Formal Constraints on Dependency Syntax

Abstract

Dependency syntax represents the structure of a sentence as a tree composed of dependencies, i.e., directed relations between lexical units. While in its more general form any such tree is allowed, in practice many are not plausible or are very infrequent in attested language. This has motivated a search for constraints characterizing subsets of trees that better fit real linguistic phenomena, providing a more accurate linguistic description, faster parsing or insights on language evolution and human processing. Projectivity is the most well-studied such constraint, but it has been shown to be too restrictive to represent some linguistic phenomena, especially in flexible-word-order languages. Thus, a variety of constraints have been proposed to seek a realistic middle ground between the limitations of projectivity and the excessive leniency of unrestricted dependency structures.

Figures (9)

• Figure 1: A dependency tree in Universal Dependencies format for an Irish sentence ("A large bed dressed in a yellow silk blanket"). The root is shown in boldface.
• Figure 2: Projectivity and 1-planarity. For each tree, the root is shown in boldface, and we show the projection of the word highlighted in italics. The top tree is projective and planar (the continuous projection of account is highlighted). The tree in the middle is planar, but not projective (the projection of перевірити is discontinuous). The bottom tree is neither projective nor planar (it has a discontinuous projection and arc crossings, marked with red circles). The second sentence is taken from a Ukrainian UD treebank (version 2.6); it can be translated as ""You might want to check out what it's like around ... 2023," O'Reilly joked". The third sentence is taken from a Czech parallel UD (PUD) treebank (version 2.6); it can be translated as "The Dutch students have yet to decide if they will be commercializing their electric motorcycle".
• Figure 3: Well-nestedness and gap degree. The top tree is well-nested and has gap degree 0 (two example projections, which are continuous and do not interleave, are shown in red and blue). The middle tree has gap degree 1 (as the projection of $a$ has a gap) but it is still well-nested. The bottom tree has gap degree 1 and is ill-nested, as the projections of $a$ and $b$ interleave.
• Figure 4: The $WG_k$ sets. The top tree is in $WG_0$, the middle tree is not in $WG_0$ but it is in $WG_1$ (a projection with gap degree 1, but which does not interleave any other projection, is highlighted), and the bottom tree is not in $WG_0$ or $WG_1$ but it is in $WG_2$ (a projection with gap degree 2, but which does not interleave any other projection, is highlighted).
• Figure 5: Multiplanarity. The 1-planar tree has no dependency crossings. In the 2-planar tree, we can split the arcs into two planes (associated here with colors) such that arcs within the same plane do not cross. The last tree is not 2-planar, so it is not possible to do this with two colors, but it is 3-planar, since it is possible with three colors, as shown. Note that the three dependency trees are linear arrangements of the tree shown above: they have the same structure, but the order of the words (represented by numbers) changes. Indeed, projectivity, planarity, and all the other properties discussed here can be seen as properties of word order. In fact, every dependency tree can be reordered into a projective tree, and some parsing strategies have exploited this nivre-2009-non.