora. In the model described immediately above, we accounted for the anaphoric opacity of an expression by &amp;quot;dropping&amp;quot; its context list after it had been processed, but such &amp;quot;dropping&amp;quot; in a system where the context lists also contain &amp;quot;compositional&amp;quot; semantic information would result in that semantic information also being lost.</Paragraph>
    <Paragraph position="45"> Rather, we structure the context list as an ordered list of the currently open DR spaces, starting at the most embedded space, and working upward through the superordinate spaces.</Paragraph>
    <Paragraph position="46"> For example, the context list for an item located in DR space K 1 in (11) would be \[ K., K~, K~, K-\], where each K. is a 1 z 4 1 set of reference markers and eon~tions, the current contents of the corresponding space. The first space on the context list is the most embedded space, ie. the current space, and identities the place where new conditions and reference markers are to be added. Since the context list consists of the active space plus all of the spaces snperordinate to it, any reference markers contained in these spaces are possible antecedents for anaphora in the active space.</Paragraph>
  </Section>
  <Section position="5" start_page="672" end_page="674" type="metho">
    <SectionTitle>
5. The Grammar
</SectionTitle>
    <Paragraph position="0"> We turn now to considering the induction of DRSs. In this section we describe a simplified version of ttle grammar that we have implemented. The grammar presented here is the actual input to the proof procedure: the parser is nothing more than a declarative statement of the well-formedness conditions of an utterance, plus a proof procedure capable of determining whether or not these conditions actually hold of a given utterance.</Paragraph>
    <Paragraph position="1"> The rules are written in DCG format (Clocksin and Mellish 1984) in a superset of Prolog that we developed in this project. This language, which we have dubbed PrAtt (for Prolog with Attributes), allows an attribute-value notation as well as the standard position-value notation of Prolog. For example, the expression &amp;quot;N:syn:index&amp;quot; refers to the value of the Index attribute of the syn attribute of the variable N.</Paragraph>
    <Paragraph position="2"> We make heavy use of the attribute-value notation to represent feature bundles associated with constituents. Two attributes that are present on every constituent are syn (for &amp;quot;syntax&amp;quot;) and sam (for &amp;quot;semantics&amp;quot;). The sam:in and sam:out attributes contain the context in-lists and out-lists respectively, while the syn attribute holds information used to construct the function-argument structure of the clause.</Paragraph>
    <Paragraph position="3"> Expressions act on the context list by opening or closing spaces (ie. pushing or poping spaces from the context list), adding reference markers and conditions to the active space, and looking through all of the spaces in the context list for antecedents for anaphora.</Paragraph>
    <Paragraph position="4"> Consider, for example, the common noun woman. It inserts a reference marker f and a condition woman(f) into the active space. Using our earlier relational notation, we can express its meaning as follows: 7 (16) \[ActiveJSuper\] I woman I \[if, woman(f) ~Active\]~uper\] In our implementation, this would be written as in (17).</Paragraph>
    <Paragraph position="5">  with a capital letter, constants with a lower-case letter, &amp;quot;ix,y\]&amp;quot; is the list that contains x and y, and &amp;quot;\[x~\]&amp;quot; is the list that consists of x CONScd onto y.</Paragraph>
    <Paragraph position="6"> Tile hracketted equations are conditions that must be satisfied in rewriting an N to the lcxical item woman. The first equation assigns a reference marker to the lexieal item, s the second equation analyses the incoming context list into two parts, the current space (Current) and a list of the superordinate spaces (Super), while the third equation requires the active space of the outgoing context list to contain the referenco marker and the condition associated with the noun.</Paragraph>
    <Paragraph position="7"> A sample entry for a verb is shown in (18). Again, the equations associated with the lexieal entry dissect the incoming context into the current space and a list of superordinate spaces, and place the condition associated with the verb into the outgoing context.</Paragraph>
    <Paragraph position="9"> One interesting property of this rule is that it is responsible for placing a condition into the context that in essence represents the compositional semantics of the entire clause.</Paragraph>
