Conjunct Lengths in E nglish, Dependency Length Minimization, and Dependency Structure of Coordination (2023)

Abstract: This paper confirms that, in English binary coordinations, left conjuncts tend to be shorter than right conjuncts, regardless of the position of the governor of the coordination. We demonstrate that this tendency becomes stronger when length differences are greater, but only when the governor is on the left or absent, not when it is on the right. We explain this effect via Dependency Length Minimization and we show that this explanation provides support for symmetrical dependency structures of coordination (where coordination is multi-headed by all conjuncts, as in Word Grammar or in enhanced Universal Dependencies, or where it single-headed by the conjunction, as in the Prague Dependency Treebank), as opposed to asymmetrical structures (where coordination is headed by the first conjunct, as in the Meaning–Text Theory or in basic Universal Dependencies).

## introduction it has been observed for various particular types of coordination in english that left-most conjuncts tend to be shorter than right-most conjuncts (e.g., @xcite @xcite ). this is illustrated in (1) from the penn treebank (ptb; @xcite ), where the left conjunct, ship, is shorter than the right conjunct, hope i get paid, in terms of the number of words (1 vs. 4), the number of syllables (1 vs. 4), and the number of characters (4 vs. 15, including spaces). however, to the best of our knowledge, there are no demonstrations of this effect that would take all kinds of coordinations into account and that would use various length metrics. filling this gap is the first contribution of this paper. there is even less work that asks whether it is really the left-to-right order of conjuncts that matters here, or whether it is perhaps the closeness to the external head -henceforth, governor. (1), where the governor to is on the left, lends support to both -"leftness" and "closeness" -hypotheses. but the two hypotheses make different predictions when the governor is on the right, as in (2)-(3). the second contribution of this paper is to establish two facts regarding the influence of the governor on conjunct lengths in english. the first fact is that left conjuncts tend to be shorter even when the governor is on the right, which immediately invalidates the "closeness" hypothesis. the second observation is more interesting and has important consequences for dependency theories of coordination: the position of the governor is crucial in how this tendency for left conjuncts to be shorter changes with differences in conjunct lengths. when the governor is on the left, this tendency becomes stronger with increasing length differences between conjuncts, but when the governor is on the right, this effect disappears. the third contribution of this paper is to provide an explanation of this effect in terms of dependency length minimization (dlm) -the robustly demonstrated tendency for natural languages to strive for maximally local dependencies. our explanation is compatible with the view that such distance minimization pressure is at work both at the level of use and at the level of grammar @xcite . the final novel contribution is to demonstrate that this explanation is possible only on two of the four main linguistic approaches to coordination, namely, on the approaches schematically represented in (4)-(5), but not on the other two approaches schematized in (6)-(7). 1 (4) conjunction-headed/prague: , , (5) multi-headed/london: we also show that dlm considerations favour the representation of coordination in the enhanced version of the current treebank annotation standard, universal dependencies (ud; https:// universaldependencies.org/ ; @xcite @xcite , over the basic ud representation of coordination. hence, the empirical results of this paper lend support to the issue of the appropriate dependency structure of coordination both in theoretical linguistics and in corpora. ## data work reported here is based on one of standard syntactic resources, the penn treebank. more precisely, we utilized the version of ptb, which we call ptb & , made available by @xcite . 2 it incorporates earlier corrections of the internal structure of nominal phrases @xcite and -importantly -it improves on ptb by offering explicit and relatively consistent information about coordinations (see @xcite 2016 for details ). unlike treebanks within universal dependencies, ptb & makes extents of conjuncts unambiguous and, in particular, it explicitly marks shared dependents of conjuncts, but it does not explicitly mark heads of constructions, reflect where a given approach is conspicuously assumed: (4) -in the prague dependency treebank ( https://ufal . mff.cuni.cz/prague-dependency-treebank; hajič et al. 2006), (6) -in the stanford dependency parser ( https://nlp . stanford.edu/software/lex-parser.shtml; de marneffe et al. 2006), ( 7 ) -in the meaning-text theory originally developed in moscow @xcite @xcite . in the same spirit, we call the approach in (5) "london", as it is often associated with word grammar @xcite @xcite , developed at university college london. the final evaluation of the program implementing these rules, performed on previously unseen random 100 coordinations, gave the 92% accuracy in locating a specific governor and, crucially, 97% in deciding whether the governor is absent, on the left, or on the right of the coordinate structure. 