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<?xml version="1.0" standalone="yes"?> <Paper uid="C00-1016"> <Title>Binding Constraints as Instructions of Binding Machines</Title> <Section position="2" start_page="0" end_page="106" type="metho"> <SectionTitle> 1 The Cohldexation Paradigm </SectionTitle> <Paragraph position="0"> The specification of binding constraints have greatly evolved in the htst three decades. The device of coindexation for marking anaphoric links has, however, remained quite stable. This stems from the fact this device is at the heart of the mainstrealn nlethodology for verifying these constraints, a methodology whose basics were proposed in (Chomsky, 80, 81) and have been adopted since then in its different variants.</Paragraph> <Paragraph position="1"> L1 Post-grammaticall overgerieratior~ and filtering This methodology can be outlined as in Fig. 1. After the grammatical parsirig of a seriterice with n NPs has been completed: (i) iteration:repeat (ii)-(iii) uritil all possible different assignments of n indices (tokens) have been exhausted; (ii) indexation:generate a tree by assigning indices to its NPs; (ill)filtering:store the arniotated tree if the indexation of NPs respects binding constraints, otherwi'~e dc:letc it.</Paragraph> <Paragraph position="2"> Fig. 1 * ('/wm,vk),'.v al:;()idegithm As noted as early as in (Correa, g/'), thi:~ approach is grossly inefficient. Later Fong, 90deg showed that its complexity is of exponential order. Moreover, this methodology disregards any concern with interfacing grarnmar with systems for reference processing. The input for such systems will riot l)c a grammatical representatiori to lie refined vis4-vis the heuristics for anaphor resohition, but a forest of differently labeled trees that have to be internally searched and compared with each other by anaphor resolvers.</Paragraph> <Paragraph position="3"> Besides the efficiency issue, this methodology implies the conceptual awkwardne.,;s of having a <2 tnodnle of ~rammar that is not made operative ~,ranallaatical processing, but as an during the <2 extra-grammatical add-on. Correa, 88, p.123~ observed that although the integration of binding constraints &quot;into rules which rnay be used to derive structure that already satisfies the \[constraints\] is not a straightforward task&quot;, that should be the path to follow, a point also strongly stressed in subsequent elaboration o11 this isstie by Merle, 93.</Paragraph> <Section position="1" start_page="104" end_page="105" type="sub_section"> <SectionTitle> 1.2 Packaginganaphoric ambiguity </SectionTitle> <Paragraph position="0"> A first proposal for enhancing integration of binding cosntraints into grammar is due to Correa, 88. Simplifying some details, the proposed algorithm can be outlined as in Fig.2.</Paragraph> <Paragraph position="1"> Start fl'om the top of the tree with two empty stacks A and B where indices will be collected, respectively local c-commanding indices and non-local c-commanding indices.</Paragraph> <Paragraph position="2"> While walking down a tree where every NP l-ias a distinct index (type): When an NP is found: (i) copy:leave a copy of A (if it is an anaphor) or B (if it is a pronoun) at the NP node; (ii) a,vsign:take the first index i of the stack copied into the NP node., take the NP iridex j, and annotate the NP with j=i; (iii) collect:add NP index j to A.</Paragraph> <Paragraph position="3"> When a local domain border is crossed: (iv) reset:reset B to A m:B.</Paragraph> <Paragraph position="4"> t,'i,g-. 2 -, Cor/ea's a&orithm This algorithm was given two different implementations, one by Correa, 88, the other by Ingria and Stallard, 89. Further elaboration by Giorgi et al., 90, and Pianesi, 91, led to a restatement of this algorithm using formal language techniques.</Paragraph> <Paragraph position="5"> The do-it-while-parsing approach of Correa's implelnenlation has the advantage of discarding )OSW a special-purpose \[ .' erammatical module for binding. That iml~lementation, however, tulns out to be del)cndent on a top-down parsing strategy. On the other hand, lngria and Stallard's implementation has the advantage of being indelmridenl of the parsing strategy adopted. This was done however at the cost of still requiring a special purpose postgrammatical parsing module for binding.