    <Paragraph position="10"> The ~yn attributes of constituents are used to councct the NP arguments of the verb with the verb itself; thus the necessary information to build tile condition associated with the entire clause is available at the verb. One can view the equations in the phrase structure rules associated with the syn attribute as directing information from the NP arguments inward and downward to the verb.</Paragraph>
    <Paragraph position="11"> The crux of the grammar is located in the lexical entries for determiners, as hinted earlier. (19) contains tim lexical entry for the indefinite artlele a.</Paragraph>
    <Paragraph position="13"> As we shall see later, the phrase structure rules are written in such a way that the value of the elauses's sam attribute is equal to its subject's determiner's sam attribute, and the semantics attribute of the restrictor and the scope of a clause are placed in that determiner's sem:res and sam:scope attri.</Paragraph>
    <Paragraph position="14"> butes respectively. As noted earlier, an indefinite determiner does not cause the creation of any additional subspaces, rather the restrietor and the scope are simply placed into the current active space. Therefore, the equations associated with the indefinite determiner simply connect the in-list asssociated with the sentence to the restrictor's in-list, feed the restrietor's out-list to the scope's in-list, and take the out-list from the scope as the out-list for the clause as a whole.</Paragraph>
    <Paragraph position="15"> The lexical entry associated with the universal quantifier every is a little more complicated. It must create two new spaces, one for the restrictor, the other for the scope, and the finally close off both spaces, and huild the structure associated with the clause as a whole.</Paragraph>
    <Paragraph position="16">  to lexieal entries; however more correctly the reference markers should be assigned to lexieal tokens, allowing two occurances of the same lexical entry to refer to different objects in the world.  The first equation in (20) pushes a new, empty space onto the determiner's in-list as the active space, and makes that list the restrictor's in-list. The second equation takes the restrictor's out-list pushes another new, empty space onto it, and makes the resulting list the scope's in-llst. The final equation takes the scope's out-list, removes the two spaces that were added for the restrietor and the scope, and produces a new list in which the original active space has a complex condition added to it representing the whole universally quantified expression.</Paragraph>
    <Paragraph position="17"> This last list serves as the outqist for the determiner, and hence for the clause as a whole.</Paragraph>
    <Paragraph position="18"> Below are the phrase structure rules responsible for connecting the various attributes of the constituents as described above.</Paragraph>
    <Paragraph position="20"> np(NP), vp(VP).</Paragraph>
    <Paragraph position="21"> It remains only to give the lexical entry associated with pronouns, and our fragment is complete. This is given in (24). (24) np(NP)--&gt; \[her\],</Paragraph>
    <Paragraph position="23"> The first three equations require that there be some space containing a reference marker of feminine type with which the pronoun's reference marker can unify: 9 the last two equations take account of the fact that an anaphoric pronoun, while not adding any conditions of its own to the context, can appear in subject position, and thus can have a scope expression.</Paragraph>
    <Paragraph position="24"> We have now completely described our declarative formulation of DRS theory. This formulation (together with phrase structure rules that analyse a discourse as a series of sentences) suffices to obtain the analyses shown below) deg  one used in Prolog (albeit interpreted by the PrAtt interpreter, while the type predicate is a set of clauses of the form type(w,feminlne)., etc.</Paragraph>
    <Paragraph position="25"> l0 Note that because later elements are pushed onto the front of a DR space, the order of the elements in the DR spaces is the reverse of their &amp;quot;normal&amp;quot; pr.~'~entation. This does not affect their truth conditional semantics, however.</Paragraph>
    <Paragraph position="26">  We have also implemented a more complex version of this grammar incorporating a treatment of unbounded dependencies, and obtained analyses like the following: (27) Every man who owns a donkey beats it.</Paragraph>
    <Paragraph position="28"> Tile parser indicates ill-formedness of its input in the standard Prolog fashion, viz. it fails to find a well-formed DRS for the input sentence.</Paragraph>
    <Paragraph position="29"> (28) A woman who loves every man kissed him.</Paragraph>
    <Paragraph position="30"> no</Paragraph>
  </Section>
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