4 out of about 49,200 sentences (1.25m tokens) in ptb & , 19,095 contain at least one coordination, with the total of 24,446 coordinations. all coordinate structures (i.e., *-ccp nodes) with exactly two conjuncts -21,825 altogether -where automatically extracted from ptb & , together with information about the location of the governor, if any. 5 there were 17,825 coordinations with a governor on the left (13,106, i.e., 73.5%) or on the right (4,719, i.e., 26.5%). the length of each conjunct was measured as in §1: in characters (textual length), in syllables (as in, e.g., @xcite @xcite ; an approximation of spoken length), and in words (as in, e.g., @xcite ; common in discussions of dlm). implementing character and word metrics was straightforward. syllable counting was done with the help of two python libraries: inflect, for converting numbers written with digits to words, and cmudict, for 3 pp stands for prepositional phrase, in is the tag used in ptb for prepositions, to -for various uses of the word to, and vbg -for gerunds. 4 the gold standard for this evaluation was created by two annotators. their initial inter-rater agreement was  = 0.71 for the task of locating a specific governor (or deciding that there is none) and  = 0.74 for deciding on the presence and position of the governor with respect to the coordination. in order to create the gold standard, all differences in annotation where then discussed and resolved. against this gold standard, values of precision, recall, and f1 of the algorithm for the task of deciding that the governor is on the left were: @xmath0.98, @xmath1.97, @xmath2.98, on the right: @xmath3.94, @xmath4.94, @xmath5.94, and absent: @xmath6.95, @xmath7.00, @xmath8.97. ## dependence on governor position the previous section showed that left conjuncts tend to be shorter, even when the governor is on the right. however, this section will demonstrate that the position of the governor matters and that the governor does attract shorter conjuncts to some extent. we first report on an unsuccessful attempt to make this demonstration. if the governor attracts shorter conjuncts, then we might expect more left conjuncts to be shorter when the governor is on the left than when the governor is on the right. moreover, by the same reasoning, when there is no governor, we might expect relevant proportions to be somewhere between those in in summary, comparing total proportions of shorter left conjuncts does not provide us with an argument for the influence of the governor. however, such an influence is clear when we investigate how these proportions change with absolute length differences. figure 1 contains the results of fitting monofactorial binary logistic regression models to the three subpopulations differing in the presence and position of the governor (see the three rows in this figure); this is done for all three length metrics (see the three columns). 9 the figure shows that when there is no governor (the first row of plots) and when it is on the left (the second row), the proportions of shorter left conjuncts grow steadily; in all six cases the probability p that this positive tendency is accidental is well below 0.001. interestingly, the situation changes drastically when we consider coordinations with a governor on the right (the third row). here, the correlation is not significantly positive, and in the case of words it is even (insignificantly) negative. additional multifactorial binary logistic regres8 by contrast, such s or vp coordinations only constitute 24% of coordinate structures with the governor on the left, and 10% with the governor on the right. 9 due to the low number of coordinations with large length differences when the governor is on the right, observations were collected into five buckets defined by the vector ~ = h0, 1, 2, 3, 6, 25i for words, where bucket i contains coordinations with absolute length differences within the interval ( ~ i, ~ i+1]; for syllables and characters the relevant vectors are 2 ⇤ ~ and 6 ⇤ ~ , as an average english word consists of approximately 2 syllables and 6 characters. ## dependency length minimization dependency length minimization (dlm) is the tendency for natural languages to prefer structures with shorter dependencies to those with longer dependencies (for overviews see, e.g., @xcite . this tendency has long been noted in linguistics @xcite , has been confirmed by numerous corpus studies (some of the earliest being @xcite combined with computer simulations (starting with @xcite @xcite , and has received various psycholinguistic and statistical explanations (e.g., @xcite @xcite . as argued in @xcite , this tendency operates both at the level of grammar and at the level of use. at the level of use, when both orders of two dependents are grammatical, the shorter dependent tends to occur closer to the governor -both in headinitial languages, where the short-long tendency is observed (e.g., @xcite @xcite , and in head-final languages, where the long-short tendency is seen (e.g., @xcite @xcite . for example, when two pp dependents of a verb are of similar lengths, both orders are perfectly fine (e.g., sing [in the club] [for an hour] and sing [for an hour] [in the club]), but as length differences between the two pps increase, so does the tendency for the shorter to occur next to the verb (e.g., sing ## dependency structure of coordination the following reasoning is based on the observation that, in english, heads of both conjuncts are on average situated the same -usually short -distance from the left periphery. in the case of pps, vps, cps (complementizer phrases, e.g., that he came; marked as sbar in ptb) and nps on their analysis as determiner phrases @xcite ), this will usually be the left-most word. in the case of nps analysed as headed by the noun, this will be the second word