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<?xml version="1.0" standalone="yes"?> <Paper uid="C88-1026"> <Title>A Binding Rule for Government-binding Parsing</Title> <Section position="1" start_page="0" end_page="126" type="abstr"> <SectionTitle> USA Abstract </SectionTitle> <Paragraph position="0"> In this paper I propose a Binding rule for the identification of pronoun and anaphor referents in phrase-structure trees, assuming the general framework of lhe Government-binding theory outlined by Chom,;ky (1981). The Binding rule, specified by means of an attribute grammar, is a particular instantiation of the Free Indexing rule and binding axioms in Chomsky's Binding theory, with certain empirical and practical advantages. The complexities of the Binding rule proposed, as well as that inherent in Chomsky's Binding theory, are studied, and it i~ shown that the new rule is more psychologically plausible and cornputationally efficient than the original theory on wtfich it is based. The fragment of the attribute grammar shown here is part of an English grammar and parser being developed in tile Prolog and PLNLP languages.</Paragraph> <Paragraph position="1"> Introduction Binding is a component subtheory of Government-binding which applies in the derivation of the logical form of utterances from their surface rcpresentation. The area of semantic interpretation dealt with by the binding theory is that of anaphora.</Paragraph> <Paragraph position="2"> Binding theory defines only syntactic conditions on anaphora; the reader is referred to /Hobbs, 1978/ for some of the extra-syntactic factors that might be involved. Binding assumes an Indexing rule which applies to an input S-Structure tree and annotates it, assigning to every NP node ha the input tree a referential index, which represents the coreferenee relation ot the NP with other NPs in the input.</Paragraph> <Paragraph position="3"> In this paper research is continued on the use of attribute grammars to provide a fully explicit and computationally oriented statement of the Governmc.nt-binding (GB) theory /Correa, 1987/.</Paragraph> <Paragraph position="4"> The Binding rule presented here improves over the standard statement of the Binding theory in two respects: From an empirical point of view, the new rule accounts for crossover binding phenomena /Kuno, 1987/ without recourse to reconstruction /Chomsky, 1981/; from a practical point of view, the new rule is more computationally sensible than the generate-and-test approach understood in Chomsky's theory, and hence is a plausible candidate for incorporation in natural-language parsers that account tot anaphora. Previous literature on GB parsing /Wehrli, 1984; Sharp, 1985; Kashket, 1986; Kuhns, 1986; Abney, 1986/has not addressed the issue of implementation of the Binding theory) The present paper intends in part to fill this gap.</Paragraph> <Paragraph position="5"> In the development below I will assume that the reader is thmiliar with attribute grammars and the basic concepts and terminology of Governmentbinding, although not necessarily with the Binding theory. The reader is referred to Waite and Goos (1984) for a concise introduction to attribute grammars, and Sells (1985) for the basic assumptions of Government-binding.</Paragraph> <Paragraph position="6"> Chomsky's Binding Theol T Binding theory defines the syntactic constraints on coreferenee that exist between the noun phrases in a sentence. In the course ot&quot; doing this, thE themy indirectly determines constraints on the distribution of certain kinds of noun phrases. In this section we review the standard formulation of the Binding theory; tile reader already familiar with it may proceed to the next section.</Paragraph> <Paragraph position="7"> The ret~rential possibilities of a noun phrase depend on the fimetional type of the NP and the Binding conditions for that type. Government-binding distinguishes three types of overt NP, shown in (1).