Download Dependency Structures and Lexicalized Grammars: An Algebraic by Marco Kuhlmann PDF

By Marco Kuhlmann

Since 2002, FoLLI has presented an annual prize for amazing dissertations within the fields of good judgment, Language and data. This publication 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 research of non-projective dependency grammars. those grammars have gotten more and more very important for ways to statistical parsing in computational linguistics that care for unfastened be aware order and long-distance dependencies. the writer offers new formal instruments to outline and comprehend dependency grammars, offers new dependency language hierarchies with polynomial parsing algorithms, establishes the sensible value of those hierarchies via corpus stories, 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 desktop technology, among theoretical and empirical ways in computational linguistics, and among formerly disconnected strands of formal language research.

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Dependency Structures and Lexicalized Grammars: An Algebraic Approach

Considering that 2002, FoLLI has offered an annual prize for amazing dissertations within the fields of good judgment, Language and data. This booklet 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 learn of non-projective dependency grammars.

Extra resources for Dependency Structures and Lexicalized Grammars: An Algebraic Approach

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It is usually attributed to Sergey Fitialov [72]. 3) This condition is equivalent to the preceding two [72, chapter 6, Theorem 11]. 1. A dependency structure D is called projective, if every yield in D is convex with respect to precedence. ✷ This is the formulation that we adopt as our formal definition of projectivity. We write D1 to refer to the class of all projective dependency structures. 3 (continued). 1d, the yield of the node 1 (the set {1, 3}) does not form a convex set: the node 2 is missing from it.

1 (a) D0 1 (b) D9 = f 2 01 (D0 ) 1 2 (c) f 102 3 4 (D9 , D0 ) 1 (d) f 2 102 3 4 (D0 , D9 ) Fig. 7. Examples for composition operations We now have everything we need to define our algebraic setting. In the following definition, we use the function dep lifted to sets in the obvious way. 4. Let Σ ⊆ Ω be a finite set of order annotations. The dependency algebra over Σ is the Σ-algebra that has dep(TΣ ) as its carrier set, and interprets each symbol ω ∈ Σ by the composition operation corresponding to ω.

The vector v orders the children of u; this order will become the left-to-right order on the children of u in our term representation. The string ı provides an ‘abstract’ order annotation that makes use of node names rather than concrete nodes: the name 0 denotes the root node of the treelet rooted at u, a name i ∈ [m] denotes the ith node in the sequence v. The term t(T ) corresponding to T is then defined recursively as t(T ) := ı (t(T /v1 ), . . , t(T /vm )) . In this definition, the string ı is understood as a term constructor of rank m.

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