Geometric representations for minimalist grammars

We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in representation space. We also propose harmony, i.e. the distance of an intermediate processing step from the final well-formed state in representation space, as a measure of processing complexity. Finally, we illustrate our findings by means of two particular arithmetic and fractal representations.Comment: 43 pages, 4 figure

A Case Study of the Convergence of Mildly Context-Sensitive Formalisms for Natural Language Syntax: from Minimalist Grammars to Multiple Context-Free Grammars

Soumis en tant que rapport de recherche INRIA Futurs - Projet SIGNESThe present work is set in the field of natural language syntactic parsing. We present the concept of "mildly context-sensitive" grammar formalisms, which are full-fetched and efficient for syntactic parsing. We summarize a number of these formalisms' definitions, together with the relations between one another, and, most importantly, a survey of known equivalences. The conversion of Edward Stabler's Minimalist Grammars into Multiple Context-Free Grammars (MCFG) is presented in particular detail, along with a study of the complexity of this procedure and of its implications for parsing. This report is an adaptation of the French Master thesis that bears the same name, from Bordeaux 1 University, June 2006

Observations on Strict Derivational Minimalism

Michaelis J. Observations on Strict Derivational Minimalism. Electronic Notes in Theoretical Computer Science. 2004;53:192-209

Observations on Strict Derivational Minimalism

Deviating from the denition originally presented in [12], Stabler [13] introduced inspired by some recent proposals in terms of a minimalist approach to transformational syntaxa (revised) type of a minimalist grammar (MG) as well as a certain type of a strict minimalist grammar (SMG). These two types can be shown to determine the same class of derivable string languages

Wide-coverage statistical parsing with minimalist grammars

Syntactic parsing is the process of automatically assigning a structure to a string of words, and is arguably a necessary prerequisite for obtaining a detailed and precise representation of sentence meaning. For many NLP tasks, it is sufficient to use parsers based on simple context free grammars. However, for tasks in which precision on certain relatively rare but semantically crucial constructions (such as unbounded wh-movements for open domain question answering) is important, more expressive grammatical frameworks still have an important role to play. One grammatical framework which has been conspicuously absent from journals and conferences on Natural Language Processing (NLP), despite continuing to dominate much of theoretical syntax, is Minimalism, the latest incarnation of the Transformational Grammar (TG) approach to linguistic theory developed very extensively by Noam Chomsky and many others since the early 1950s. Until now, all parsers using genuine transformational movement operations have had only narrow coverage by modern standards, owing to the lack of any wide-coverage TG grammars or treebanks on which to train statistical models. The received wisdom within NLP is that TG is too complex and insufficiently formalised to be applied to realistic parsing tasks. This situation is unfortunate, as it is arguably the most extensively developed syntactic theory across the greatest number of languages, many of which are otherwise under-resourced, and yet the vast majority of its insights never find their way into NLP systems. Conversely, the process of constructing large grammar fragments can have a salutary impact on the theory itself, forcing choices between competing analyses of the same construction, and exposing incompatibilities between analyses of different constructions, along with areas of over- and undergeneration which may otherwise go unnoticed. This dissertation builds on research into computational Minimalism pioneered by Ed Stabler and others since the late 1990s to present the first ever wide-coverage Minimalist Grammar (MG) parser, along with some promising initial experimental results. A wide-coverage parser must of course be equipped with a wide-coverage grammar, and this dissertation will therefore also present the first ever wide-coverage MG, which has analyses with a high level of cross-linguistic descriptive adequacy for a great many English constructions, many of which are taken or adapted from proposals in the mainstream Minimalist literature. The grammar is very deep, in the sense that it describes many long-range dependencies which even most other expressive wide-coverage grammars ignore. At the same time, it has also been engineered to be highly constrained, with continuous computational testing being applied to minimize both under- and over-generation. Natural language is highly ambiguous, both locally and globally, and even with a very strong formal grammar, there may still be a great many possible structures for a given sentence and its substrings. The standard approach to resolving such ambiguity is to equip the parser with a probability model allowing it to disregard certain unlikely search paths, thereby increasing both its efficiency and accuracy. The most successful parsing models are those extracted in a supervised fashion from labelled data in the form of a corpus of syntactic trees, known as a treebank. Constructing such a treebank from scratch for a different formalism is extremely time-consuming and expensive, however, and so the standard approach is to map the trees in an existing treebank into trees of the target formalism. Minimalist trees are considerably more complex than those of other formalisms, however, containing many more null heads and movement operations, making this conversion process far from trivial. This dissertation will describe a method which has so far been used to convert 56% of the Penn Treebank trees into MG trees. Although still under development, the resulting MGbank corpus has already been used to train a statistical A* MG parser, described here, which has an expected asymptotic time complexity of O(n3); this is much better than even the most optimistic worst case analysis for the formalism