</Paragraph> <Paragraph position="8"> I Sharp (1985) checks correclness of binding in traces; we consider lexical NPs here. O) a. anaphor (reflexive and reciprocal) b. pronominal c. referential An anaphor is an expression that has no independent reference mad must take its reference from some other expression in the sentence in which it occurs. English has reflexive and reciprocal anaphors, such as 'themselves' and &quot;each other&quot; in (2). The NP from which an anaphor or pronominal takes its reference is called its antecedent, since an anaphor must have an antecedent within the sentence in which it is used, we obtain the contrast between (2.a) and (2.b). If there is no appropriate antecedent, the string is ill-formed at the Logical Form level. The antecedent of the anaphor must, furthermore, c-command the anaphor and be found within a certain local domain, notions to be made precise below. Thus, in (2.c), although there is a potential antecedent for the anaphor, namely 'Greeks', it is not within the required local domain. In (2.d), there is a potential antecedent &quot;donkey', but it does not c-command the anaphor. Hence :i~e string is also ill-formed.</Paragraph> <Paragraph position="9"> (2) a. Greeks like themselves/each other.</Paragraph> <Paragraph position="10"> b. * Each other/Themselves like Greeks.</Paragraph> <Paragraph position="11"> c. * Greeks i think that each otheq/themselves i are smart.</Paragraph> <Paragraph position="12"> d. * Every man who owns a donkey i beats itself.</Paragraph> <Paragraph position="13"> A pronominal is a pronoun in any of its inflected forms (e.g., as due to agreement and Casemarking), as in (3). Pronominals exhibit a distribution in phrase structure trees nearly complementary to that of anaphors. A pronominal need not pick its reference from some other NP in the sentence, but rather may have independent (deictie) interpretation, as in the first reading of (3.a). The pronominal may also be read anaphorically, having its reference determined by some other NP in the sentence (3.a-b). In tlfis case, though, the antecedent must either be outside the local domain of the pronominal, or not c-command it. Hence, the assigned coreference in (3.a-b) is possible, while that in (3.c) is not.</Paragraph> <Paragraph position="14"> Within a local domain, where an anaphor must have an antecedent, a pronominal cannot.</Paragraph> <Paragraph position="15"> (3) a. Brigitte i said that Shell i is tired.</Paragraph> <Paragraph position="16"> b. Every man who owns a donkey i beats it i.</Paragraph> <Paragraph position="17"> c. * Sibylle i loves her i.</Paragraph> <Paragraph position="18"> Lexical or fully referential expressions are names like &quot;John&quot; and &quot;the man&quot; in (4); the class inchldes all nominals headed by a common or proper noun.</Paragraph> <Paragraph position="19"> A referential expression defines its reference independently and must be free in every domain, in the sense that it may not have a c-commanding antecedent. Tiros the interpretations in (4.a-b) are unwarranted. Coreference between referential NPs is possible only if the first NP does not c-command the second (4.c-d); the result, though, may be awkward or place emphasis on the anaphoric noun phrase.</Paragraph> <Paragraph position="20"> (4) a. * John i likes John i.</Paragraph> <Paragraph position="21"> b. * .lohn i wants that John i leaves.</Paragraph> <Paragraph position="22"> c. The man who hired John i likes .lohn i.</Paragraph> <Paragraph position="23"> d. John i came and .lohn i left.</Paragraph> <Paragraph position="24"> The most difficult area of the Binding theory is the tbrmulation of the notion local domain referred to above. This notion is defined such that it is identical for anaphors and pronouns. We note in advance, however, that while the notion is nearly identical for both, it should not be defined the same, as sentences (5.a-b) show (Chomsky, 1986).