Scarcity of crossing dependencies: A direct outcome of a specific constraint?

Abstract

The structure of a sentence can be represented as a network where vertices are words and edges indicate syntactic dependencies. Interestingly, crossing syntactic dependencies have been observed to be infrequent in human languages. This leads to the question of whether the scarcity of crossings in languages arises from an independent and specific constraint on crossings. We provide statistical evidence suggesting that this is not the case, as the proportion of dependency crossings of sentences from a wide range of languages can be accurately estimated by a simple predictor based on a null hypothesis on the local probability that two dependencies cross given their lengths. The relative error of this predictor never exceeds 5% on average, whereas the error of a baseline predictor assuming a random ordering of the words of a sentence is at least 6 times greater. Our results suggest that the low frequency of crossings in natural languages is neither originated by hidden knowledge of language nor by the undesirability of crossings per se, but as a mere side effect of the principle of dependency length minimization.

Are crossing dependencies really scarce?

“…The challenge for future research is to determine the true reason for the low number of crossings in sentences. A long standing hypothesis is that the low number of crossings of real sentences is a side effect of the principle of dependency length minimization, namely, the minimization of the distance between linked vertices in the linear sequence [20,38,26,44]. The low hubiness of real sentences suggests that hubiness may have a secondary role in reducing crossing dependencies.…”

Edge crossings in random linear arrangements

“…In the following subsections, we obtain general expressions for the f ω 's based on the formalization given in [10]. These expressions are designed based on three non-exclusive principles: easing the computation of V * [C], linking with standard graph theory and linking with the recently emerging subfield of crossing theory for linear arrangements ([10, Section 2] and also [8]). In [10], the expressions for the f ω 's were linked with graph theory via (recall Section 2)…”

“…Crossings are scarce in road networks and imply bridges and tunnels [6]. In syntactic dependency networks, C, the number of crossings, has been shown to be low with respect to random linear arrangements of the words of the sentences [7] and predictable to a large extent by the Euclidean distance between syntactically related words: crossings are more likely for dependencies involving distant words, for the range of distances that is typically found in real sentences [8].…”

Inherent Dependency Displacement Bias of Transition-Based Algorithms

“…Other works have investigated different syntactic traits of languages associated with dependency length such as highlighting a correlation with an increase in dependency length and free-order languages (Gulordava and Merlo, 2015) and with an increase in non-projective dependencies (Ferrer-i-Cancho and Gómez-Rodríguez, 2016;Gómez-Rodríguez and Ferrer-i-Cancho, 2017).…”