Dependency Structures and Lexicalized Grammars: An Algebraic by Marco Kuhlmann

By Marco Kuhlmann

Since 2002, FoLLI has presented an annual prize for extraordinary dissertations within the fields of good judgment, Language and knowledge. This booklet relies 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 techniques to statistical parsing in computational linguistics that take care of unfastened 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 value of those hierarchies via corpus stories, and hyperlinks his paintings to the phrase-structure grammar culture via an equivalence end result with tree-adjoining grammars. The paintings bridges the gaps among linguistics and theoretical machine technology, among theoretical and empirical methods in computational linguistics, and among formerly disconnected strands of formal language research.

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

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The cardinality of the quotient of a set S modulo the coarsest congruence relation on S provides us with a way to measure the ‘non-convexity’ of S: the more convex sets we need to cover all the elements of S, the less convex it is. 2. Let C = (A ; ) be a chain, and let S ⊆ A be a set. A block of S with respect to C is an element of the quotient S/≡S . 1 The Block-Degree Measure 35 of S with respect to C is the cardinality of the set S/≡S , that is, the number of different blocks of S. 3 (continued).

The block-degree of D is the maximum among the block-degrees of its nodes. 5. 2 shows two examples of non-projective dependency structures. For both structures, consider the yield of the node 2. In structure D1 , the yield 2 falls into two blocks, {2, 3} and {6}. Since this is also the maximal number of blocks per yield, the block-degree of D1 is 2. In structure D2 , the yield 2 consists of three blocks, {1}, {3}, and {6}; the block-degree of D2 is 3. ✷ Let us say that a dependency structure is block k, if its block-degree is at most k.

The yield of a consists of a single block, which contains all the nodes of the structure, positions 1 to 5 in the precedence order. This information is represented in the span tree in that the root node of this tree is labelled with the triple (a, 1, 5). 3 Algorithmic Problems 45 (a, 1, 5) (a, 1, 1)(b, 2, 3) (d, 4, 4)(b, 5, 5) (b, 2, 2)(e, 3, 3)(d, 4, 4)(e, 5, 5) 1 2 3 4 5 a b c d e (c, 3, 3) (e, 5, 5) (c, 3, 3) Fig. 7. A non-projective structure and the corresponding span tree in their order of precedence, these are: the singleton {a}, the first block of the node b, the block of the node d, and the second block of b.

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