</Paragraph> <Paragraph position="25"> In this paper we shall not be concerned with the solution of this still open problem.</Paragraph> <Paragraph position="26"> (~ a. The children i like each other'sipictures.</Paragraph> <Paragraph position="27"> b. The children i like theiq pictures.</Paragraph> <Paragraph position="28"> Chomsky's axiomatic statement of the Binding theory is as tollows. Chomsky (1981) assumes a Free Indexing rule which appfies at LF and assigns (randomly) a referential index to every NP in tim input structure. Two NPs are said to be coreferential if they bear the same referential index. The indexhlg rule massively overgenerates logical forms, and indiscriminately assigns unwarranted coreference relations. The annotated structttres produced by the rule are subject to a number of well-formedness conditions, which are constraints on the assigned coreference relations.</Paragraph> <Paragraph position="29"> The most elementary condition is the agreement conditkm (6). The main component of the theory is given by the Binding axioms (7), where tim notions of binding and local domain are as in (8) and (9), respectively. Notice that the definition (9) of local domain does not distinguish between anaphors and pronominals, and thus is problematic, as the examples (5) indicate. We assume this definition, though, for the development below.</Paragraph> <Paragraph position="30"> The notion of c-command used in (8) is given in (10), (6) Agreement Condition If NP l and NP2 are coindexed, then their agreement features A GR = < Person, Gender, Number> agree.</Paragraph> <Paragraph position="31"> (7) Binding Axioms (8) (9) A. An anapkor must be bound within its local domain.</Paragraph> <Paragraph position="32"> B. A pronomb,al must be free within its local domain.</Paragraph> <Paragraph position="33"> C. A referential expression must be free in every domain.</Paragraph> <Paragraph position="34"> For nodes a and fl, a binds \[1 if (i) a is coindexed with fl, and (ii) a c-commands ft.</Paragraph> <Paragraph position="35"> A node a is free (within a given domain) if it is not bound (within that domain).</Paragraph> <Paragraph position="36"> The local domain of a node a is the subtree dominated by MGC(a), where MGC(~), the minimal governing category of a, denotes the maximal projection # nearest to C/z such that /~ dominates a, and /~ has an accessible Subject, and /L dominates a governor ~ of a (to) For nodes a and \[1, a e-commands \[I if the firsi; branching node dominating a also dominates ft.</Paragraph> <Paragraph position="37"> It is a straightforward task to verify that the Binding axioms in (7) explain the grammaticality judgements and interpretation possibilities of the examples presented thus far, except those in (5). The theory is explanatorily adequate, in the sense that it applies to a wide range of natural languages. The Binding theory just outlined follows the style of most recent work within the Government-binding framework. Extremely general rules, such as the Free Indexing rule, are assumed for the generation and annotation of syntactic structure; the bulk of the grammar then consists of well-formedness conditions or axioms that must be satisfied by the generated structures. This approach: due to it:; extreme inefficiency, is problematic as a model of linguistic performance or natural language parsing. It seems more appropriate to view the general rules and axioms that constrain them as Ifigh-level specifications of certain grammatical processes, rather than as models of how the processes are actually carried out.