A Treebank-based Investigation of IPP-triggering Verbs in Dutch

the sequential order of nodes in a sentence.
Projectivity : A dependency tree D = (V, E, ≼) is projective if it satisfies the following
condition: i → j, υ ∈ (i, j) =⇒ υ ∈ Subtree i . Otherwise D is non-projective.
3.2 Relaxations of Projectivity
As [12] remarks, natural languages approve grammatical constructs that violate
the condition of projectivity. In the following, we define the global and edge based
constraints that have been proposed to relax projectivity.
Planarity : A dependency tree D is non-planar if there are two edges i 1 ↔ j 1 , i 2 ↔
j 2 in D such that i 1 ∈ (i 2 , j 2 ) Λ i 2 ∈ (i 1 , j 1 ). Otherwise D is planar. Planarity is a
relaxation of projectivity and a strictly weaker constraint than it. Planarity can be
visualized as ‘crossing arcs’ in the horizontal representation of a dependency tree.
Well-nestedness : A dependency tree is ill-nested if two non-projective subtrees (disjoint)
interleave. Two disjoint subtrees l 1 , r 1 and l 2 , r 2 interleave if l 1 1. The gap degree of a node gd(x n ) is the number of such gaps in
its projection. The gap degree of a sentence is the maximum among the gap degree
of its nodes [8]. Gap degree corresponds to the maximal number of times the yield
of a node is interrupted. A node with gap degree > 0 is non-projective.
Edge Degree : For any edge in a dependency tree we define edge degree as the
number of connected components in the span of the edge which are not dominated
by the parent node of the edge. ed i↔j is the number of components in the span(i, j)
and which do not belong to π parenti↔j .
4 Empirical Results
In this section, we present an experimental evaluation of the dependency tree constraints
mentioned in the previous section on the dependency structures across
IL treebanks. Among the treebanks, Hindi treebank due to its relatively large
size provides good insights into the possible construction types that approve nonprojectivity
in ILs. Urdu and Bangla treebanks, though comparatively smaller in
size, show similar construction types approving non-projectivity. Telugu, on the
other hand, as reflected by the analysis of the Telugu treebanks, does not have any
non-projective structures. Possible types of potential non-projective constructions
and the phenomena inducing non-projectivity are listed in Table 3. In Table 2,
we report the percentage of structures that satisfy various graph properties across
IL treebanks. In the treebanks, Urdu has 23%, Hindi has 15% and Bangla has
5% non-projective structures. In Hindi and Urdu treebanks, highest gap degree
and edge degree for non-projective structures is 3 and 4 respectively which tallies
with the previous results on Hindi treebank [10]. As shown in Table 2, planarity
accounts for more data than projectivity, while almost all the structures are wellnested,
Hindi has 99.7%, Urdu has 98.3% and Bangla has 99.8% of structures
as well-nested. Despite the high coverage of well-nestedness constraint in these
languages, there are linguistic phenomena which give rise to ill-nested structures.
The almost 1% of ill-nested structures are not annotation errors but are rather linguistically
justified. Few phenomena that were observed upon close inspection
of the treebanks are extraposition and topicalization of verbal arguments across
clausal conjunctions. Extraposition, as a reason behind ill-nestedness, is also observed
by [9]. Sentence (1) shows a typical ill-nested dependency analysis of a
sentence from Hindi treebank. In this sentence, vyakti ‘person’ in complement
clause is relativized by an extraposed relative clause which contains a nominal
expression esa koi jawaab ‘any such answer’ relativized by another extraposed
relative clause.
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