on average (first, in the case of determinerless plurals and mass terms, third when both a determiner and an adjective is present, etc.), in the case of typical sentences the head will be offset by the subject, etc. let us first consider the bouquet/stanford approach. as can be seen in (12a-b), which illustrates coordination with the governor on the left, the total dependency length is smaller when the shorter conjunct occurs on the left (as in (12a)) than when it occurs on the right (as in ( 12b )). the same holds for coordinations with no governor, in which case the head of the first conjunct is the root; see ( 12c-d ). this agrees with the tendencies illustrated in figure 1. however, also when the governor is on the right, as in (12e-f), shorter left conjuncts minimize dependency length. moreover, the gain is the same as in the other two situations: it is the length difference of the conjuncts. so, if the stanford approach accurately reflected dependencies in coordination, we would expect the third row in figure 1 to look the same as the first two rows, contrary to facts. hence, the moscow approach also does not provide a good linguistic model of our empirical findings. on the other hand, the conjunctionheaded/prague approach is compatible with our corpus observations. in this case, when the governor is on the left (see (14a-b)), the dependency minimization gain is twice greater than when there is no governor (see (14c-d)): it is twice the length difference between conjuncts. this larger minimization gain may explain the above observation that the slopes in figure 1 tend to be steeper when there is a governor on the left than when there is no governor. interestingly, unlike in the case of the previous two approaches to coordination, relative conjunct lengths do not matter for dependency length minimization when the governor is on the right (see (14e-f)). hence, the prague approach makes it possible to explain the effects observed in figure 1 and, moreover, the explanation is purely at the level of use: it does not invoke any conventionalized effects of dlm. let us finally consider the multi-headed/london approach. at first, it seems incompatible with our empirical findings: when the governor is on the left (see (15a-b)), shorter left conjuncts minimize dependency length, as confirmed by empirical observations, but when there is no governor (see (15c-d)), lengths of conjuncts do not matter for dependency minimization, and the significantly positive slopes in plots in the top row of figure 1 remain unexplained. moreover, when the governor is on the right (see (15e-f)), shorter right conjuncts seem to minimize dependencies, so the lines in the third row of figure 1 are expected to have significantly negative slopes, symmetrical to the positive slopes of lines in the middle row, contrary to facts. however, the london approach to coordination is compatible with figure 1 on the assumption that the at-use pressure for shorter left conjuncts in the majority of governed coordinate structures is conventionalized as an at-grammar preference for shorter left conjuncts. that is, just as in the case of np and pp dependents of verbs, dlm may be assumed to work in coordination both at the level of use and at the level of grammar. in the case of coordination with no governor, where there are no at-use preferences for relative conjunct lengths (see (15c-d)), this at-grammar preference still has the effect that shorter conjuncts are preferred on the left, as seen in the top row of figure 1 . moreover, this at-grammar preference makes it possible to explain the steeper slopes when the governor is on the left (the middle row), namely, as an additive effect of the at-use pressure (see (15a-b)) and the at-grammar convention. finally, in the case of governor on the right (see (15e-f)), the at-use pressure for shorter right conjuncts is at conflict with the at-grammar preference for shorter left conjuncts, and they seem to largely cancel each other out, as observed in the third row of figure 1 . in partial summary, out of the four standard dependency approaches to coordination, only two make it possible to explain the curious tendencies in figure 1 as dlm effects, with dlm operational either only at use (the prague approach) or both at use and at grammar (the london approach). paradoxically, while these tendencies are not symmetrical -shorter left conjuncts are preferred when the governor is on the left (or absent), but there is no clear preference either way when it is on the right -the two approaches that are compatible with it are symmetrical in the sense that they treat both conjuncts on par. on the prague approach, coor-dination is headed by the conjunction and each conjunct is its dependent, while on the london approach coordination is multi-headed -equally by the head of each conjunct. this should be contrasted with stanford and moscow approaches, in which coordination is -asymmetrically -headed by the first conjunct. interestingly, more symmetrical variants of these two asymmetric approaches to coordination are compatible with the empirical observations in figure 1. to see that, consider the simple variants of the "first conjunct is the head" approaches in which coordination is still headed by the first conjunct when there is no governor, but otherwise it is headed by the conjunct closer to the governor. such variants may be justified by the occasional observations that, in various languages, the governor seems to have a special relation to the closest conjunct, e.g., in the phenomenon of closest conjunct agreement (see nevins and weisser 2019 for an overview). these variants differ from the original approaches only when the governor is on the right, i.e., only in configurations in which the original approaches were incompatible with corpus findings: the vanilla ud standard follows the stanford approach to coordination. enhanced ud retains all dependencies of the vanilla ud and adds dependencies from the governor to all non-initial conjuncts. 