</Paragraph> <Paragraph position="38"> The refinement of the general rules and axioms associated with them into procedural rules which may be used to derive structure that already satisfies the axioms is not a straightforward task, and has only recently begun to be addressed /Abney and Cole, 1986; Barton, 1984/. The incorporation of axioms into the rules leads to grammars which are more sensitive to psychological issues/linguistic processing, rather than mere linguistic description. It seems clear that only these new rules may be used in practical natural language parsers. Furthermore, the formulation of procedural mechanisms provides a new way of looking at linguistic phenomena, which may in turn lead to insights for the solution of outstanding problems. I offer the following Binding rule as an illustration.</Paragraph> <Paragraph position="39"> The Binding rule is defined by means of attribution rules associated with productions in the base. It applies at S-Structure and assigns to each NP node in the structure a referential index, in such way that the Binding axioms are satisfied by the assignment. The generate-and-test method implicit in Chomsky's account is avoided. In those S-Structures for which there is no possible correct assignment, tile rule blocks, and the structures are marked ill-formed, due to some violation of the 13inding theory. The rule applies after the timetional type of every NP has been determined, according to lexical features of the head nominal and principles of the Government and Case theories. Functional classification of an NP consists of determining the values of its attributes anapkoric and pronominal /van Riemsdijk and Williams, 1986/. The first approximation to the rule is limited to cases of backward reference only; assignment of forward eoreference, as in (IlL will not be covered by the rule. Also, we ignore cases where referential expresskms may be used anaphorically, as in (4.c-d).</Paragraph> <Paragraph position="40"> (i I) Men who met her i saw how kind Mary i was. The formulation of the rule relies crucially on the following hypothesis: For every NP node in an S-Structure, it is possible to define two sets of nominal expressions AAS and PAS, which contain, respectively, potential anaphoric and pronominal antecedents. Given a mechanism to compute the two sets noted, an antecedent for the current node may be selected from the appropriate set, according to the current node's functional type, as in (12). Attribution rule (12) is associated with every produetion for NP and defines the value of the NP's referential index. The function se&ct-from takes an ordered set as argument and selects (arbitrarily) the The main component of the Binding rule consists of the attribution rules that define the values of the AAS and PAS sets at each node. I now proceed to describe the types of the attributes involved in the computation and the manner in which these values are defined.</Paragraph> <Paragraph position="41"> Binding attributes and their types Assume integer-valued attributes node and Re/Index. The attribute node is associated with every node in an S-Structure tree, enumerating them in preorder. Thus the node number of an NP may be used to identify the NP. Reflndex represents the referential index of the NP with which it is associated. This attribute is synthesized by rule (12) and its value is equal to the referential index of the first NP with which the current NP corefers (assuming a preorder enumeration of tree nodes).</Paragraph> <Paragraph position="42"> When NP.RefIndex = NP.node, for some NP, we say the NP has independent reference.</Paragraph> <Paragraph position="43"> The attribute AAS contains, for a given NP, the sequence of c-commanding NPs found within the local domain of the current node. Thus, any NP in this set is a potential antecedent for the current node, if that node is anaphoric. Each element in the AAS is a pair of the form < NP.Reflndex, NP.AGR >, for some NP to the left of the current node. NPs are ordered in the AAS in such way that the most recently found NP is ranked first (AAS is a stack, or ordered set). The attribute IMS is similar to the AAS, except that each element in it either does not c-command the current node, or is outside its local domain. Thus, each NP in the PAS is a potential antecedent for the current node, if that node is pronominal.