Breaking Ties: Some Methods for Refactoring RST Convergences (2025)

Abstract: Among the set of schemata specified by Rhetorical Structure Theory is a pattern known variously as the request schema, satellite tie, multisatellite nucleus, or convergence. The essential feature of this schema is that it permits multiple satellites to attach to a single nucleus. Although the schema has long been considered fundamental to RST, it has never been subjected to detailed evaluation. This paper provides such an assessment. Close examination shows that it results in structures that are ambiguous, disjoint, incomplete, and sometimes incoherent. Fortunately, however, further examination shows it to be unnecessary. This paper describes the difficulties with convergences and presents methods for refactoring them as explicit specifications of text structure. The study shows that convergences can be more clearly rendered not as flat relational conjunctions, but rather as organized expressions of cumulative rhetorical moves, wherein each move asserts an identifiable structural integrity and the expressions conform to specifiable scoping rules.

## introduction among the fundamentals of rhetorical structure theory is a set of abstract relational patterns, one of which permits linking multiple satellites to a single nucleus. this pattern has been referred to variously as the request schema, satellite tie, multisatellite nucleus, and convergence. opinions vary as to the validity of this schema. it was baselined in @xcite original rst specification, endorsed by @xcite and by @xcite , but rejected by @xcite as well as by @xcite . however, none of these studies, either pro or con, has provided any rationale for the position taken. that leading researchers in rst disagree over a fundamental property of satellite-nucleus structures and yet provide no grounded account for the discourse pattern is concerning. this has implications for rst parsers and other applications, as well as for the theory's efficacy in describing discourse. moreover, if the schema is to be rejected, what criteria are to be applied in determining the structures used in its stead? thus, the motivation for this study is not merely theoretical, but is of practical interest as well. our primary finding is that the convergence is problematic. convergences are found to be functionally ambiguous, implicitly disjoint, structurally incomplete, and sometimes incoherent. these problems arise, due not to any issue in the texts under analysis, but as a result of the analytical abstraction itself. the good news, however, is that convergences are also entirely unnecessary. moreover, their avoidance results in greater functional specificity than would otherwise be attainable. since it is possible to produce highresolution analyses without using convergence, and since the status of convergence is questionable at best, methods for refactoring rst convergent structures should be of interest. the process for inferring asymmetric structures from convergences is referred to as refactoring. we implemented and assessed three refactoring algorithms. the first of these we call the chaining method. using chaining, the convergence is restructured as a sequence of relations in which each successive satellite feeds into the satellite next closest to the nucleus. although such patterns do occur in rst discourse, refactoring convergences as chains did not usually result in plausible rst analyses. the second algorithm is limited to ## related work two closely related theories of text organization are foundational to this research. the first of these is, obviously, rhetorical structure theory. rst is a conceptual framework that explains clausal text organization in terms of the way the text spans comprising the text relate to one another @xcite . rst postulates a small number of patterns (or schemas) for defining the structural possibilities among spans, and it defines a set of rhetorical relations for use when applying a schema to the text spans. second, relational propositions, also developed by @xcite , are implicit coherence-producing assertions that serve to bind together explicit parts of a text and are essential to the effective functioning of the text. rst analyses and relational propositions are isomorphic. for every relation in the rhetorical structure, a corresponding relational proposition is asserted @xcite . @xcite extended man and thompson's theory of relational propositions to make it interchangeable with rst. this included development of a predicate notation conformant with the python programming language. this enables the treatment of rst analyses as data, code, or diagrams, serving as an enabling research technology. the refactoring methods used here were implemented as python scripts, all working within this framework. a key addition to this is a program developed to reverse the process, transforming relational propositions back into rst, storing the result as rs3/xml files, the format developed by @xcite and the de facto data sharing format for rst. an overview of endto-end refactoring is shown in figure 1 . this software was used to generate the refactored analyses directly from the originals. the use of convergent structures has been widely accepted among many rst researchers. they appear regularly in the seminal publications of mann and thompson, and they have been used without question in numerous other research publications (e.g., @xcite @xcite . a few researchers have, however, sown seeds of doubt. @xcite suggested that, to the extent that discourses could be analyzed as trees, the possibility of convergent structures seemed