</Paragraph> <Paragraph position="6"> Besides the issue of bringing binding into grammar, it is worth noticing that this evolution inside the coindexation paradigm presented a significant improvement and yet a clear drawback. On the one hand, if one disregards step (ii) (a disguised recency heuristic spuriously mixed with binding constraints) and considers the result of verifying binding constraints to be the assignment to an NP of the set of indices of its antecedent candidates, then it is possible to discard the proliferation of indexed trees as a way to express anaphoric ambiguity.</Paragraph> <Paragraph position="7"> On the other hand, the algorithm is acknowledged not to be able to cope with constraints possibly involving non-local anaphoric links. Principle C, backwards anaphora or cross-over cases were not accounted for (Correa, 88, p.127, Ingria and Stallard, 89, p.268). Moreover, as stack B only contains indices of the non-local c-commanders 2, but not all indices in the tree except those of the local c-commanders, Principle B is also not correctly accounted for.</Paragraph> </Section> <Section position="2" start_page="105" end_page="106" type="sub_section"> <SectionTitle> 1.3 Packaging non-locality </SectionTitle> <Paragraph position="0"> Other contributions to improve the coindexation method are due to Dalrymple, 93 and Johnson, 95. Instead of being directed to packaging ambiguity as the one above, they have in common being concerned with packaging non-locality.</Paragraph> <Paragraph position="1"> 1.3.1 Nodes as mirrors of trees Johnson's algorithm is embodied in Prolog code. Abstracting away from details associated to that format, it gets the outline in Fig.3.</Paragraph> <Paragraph position="2"> 2 C-command is a configurational version of the command relation where x c-commands y iff the first branching node that dominates x dominates y.</Paragraph> <Paragraph position="3"> Although this outline renders the algorithm in a bottom up fashion, Johnson ingeniously developed an implementation that is independent of the parsing strategy resorting to delaying mechanisms. Crucially, in spite of its post grammatical flavor, likewise Correa's implementation, this algorithm does not require postgrammatical processing.</Paragraph> <Paragraph position="4"> These results were obtained with some (i) Repeat (ii) until all NP~ (l<_i_<n) in the tree have been used as starting points; (ii) Walk up the tree from NPi and repeat (iii) until the top node of the tree is reached; (iii.i) When other locally c-commanding NPj is found: (iii.i.i) if NPi is a short-distance reflexive, annotate NPi with i=j; (iii.i.ii) if NPi is a non-reflexive, annotate NP~ with i:~j; (iii.ii) When other non-locally c-commanding NP 3 is found: if NP~ is a non-pronoun, annotate NP~ with i~j.</Paragraph> <Paragraph position="5"> Fig. 3 - .lohnson's algorithm accessory devices: Each node in the tree is &quot;conceptualized as a pair consisting of a tree and a vertex in that tree&quot; (p.62). Consequently, the whole tree where a given NP appears is locally accessible to be &quot;walked up&quot; since its replica is present at the pair (Category, Tree), which is the NP node itself.</Paragraph> <Paragraph position="6"> This algorithm improves the coindexation methodology in terms of efficiency as it does not resort to free indexation. Note, however, that the anaphoric ambiguity of pronouns and nonprououns is not captured (Principles B and C) since grammatical coindexation of pronouns or nonpronouns with their possible antecedents is dismissed. Only reflexives and their antecedents end up coindexed, while the index of a pronoun is only made &quot;unequal&quot; with the indices of its (non-grammatical) locally c-commanding antecedents. Nevertheless, even dispensing with free indexation and restricting the representation of anaphoric ambiguity to reflexives, this approach does not get rid of the proliferation of trees: For a given reflexive, each corresponding tree/coindexation represents a different antecedent candidate.</Paragraph> <Paragraph position="7"> The I_,FG/I)alrymple, 93, account of binding resorts to a different approach to generalize over the eventual non-locality of anaphoric links. It uses lexical &quot;inside-.out equations&quot;, a special-purpose extension of the description formalism which may include regular' expressions (as in (3) below for long-distance reflexives): (1) John/introduced Billj to himself//)-.</Paragraph> <Paragraph position="8"> kimse(\[! ((()Bi-c;<,,,i &quot;1&quot; ) SUB J) o. = 1&quot;c~ or ((()13L(;<,~u &quot;1&quot; ) ()B\])c ~ = ~'o (2) *John introduced Bill/to hirrli.</Paragraph> <Paragraph position="9"> him: ((()BI<<,:,I I&quot; ) ()BJ)o. ~ &quot;i&quot; o. (3) Zhangsani yiwei \[LMi yiwei\[...z_~i_i/j/k/...\]...