</Paragraph> <Paragraph position="44"> An important difference between the AAS and PAS is that, if the current node is an NP, say NPi, the pair < NPi.node, NPi.AGR > is a member of PAS, but not AAS. Because of this, a pronominal's referential index may be set to its own node number (i.e., may be interpreted deictically), while an anaphor's may not. This difference between the AAS and PAS need not be stipulated as a special case, but rather follows naturally if we assume the c-command relation is irreflexive.</Paragraph> <Paragraph position="45"> The distribution of values tor the AAS and PAS attributes in an SoStructure may be illustrated hy means of example (13), ill which the subscripts are NP node numbers; we ignore their actual values.</Paragraph> <Paragraph position="46"> (13) John h told \[his i parents\]j about himself k. The values that result for the AAS and PAS are shown in (14); the reader may verify their correcthess with the aid of .examples (15). For the tirst NP, &quot;John', there is no potential anaphoric antecedent (15.a), so the AAS is empty (14.a).</Paragraph> <Paragraph position="47"> Ilowever, at that position it is possible to have a free pronoun, so the PAS contains a single erthy, the pair <h, AGRh>. For the second NP, &quot;his', the values of AAS and PAS are as in (14.b). Thus the AAS is empty and no anaphor is permissible at the position (15.b), while a pronoun is, in which case it may be interpreted deictically or anaphorically, referring back to &quot;John'. The values of the AAS and PAS attributes associated with NP i and NP k are as shown in (14.c-d).</Paragraph> <Paragraph position="49"> (1~ a. * Himself/ He i told his parents about himself.</Paragraph> <Paragraph position="50"> b. Jolm i told \[*himself s~ hisj/i pa.rents\] ahout himself.</Paragraph> <Paragraph position="51"> c. John i told himself/ *him i to stop smoking. t c. John i told \[Mary: s parents\]k about himself/each otherk/ tler~/i 2' No theoretical significance is attached to the order of' the elements in the AAS and PAS. Psycholinguistic evidence, however, suggests that gaps &quot;reactivate&quot; their antecedents, which hears on the order of the sets. r'ilc, mi,l:)ht!5 the pr~:vhms apT~I{c:~tio~< <>i a t:~:umfb~'. J ii&quot;tti<>~t, {<; tuU: w;;ty U?pcalini,,: I)rt)ccdc+c,ll i}iudi~g rid{: lflay be w.tTuc;l (.(J ;..tcco/lil\[ {'01 (\]6) bVi\[ilOI!\[ \]'CC()ItJ):;I:, \[+) r'.;c:oslstruct.ion, t:l{i.t':~:-; <)bservc~ that the mll:(w, odolli; (3\[ ;u~ ail3p\]i;ios l:flllS\[ C'COYllIit~VO.,'-( a~t(~ i)(: wil.hill it/(: lu<:ai d()lJlaiii Of ci!hcr i.Jw +mai>}~or , of orJc. of l:iic i;laces o\[ the /,lt\[{~<;~:;O i>'L 'C/V\[~'Ii#\['.}I i\[!-tC ~Nl~tsi..)t\](')~{' i~; ernlw.dctcd. Thi,~; }oprl::;i.::iit:-; .-+l 5i~.ti:tii;ic:+ilti; Icg)lJCl.tl~\];i.i.iOt~. ,:)J' ih.c; biudiu/,~ :lxkmts, to. h~c:lu:!, rcii:svucc it; iV. lkw t:lv;i:;x, The .>fi:f.l'ibtti:i(;ll t'ulcx i:{i:-ii. (h:;Jhlc lhc v~:lue:~ 'd du'. AAS' <iild \[>/>{,+)+ sc{<s Ii!.37 {'~t: modified I:o lake intu ~-tCCOUII\[ !Piis obsetvati(+;~. The; chuuK,: ;c<tuh+x\] L<; ++) ({e~liitt: i7~+; V{l\]\[lJ(:,c; 31 ill(; lO()t \[)l' ilJC HIOVtJf\] phJ'~l+;c c;.s i.hc a+,.+iOll o( t}tc valu~ dciinc.d by the t;l!rrc++t i+uic, phu; !i., ,!~c.:; d,~iincd ;;t i:hc traces in tim chain headed .,. ~} +: i: ll.~.<+:. 'Ftui~, in (16) NP. AdS arid e tlA5 + : ~<:,ti,~: u,c c..~:;u~c!:,C/. -<:i, A(,\],~i> , aild the attrii,tlti(m iO!t:S dc,~ciJilX,.!J hi the previous section make i!~i; V~i.iUC au..C,<;<;i1<)iO i:O i.hc armphor him,s'eU: ~'t.; cx:,.:i r,ibi,iulati<.m_ of the attribution rules for .i,'i,? u,l P,C;' iu~O~ bc dent iu diltbronl ways, (hm ;iN,.:~+~-~iivc b; io cm~q:,utc th,'; extended AAS and /'d,<; :~:!a b~ two p:-,_sscs through the tree, with the, .'