unlikely. their assumption was that relations interpreted as tree nodes could have no more than one parent. they further suggested that convergent structures might be genre-dependent, perhaps found mainly in fund-raising letters, as found in studies by @xcite and @xcite . however, the corpora examined in this study suggest that the use of convergences is in fact broadly applied across multiple genres. about a third of the analyses in the potsdam corpus @xcite , and one fourth of the analyses in the online learning corpus @xcite contain at least one convergence. since this structural pattern is at best unnecessary (as this paper demonstrates), perhaps its presence or absence has more to do with analyst preference than with any particular genre. @xcite viewed rst convergent (as well as other) relations as static and discrete, such that each relation is to be understood in isolation from its neighbors. thus they viewed satellites of convergences as independent or separate modifications to the nucleus. this would suggest that a convergence is merely a diagrammatic overlay of unrelated structures, rather than an integrated explanation of text organization. the interpretation described in this paper provides an alternative view, that the assertion of a relational proposition is a discursive event with an identifiable effect, such that multiple interrelated relational propositions will have a developing effect, and these effects are observable by means of refactoring. that this should be the case becomes clear when considering the incoherence that arises when inconsistent satellites are associated with a shared nucleus. as far as we know, zeldes (2023) and @xcite are the only researchers who have rejected convergences (or satellite ties, in zeldes' terminology). although zeldes used convergences in earlier research (2016), more recent versions of the gum corpus contain no convergences, but rather follow a strict hierarchical regimen @xcite . ## the corpus as mentioned above, the corpus consists of 279 rst analyses drawn from a variety of research publications and open-source corpora. all analyses include at least one convergent relation. some basic examples come from mann and thompson's early rst publications @xcite . others were chosen selectively, including papers by @xcite and by @xcite . these include satellite-nucleus-satellite patterns they identified as of special interest (discussed in section 5.3). @xcite example of convergence as list motivated the evaluation given in section 5.2. others are from @xcite , @xcite , @xcite , @xcite , @xcite , and zeldes (2017), whose evolving gum news worship analysis provides external validation of the ladder method described in section 5.3. the critical mass of analyses come from open-source corpora. these include 12 analyses (translated into english) from the potsdam commentary corpus of german newspaper editorials @xcite , 14 messages from the sts-corpus of listserv emails exchanged in a scholarly debate @xcite ## the refactoring software the software developed for this research leverages two open-source applications. the first of these converts rs3 formatted rst files into pythonic relational propositions. the second evaluates nested relational propositions as python expressions, with each relation defined as a function. both algorithms are described in detail by @xcite . we also developed a script that converts pythonic relational propositions to rs3 format for end-to-end interchangeability. the software, as well as the corpus used in this study are as open source from github. ## problems with convergence there has been a longstanding tendency to treat rst analyses as top-down hierarchies. this follows from the orientation of the diagrams and has been reinforced by marcu's strong nuclearity assumption. and yet, unless we wish to view satellites as dispensable, we must recognize that a nucleus obtains its stature from the satellites that support it. to understand what is happening in an rst diagram, then, it is appropriate to start at the bottom of the structure, with the outermost extremities, and follow the arrows through the series of relations to the ultimate locus of intended effect. within the structure, span nodes function as precedence operators, nesting the relational propositions, one within one another, building outward @xcite . this is what gives rst structures their tree-like appearance. in contrast to this, convergences have a flattening effect on the structure. a convergence asserts that multiple relational propositions terminate on a shared convergence( concession( 1,2), restatement( 3,2)) concession( 1, restatement( 3,2)) convergence( concession( 1,2), restatement( 3,2)) concession( 1, restatement( 3,2)) nucleus, with each satellite occupying a shared level of precedence. but this misrepresents what happens in discourse. consider the convergence shown in figure 2 . it contains two rhetorical moves, one corresponding to relational proposition motivation(1,3) and the other to relational proposition enablement(2,3). the intended effect of the first relational proposition is to motivate the reader to make the call, and the intended effect of the second is to enable the reader to make the call. these effects enact separate moves. that the writer has deemed both moves as necessary to achieve the shared effect informs us that their synergy is realized cumulatively, not simultaneously. this means that either enablement is subordinate to motivation, or motivation is subordinate to enablement. the precedence within the text is unspecified in the diagram. similar difficulties arise when satellites converge to the