Learnability of Pregroup Grammars

International audienceThis paper investigates the learnability by positive examples in the sense of Gold of Pregroup Grammars. In a first part, Pregroup Grammars are presented and a new parsing strategy is proposed. Then, theoretical learnability and non-learnability results for subclasses of Pregroup Grammars are proved. In the last two parts, we focus on learning Pregroup Grammars from a special kind of input called feature-tagged examples. A learning algorithm based on the parsing strategy presented in the first part is given. Its validity is proved and its properties are examplified

Complexity of Grammar Induction for Quantum Types

Most categorical models of meaning use a functor from the syntactic category to the semantic category. When semantic information is available, the problem of grammar induction can therefore be defined as finding preimages of the semantic types under this forgetful functor, lifting the information flow from the semantic level to a valid reduction at the syntactic level. We study the complexity of grammar induction, and show that for a variety of type systems, including pivotal and compact closed categories, the grammar induction problem is NP-complete. Our approach could be extended to linguistic type systems such as autonomous or bi-closed categories.Comment: In Proceedings QPL 2014, arXiv:1412.810

Efficiency in ambiguity: two models of probabilistic semantics for natural language

This paper explores theoretical issues in constructing an adequate probabilistic semantics for natural language. Two approaches are contrasted. The first extends Montague Semantics with a probability distribution over models. It has nice theoretical properties, but does not account for the ubiquitous nature of ambiguity; moreover inference is NP hard. An alternative approach is described in which a sequence of pairs of sentences and truth values is generated randomly. By sacrificing some of the nice theoretical properties of the first approach it is possible to model ambiguity naturally; moreover inference now has polynomial time complexity. Both approaches provide a compositional semantics and account for the gradience of semantic judgements of belief and inference

Learning categorial grammars

In 1967 E. M. Gold published a paper in which the language classes from the Chomsky-hierarchy were analyzed in terms of learnability, in the technical sense of identification in the limit. His results were mostly negative, and perhaps because of this his work had little impact on linguistics. In the early eighties there was renewed interest in the paradigm, mainly because of work by Angluin and Wright. Around the same time, Arikawa and his co-workers refined the paradigm by applying it to so-called Elementary Formal Systems. By making use of this approach Takeshi Shinohara was able to come up with an impressive result; any class of context-sensitive grammars with a bound on its number of rules is learnable. Some linguistically motivated work on learnability also appeared from this point on, most notably Wexler & Culicover 1980 and Kanazawa 1994. The latter investigates the learnability of various classes of categorial grammar, inspired by work by Buszkowski and Penn, and raises some interesting questions. We follow up on this work by exploring complexity issues relevant to learning these classes, answering an open question from Kanazawa 1994, and applying the same kind of approach to obtain (non)learnable classes of Combinatory Categorial Grammars, Tree Adjoining Grammars, Minimalist grammars, Generalized Quantifiers, and some variants of Lambek Grammars. We also discuss work on learning tree languages and its application to learning Dependency Grammars. Our main conclusions are: - formal learning theory is relevant to linguistics, - identification in the limit is feasible for non-trivial classes, - the `Shinohara approach' -i.e., placing a numerical bound on the complexity of a grammar- can lead to a learnable class, but this completely depends on the specific nature of the formalism and the notion of complexity. We give examples of natural classes of commonly used linguistic formalisms that resist this kind of approach, - learning is hard work. Our results indicate that learning even `simple' classes of languages requires a lot of computational effort, - dealing with structure (derivation-, dependency-) languages instead of string languages offers a useful and promising approach to learnabilty in a linguistic contex

Mathematical linguistics

but in fact this is still an early draft, version 0.56, August 1 2001. Please d