.;('.colld Vx,:+:~ used to compute the IlIliOll<'; not0d. A sccoi~i xpvmac\].,, dclay:~ anaphora, resolution for ~ucprv.~:.;io~i>; inside an m.~teccdcnt (cliaitl head) tmtil ih~. i~u;! !~a~:c: ;d' the chain i<<~ fotntd. At this lime +h,: ,4,1/7 mid P./IS a;t.s o\[ tbc antecedent nlay l>C cvalt++iic(t, baviitg access {() tl!:: c;OIiOS\])Ott(\]il/+~ SOtS iU the tim-cs. 't'his sc'.coud ai~pioach seems more '+.iJ~;ibic, :.;into; it !,ctmita ;~lhqicalicni of t\[t?, l\]indhig i,tl<: i,i oJ,c Iov.<.IcJwu, i(.:i\]r'\[O &quot; right pass through the ii'CO. We do iiot; i)tlt:n\]c the &:tails of the revised ru!c here.</Paragraph> <Paragraph position="52"> l,'h',,;t wu consldcr Ch<~m,<d~y's Bindin/, theory. The combilmtion ol&quot; ih(: !&quot;~ee l+~dr.xiug lute aud Bin(iini4 ,xiom:.~ d,:\[h;{:s , gcncrai~>-aNd4cs~t ~d::o~iihm ~ ;i,/~:~i as::,.mKl>li:~n.:+ o' tbc X' i!icury, thc nun~bcr of !-4P,<; il~ uit i,li,lu <iirhU~ ia ilur:ariy related to th+~ !cnp, ih o\[&quot; ihc xt.i~!!;. ~h:uce \[br ,s(m~e fixed and :+ul;,ll \]g ~br a xcu.ic~,x&quot;; o\[&quot; lcn:gth n i.lacre will ix; n/# Ni&quot; ~.:~><h;.~. ~u~.<;umhuy a slight mcxtificaticm of the iudcxing ride. (which improves it), accordil~g to which ii..<;clcci.s imcgcrs in the range l ..... n/k to :,:;silSJt ,.'ts potential rd?',rcnt.ial in:ticc.s to dt~: VII'.,: i~+vo!vcd, iJw.rc will bc (n/k)n/k caudidatc i,i&quot; ,:;:;iBnmuuts tr~ be. checked again.<;t the Bimlhig axioms (7). Assuming that thu 13indhlg axion!a ~,Jay t)< chcck,.:d hL constant time, thc, rt nnim! tiiuc iLr the ;ligorithm is exponentially related to i}lc Icugt.Jt '&quot; '~ ,:~I um input ,~tring.</Paragraph> <Paragraph position="53"> I~or the procedural Binding rule iommlatcd hero, iilc tiinc needed to coinpui:c the synth0<'dzcd AA/7 and I>,4S aitributcs at each node \]?om the attrihules at that node on which AdS a,d t'AS direct(y depel~d may bc assumcd to be constant; the operations inwflved are assignment, push, and pop ouly. Asamling f'urthel ~ tlmt the number o\[ empty catc+>~orics hlsc'rted between tcmdnal clement.<; is proportional to the k;rigth of t|lc hiput string, the mmcib~:r of nodes iri the dc, rivation trees generated is proportional to ttl~: input length. Since (:lie AAS and PAS attribuk'.s arc computed at me, st once ai each node, iu the tree, the l~roce, ssing time for the.</Paragraph> <Paragraph position="54"> nc.w Binding rule i.<~ linear -+ a siguificant improve-Hicut over qm abstract specification (6)-(10).</Paragraph> <Paragraph position="55"> \] 2}'</Paragraph> <Section position="1" start_page="126" end_page="126" type="sub_section"> <SectionTitle> 2onclusions </SectionTitle> <Paragraph position="0"> n this paper an attribute-grammar specification of Binding rule for the identification of pronoun and naphor referents has been proposed. The rule ~rovides a correct account of backward reference of qPs, and also of forward reference due to movenent, without recourse to reconstruction. The rule ~resents a model of Binding in which sets of potenial anaphoric and pronominal antecedents are ncrementally defined at each node in a tree.</Paragraph> <Paragraph position="1"> ;torage use may be optimized by use of global '.torage cells, as described by/Sonnenschein, 1985/.</Paragraph> <Paragraph position="2"> n more general terms, tiffs rule presents a trend :omplementary to that of recent linguistic theory.</Paragraph> <Paragraph position="3"> Fhe rule formulation indicates how conditions on 'eprescntations may be incorporated into the rules s, hich generate the representations in the first place. I'his leads to grammars more geared to linguistic ~rocessing, and to which a higher degree of &quot;psy:hological reality&quot; may be ascribed. The rule is a ikely candidate for incorporation in natural language parsers.</Paragraph> </Section> </Section> class="xml-element"></Paper>