12 in (18), there are two such eud-specific dependencies from the governor to non-initial conjuncts (drawn in red above all other dependencies). note that removing some of the basic ud dependencies, namely, those which are shown in (18) as dashed arcs, would make the structure purely multiheaded. but, as it stands, the full eud structure contains all dependencies of both approaches: stanford and london. it turns out that, because of that, such structures are compatible with the empirical findings of this paper. as can be seen in ( 19 ), shorter left conjuncts again minimize dependency lengths when the governor is on the left (see (19a-b)) or absent (see @xcite ). however, when the governor is on the right, the total dependency length does not depend on the order of conjuncts (see (19e-f)). this is compatible with the empirical findings of this paper in a way fully analogous to how the prague approach fits these empirical findings. we conclude that, out of the theoretical linguistic approaches to the dependency structure of english coordinations, both conjunction-headed/prague and multi-headed/london approaches may explain the patterns observed in ptb & . in particular, the results of this paper provide an argument against the theoretical linguistic validity of the basic version of the universal dependencies standard, commonly used in nlp applications, given that basic ud implements the bouquet/stanford approach. however, they also provide support for the enhanced version of this standard, which -on top of dependencies present in basic ud -adds dependencies from the governor to each conjunct, thus making the structure effectively multi-headed. ## previous work this work carries out the research program briefly suggested in @xcite iven the strong evidence for dlm, a finding that one syntactic analysis of (say) coordinate phrases resulted in shorter dependencies than another analysis [. . . ] could be regarded as a strong point in its favor." the only earlier attempt to do that that we are aware of is temperley 2005. it identifies 6 constructions with the governor on the left and 3 with the governor on the right and attempts to extract them from the original ptb, reporting that "in many cases [relevant dependencies] can be inferred quite reliably from the constituent structures". temperley shows that -in these constructions -left conjuncts tend to be shorter in terms of words, even when the governor is on the right. temperley considers two dependency approaches to coordination, multi-headed/london and chain/moscow, and argues that both are compatible with this tendency: the moscow approach at the level of use, and the london approach at the level of grammar. by contrast, we show that dlm must be at work in english coordination at both levels in order to be compatible with the multiheaded/london approach and, crucially, that the observed facts cannot be explained via dlm by asymmetrical approaches such as chain/moscow. 13 while @xcite does not consider the dependence of the proportion of shorter left conjuncts on the length difference between conjuncts, this effect is demonstrated by @xcite . they show that, in np coordinations in ptb and in the brown corpus @xcite , proportions of shorter left conjuncts grow proportionally to length differences between conjuncts. while they do not consider the dependence of this effect on the presence and position of the governor, so they do not notice that this tendency disappears when the governor is on the right, their results are broadly compatible with ours. 14 apart from these two highly relevant previous publications, there is little corpus work on the order of conjuncts in coordination, the most important being lohmann 2014. while it is limited to english nominal coordinations, it confirms the short-long tendency (measured in syllables there) observed elsewhere, but also shows that semantic factors have a stronger effect (where applicable), which explains why -even when differences in length are very large -the proportion of shorter left conjuncts is still much lower than 1. ## conclusion this paper makes the following empirical contributions: 1) it demonstrates -more robustly than previous work -the general short-long tendency in binary coordinations in english, and 2) that this tendency also holds for coordinations followed by their governor. the novel observation is 3) how this effect depends on differences in conjunct lengths and on the position of the governor: the strong statistically highly significant positive correlation between length differences and proportions of shorter left conjuncts disappears when the governor is on the right. on the theoretical side, 4) we argued that this effect is explained by dlm, possibly operating at both levels: use and grammar, and 5) that this explanation is only possible when the symmetrical dependency structures of coordination are assumed. to the extent to which no other explanations of the effects observed in figure 1 are forthcoming, this provides an argument for the linguistic validity of symmetrical approaches to coordination such as conjunction-headed/prague and multiheaded/london and against those approaches which assume that coordinations are headed by the first conjunct, such as bouquet/stanford and chain/moscow approaches.