\]</Paragraph> <Paragraph position="11"> The right-hand side of the equation stands for the sernantic representation (c~) of tile functional-strncture ('\]') of the anaphor. The left hand side stands for the semantics of the antecedent: In (3) the Chinese long-distance reflexive is an Object in a functional--structure where one of the upstairs Subjects may be the antecedent.</Paragraph> <Paragraph position="12"> Although initial scepticism about the tractability of these equations was dissipated by Kaphm and Maxwell, 88, the survey by Backofen et al., 96, reports that no iml~lemented I,FG grammar was known to handle binding. To a significant extent this bears on tile fact that many different equations have to be defined for every anaphor: Each equation specify concrete grammatical functions for the anaphor and its potential antecedent, but either the anaphor or the antecedents may occur with one of a range of several grammatical functions (see a n-finimal ex,'lnlple ill (1)). Moreover, it is not defined how non-lexical NPs (e.g. anaphoric definite descriptions, ruled by Principle C) may be assigned the respective equation.</Paragraph> <Paragraph position="13"> However these difficulties turn out to be solved, the LFG variant of the coindexation methodology presents the same type of problems of Johnson's approach. The proliferation of representations is not avoided: The ambiguity of reflexives may end up represented by several different grammatical representations. These representations correspond to the satisfaction of the different equations involving different grammatical functions, as in (1), and possibly result also from the several existential interpretations of functional tmcertainty in the case of long-distance reflexives, as in (3).</Paragraph> <Paragraph position="14"> Likewise, the ambiguity of pronouns is omitted in the single functional-structure resulting from the universal interpretation of negative equations associated with these anaphoric expressions.</Paragraph> <Paragraph position="15"> Moreover, the positive equations for reflexives do not require identity of indices between anaphorically related expressions, but instead impose identity of semantic representations, this way incorrectly enforcing any type of anaphora (bound, bridging, e-type, &quot;donkey&quot;, etc.) to the sole modality of coreference.</Paragraph> </Section> </Section> <Section position="3" start_page="106" end_page="107" type="metho"> <SectionTitle> 2 The Concept of Binding Machine </SectionTitle> <Paragraph position="0"> Being partially successful in overcoming problems of tile original post-gramnmtical &quot;overgenerate & filter&quot; methodology, each of tile contributions mentioned above brought to tile fore essential dimensions of binding that have to be concomitantly acconnted for. Accordingly, an alternative methodology for binding constraints verification should find a way to harmonize all these dimensions: lexicalization, anaphoric ambiguity, packaging and non-local context packaging.</Paragraph> <Paragraph position="1"> Given these hints, a breakthrough depends now on changing some entrenched primitives underlying the conception of binding constraints. These constraints have been basically taken as syntactic well conditions: &quot;\[they\] capture the distribution of pronouns and reflexives&quot; (Reinhart and Reuland, 93, p.657). In line with Gawron and Peters, 90, however, we take them as conditions on semantic interpretation, as they delimit non-local aspects of meaning composition.</Paragraph> <Paragraph position="2"> In what follows, we set up a semantics-driven methodology for verifying binding constraints, organized under the rationale that an NP is a binding machine: (i) it reads a representation of the context; (ii) updates its own semantics given this context and its own anaphoric potential (in accordance with its binding constraint, if it is a non-quantificational NP); (iii) and makes a contribution to the context, against which other NPs are interpreted. This rationale is in line with the insights of Johnson and Klein,90 concerning the processing of the semantics of nominals, and also the spirit (but by no means the letter) of the dynamic semantics framework (Chierchia, 95).</Paragraph> <Paragraph position="3"> The output of a nominal n as a binding machine is simply the incrementing of the context with a copy of its reference marker (Kamp and Reyle, 93). The internal state of the machine after its operation is a compacted representation of the anaphoric potential of n, if any, under the form of the set of the reference markers of the grammatically admissible antecedents of n -this internal state results fiom the binding constraint, lexically associated to n, being applied to the input. The input is a representation of the relevant aspects of the context under the form of a set of three lists of reference markers, A, Z and U, from which the internal state/semantics of anaphors can be computed.