right of the nucleus. and if the satellites are repositioned so that one precedes the nucleus and another follows, although the disjuncture is avoidable, the ambiguity persists. either the left-hand side takes precedence over the right, or the right over the left. in their discussion of what they called the satellite-nucleus-satellite (sns) pattern @xcite proposed that convergences similar to this are argumentatively strategic. however, the strategy they describe, while perhaps evident in the text, is unsupported by the symmetry of the convergent structure. for rst to do its work, any such strategy must be reflected in the structure. but convergent structures conceal rather than present this structural functionality. and this is only the beginning of the problem. convergences such as motivation-enablement may seem readily intuitive, with each proposition contributing to a shared intentionality. and convergences consisting of pilings-on of multiple instances of identical relations, such as repetitive elaboration relations likewise have intuitive appeal. @xcite syncom analysis is a good example of this. but this intuitiveness masks a difficulty. rst schemas place no constraints on what relations may be combined, allowing a mix of any sort whatsoever. this might at first seem reasonable, as it would seem the text under analysis should be the deciding factor. but in practice this results in some odd bedfellows. consider this example from ducasse and brown (2023), shown in figure 3 . as far as classic rst is concerned, there is no problem here. that there is a concession relation from unit 1 to 2 seems clear, as is the restatement from 3 to 2. however, the analysis as a whole is problematic. as analyzed, the scope of the concession relation applies only to unit 2, and the scope of the restatement also applies only to unit 2. but if unit 3 is indeed a restatement of 2, the scope of the concession will be applicable to both 2 and 3. there is a structural discrepancy with the analysis arising, not from the choice of relations, but from the use of convergence. disorganizations of this sort become more pronounced with complex structures. but rst has everything it needs to make the development explicit. convergence is not among them. and that is a problem that can be addressed by refactoring. ## refactoring convergences refactoring consists of a set of methods for restructuring convergences to conform to satellitenucleus, nucleus-satellite, or multinuclear patterns. as shown in figure 4 , chaining links successive satellites, each attaching to its successor in a stairstep pattern; listing groups convergent satellites as multinuclear list; and laddering links satellites to a cumulative nuclear span using the most direct path available. a scoping heuristic is provided for determining satellite subordination when the convergence straddles its nucleus. all three methods conform to the minimal rst constraints for completeness, connectedness, uniqueness, and adjacency. beyond that, their differences are considerable. figure 2. convergence as a set of distinct rhetorical moves (mann & thompson, 1986) ## conclusion precedence and scoping are fundamental to the representation of discourse processes. the order of moves depends on satellite positioning with respect to the nucleus and to neighboring satellites. the closer a satellite is to its nucleus, the higher its precedence. with satellites to the right of the nucleus, precedence decreases with each successive satellite. the contribution of each is evaluated in light of its predecessor. satellites to the left of the nucleus gain precedence the closer they are to the nucleus. like the right-hand side, the effects are cumulative, but rather than reinforcing, the effect is anticipatory, such that they lead up to and prepare for the locus of intended effect. the interchangeability between rst diagrams and relational propositions supports scalability, consistency, and reproducibility. one might well ask, however, if convergences are so undesirable, how is it that rst has gotten along with them so well for so long? even assuming refactoring is an improvement, is it significant? these questions go to the heart of what makes rst interesting. rst has been used in a wide range of applications, and yet these applications tend to make little use of the diagrams per se. yet it is the diagrams that make rst distinctive. in this light, we can say that while an rst analysis is an articulation of the intentional structure of a discourse, an rst diagram is a pointby-point account of a discourse process. the process initiates with the outermost elementary relational propositions. these propositions join to form more complex expressions which ultimately specify the comprehensive discourse process terminating with the ultimate locus of intended effect. thus, the process of reading of a diagram is, rather than a top-down activity, a bottom-up process, a process of following the arrows. as we consider rst diagrams as pictures of processes, we raise the possibility of concurrent threads. recent work by @xcite indicates that concurrent relations are common. although little attention has been given to simultaneous analyses, might not the ambiguity of convergent structures suggest that simultaneity may be more common than has been hitherto supposed? although the scoping criteria for determining precedence between left-and righthand satellites appear generalizable, there might be sufficient exceptions to make simultaneity commonplace. further studies in which rst diagrammatic semantics are a focus, not merely representations of analyses, would be useful here.