Dependency Structures and Lexicalized Grammars: An Algebraic by Marco Kuhlmann

By Marco Kuhlmann

Since 2002, FoLLI has presented an annual prize for amazing dissertations within the fields of good judgment, Language and data. This e-book is predicated at the PhD thesis of Marco Kuhlmann, joint winner of the E.W. Beth dissertation award in 2008. Kuhlmann’s thesis lays new theoretical foundations for the examine of non-projective dependency grammars. those grammars have gotten more and more very important for methods to statistical parsing in computational linguistics that care for loose observe order and long-distance dependencies. the writer presents new formal instruments to outline and comprehend dependency grammars, provides new dependency language hierarchies with polynomial parsing algorithms, establishes the sensible importance of those hierarchies via corpus reviews, and hyperlinks his paintings to the phrase-structure grammar culture via an equivalence consequence with tree-adjoining grammars. The paintings bridges the gaps among linguistics and theoretical laptop technology, among theoretical and empirical ways in computational linguistics, and among formerly disconnected strands of formal language research.

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First, assume that d = 0. In this case, the node u is the only node in T , and we have order [u] = [u]. Therefore, lin(T ) = [u], and dep(T ) is the trivial dependency structure. The yield u , like all singleton sets, is convex with respect to lin(T ). Now, assume that d > 0. In this case, the tree T can be decomposed into the node u and the collection of subtrees rooted at the children of u. Let w = u be a node in T , and let v be the uniquely determined child of u that dominates w. By the induction hypothesis, we may assume that the yield w is convex with respect to the linearization that was computed by the recursive call Treelet-Order-Collect(v).

We write Ωm for the set of all such constructors, and put Ω := m∈N Ωm . Every term over Ω encodes a treelet-ordered tree in the way that we have just described, and every such tree can be encoded into a term. In this way, we can view the function dep as a bijection dep: TΩ → D1 in the obvious way. We put term := dep−1 . 4. 5a. 4 Dependency Algebras Using the ranked set Ω and the bijection dep: TΩ → D1 between terms over Ω and projective dependency structures, we now give the set D1 an algebraic structure: with every order annotation, we associate an operation on projective dependency structures.

We proceed by induction on the depth d of the tree structure underlying D. First, assume that d = 0. In this case, we have only one choice to assign an order annotation to u, order [u] = [u]. With this annotation, we indeed have lin(T ) = [u]. Now, assume that d > 0. In this case, the node u has an out-degree of n > 0. The set C(u) of constituents of u forms a partition of the yield u . Furthermore, every constituent is convex with respect to the order underlying D: the set {u} trivially so, and each set v because the structure D is projective.

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