</Paragraph> <Paragraph position="4"> Taking n and its subcategorizing predicator p, A is the list with the reference markers of the complements of p ordered according to their relative obliqueness; Z includes the elements of A plus the reference markers of the upstairs predicators directly or indirectly selecting the domaiu of p, observing the multiclausal obliqueness hierarchy; and U is the list of all reference markers in the discourse context.</Paragraph> <Paragraph position="5"> Given this setup, the verification of binding constraints consists in a few simple steps. If n is a short-distance reflexive, A' is associated to its semantic representation, where A' contains the reference markers of the o-commanders of n in A. If n is a long-distance reflexive, its semantic representation includes Z', such that Z' contains the o-commanders of n in Z. If n is a pronoun, the set B=U\(A'u{refin,,}) is coded into its representation. Finally if n is a nonpronoun, its semantics keeps a copy of C=US(Z'u{ refin,,}).</Paragraph> </Section> <Section position="4" start_page="107" end_page="108" type="metho"> <SectionTitle> 3 An HPSG exercise </SectionTitle> <Paragraph position="0"> This methodology can be easily accommodated in a unification-based framework such as HPSG.</Paragraph> <Paragraph position="1"> We designed an extension to the UDRT component for HPSG of Frank and Reyle, 95.</Paragraph> <Paragraph position="2"> This component is encoded as the CONT(ENT) value, which is enhanced now with feature ANAPH(ORA). On a par with this extension, also the NONLOC(AL) value is extended with the new feature BIND(ING), with subfeatures LIST-A, The relational constraint ~on-loc-ocomm takes (in first argnnlent) all markers in the context. ~iven in LISI'-U wflue, and remove l'rom them both the local o-commanders (included in second argunrent) of tlie t)ronoun and the pronoun itself (in third argument).</Paragraph> <Paragraph position="3"> Under the conception of nominals as binding machines, LISTSA, LIST-Z and LIST-U stand for the input, ANTEC(EDFNTS) encodes the internal state, and REF(ERENCE)M(ARKF.R) encodes the output. The SYNSEM of other anaphors, ruled by Principles A, C or Z, art quite similar to the one above. The major difference lies in the relational constraints in ANTEC value, which encode the corresponding binding constraint 3.</Paragraph> <Paragraph position="4"> Turning now to the lists with reference markers, we handle them by means of a new HPSG principle, the Binding I)omains Principle. This principle consists of three clauses constraining signs and their values with respect to these lists. I)ue to space limitations a, we illustrate this Principle with its ('lause 1, for LIST-U and LIST-protoU: Binding Domain~ Principle, Clause I (i) in every sign, LlST-protoW value is identical to the concatenation of LlST-protoU values of its daughters; (ii) in a sign of sort discourse, I,IST-protoU and LIST-U wflues are token-identical; (iii) in a non-NP sign, LIST-U wflue is token-identical to each LIST-U value of its daughters; (iv) in an NP sign k: (iv.i) in Spec-daughter, LIST-U value is the result of removing the elements of LIST-e\ value of Head-daughter from the I,IST-U value ot' k; 3 Binding constraints fin non-lexical nominals are lexically stated in their determiners.</Paragraph> <Paragraph position="5"> 4 Binding constraints are fttlly integrated in a computational lIPS(; gramma,, documented in (Branco, 99).</Paragraph> <Paragraph position="6"> (iv.ii) in Head-daughter, LIST-U value is the result of removing the value of REFM of Spec-daughter from the IJST-U value of k.</Paragraph> <Paragraph position="7"> The HPSG ontology was extended with the sort discourse corresponding to sequences of sentential signs. Subclause (iv) above is meant to avoid what is known as i-within-i effect.</Paragraph> <Paragraph position="8"> Conclusion In this paper we designed an alternative to the mainstream postgrammatical &quot;overgenerate & filter&quot; methodology for the verification of binding constraints. Our semantics-driven methodology is based on the conception of NPs as binding machines. We showed how this innovation helped to integrate binding constraints into grammar representation and processing and to avoid the intractability implied by the mainstream methodology.</Paragraph> </Section> class="xml-element"></Paper>