Counting dependencies and Minimalist Grammars

Maxime Amblard 1
1 SEMAGRAMME - Semantic Analysis of Natural Language
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : Minimalist Grammars (MG) are a formalism which allows a flexible syntactic analysis of natural languages. It was introduced by Stabler in [St 97]. Its generative capacity has been studies in [Ha 01]. This article describes the existence of a MG generating the counting dependencies L m = {1 n 2 n · · · m n , n ∈ IN}, and an algorithm of construction of the lexicon Lex m producing this language. It is a generalization of the Stabler presentation with n = 5 [St 97]. This class of languages belongs to the context-sensitive languages in the hierarchy of Chomsky. In a linguistic way, we could find example of this structure in sentence like : "Peter, Mary and Charles had respectively 14, 12 and 6 in math, history and sport". 1 Stabler's MG Stabler's Minimalist Grammars are lexicalised grammars. Therefore the generated language is the transitive closure of the lexicon under the generating functions. Each lexical entry is a list of features. The features are of two different natures and take part in the release of two distinct operations. Different types of feature : The set of base features is noted BF. The following features are also defined : – select : {= d | d ∈ BF}. The set of move features is noted MF. The following features are defined : – licensors : {+k | k ∈ MF}. – licensees : {−k | k ∈ MF}. Generating functions : – Merge : unification of a base feature with the corresponding selector. The result is the concatenation of the other feautures. – Move : unification of a licensor with a licensee. It corresponds to the move of the features to the components carrying the licensees in front of the structure. We use the following notation : e stand for a feature of an arbitrary type and E for a sequence of features. A lexical entry is made of a list of features and the associated phonological form, noted between oblique bars : e1. . ./z1/. The word generated is recognized by a left-right-hand side reading of the phonological forms in the analysis. The phonological form will be called "terminal" and the other elements of the list of features "non-terminal". Traditionally, the analyses are finite, binary and ordered trees with projections -which preserve the position of the head of the component. This order is marked on the nodes of the tree by '< ' or '> ' -for the direction of the head. In this article, we will use list ordered from left to right. A component will be delimited by an under-brace and the head of this last will be marked in bold. To simplify the graphical representation, the group containing only one element and those containing only a phonological form will not be marked by a under-brace and the head will take back a normal font. The linear representation contains less information than the tree form but this information is sufficient to describe the mechanisms of our paper. Here an example of translation of an analysis in tree form to a linear representation :
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Maxime Amblard. Counting dependencies and Minimalist Grammars. Logical Aspects of Computational Linguistics, student session, Apr 2005, Bordeaux, France. 〈hal-01079268〉

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