Contents 1 Introduction: grammatical reasoning 1 2 Linguistic inference: the Lambek systems 5 2.1 Modelinggrammaticalcomposition ............................ 5 2.2 Gentzen calculus, cut elimination and decidability . . . . . . . . . . . . . . . . . . . . 9 2.3 Discussion: options for resource management . . . . . . . . . . . . . . . . . . . . . . 13 3 The syntax-semantics interface: proofs and readings 16 3.1 Term assignment for categorial deductions . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Natural language interpretation: the deductive view . . . . . . . . . . . . . . . . . . . 21 4 Grammatical composition: multimodal systems 26 4.1 Mixedinference:themodesofcomposition........................ 26 4.2 Grammaticalcomposition:unaryoperations ....................... 30 4.2.1 Unary connectives: logic and structure . . . . . . . . . . . . . . . . . . . . . . . 31 4.2.2 Applications: imposing constraints, structural relaxation

this paper I present the EMILE 3.0 algorithm

The purpose of this work is to investigate the process of grammatical acquisition from data. In order to do that, a computational learning system is used, composed of a Universal Grammar with associated parameters, and a learning algorithm, following the Principles and Parameters Theory. The Universal Grammar is implemented as a Unification-Based Generalised Categorial Grammar, embedded in a default inheritance network of lexical types. The learning algorithm receives input from a corpus of spontaneous child-directed transcribed speech annotated with logical forms and sets the parameters based on this input. This framework is used as a basis to investigate several aspects of language acquisition. In this thesis I concentrate on the acquisition of subcategorisation frames and word order information, from data. The data to which the learner is exposed can be noisy and ambiguous, and I investigate how these factors a#ect the learning process. The results obtained show a robust learner converging towards the target grammar given the input data available. They also show how the amount of noise present in the input data a#ects the speed of convergence of the learner towards the target grammar. Future work is suggested for investigating the developmental stages of language acquisition as predicted by the learning model, with a thorough comparison with the developmental stages of a child. This is primarily a cognitive computational model of language learning that can be used to investigate and gain a better understanding of human language acquisition, and can potentially be relevant to the development of more adaptive NLP technology.

We extend Angluin's (1980) theorem to characterize identifiability of indexed families of r.e. languages, as opposed to indexed families of recursive languages. We also prove some variants characterizing conservativity and two other similar restrictions, paralleling Zeugmann, Lange, and Kapur's (1992, 1995) results for indexed families of recursive languages. 1 Introduction A significant portion of the work of recent years in the field of inductive inference of formal languages, as initiated by Gold 1967, stems from Angluin's (1980b) theorem, which characterizes when an indexed family of recursive languages is identifiable in the limit from positive data in the sense of Gold. Up until around 1980, a prevalent view had been that inductive inference from positive data is too weak to be of much theoretical interest. This misconception was due to the negative result in Gold's original paper, which says that any class of languages that contains every finite language and at least one infini...

In this paper we report on an unsupervised ap- proach to learning Categorial Grammar (CG) lexicons. The learner is provided with a set of possible lexical CG categories, the forward and backward application rules of CG and unmarked positive only corpora. Using the categories and rules, the sentences from the corpus are probabilistically parsed. The parses and the history of previously parsed sentences are used to build a lexicon and annotate the corpus. We report the results from experiments on a number of small generated corpora, that contain examples from subsets of the English language. These show that the system is able to generate reasonable lexicons and provide accurately parsed corpora in the process. We also discuss ways in which the approach can be scaled up to deal with larger and more diverse corpora.

The logical problem of language is grounded on arguments from poverty of positive evidence and arguments from poverty of negative evidence. Careful analysis of child language corpora shows that, if one assumes that children learn through item-based constructions, there is an abundance of positive evidence. Arguments regarding the poverty of negative evidence can also be addressed by the mechanism of conservative item-based learning. When conservativism is abandoned, children can rely on competition, cue construction,

In (Buszkowski, 1987) and (Buszkowski and Penn, 1990) certain `discovery procedures' for classical categorial grammars were de ned. These procedures accept a sequence of structures (strings labeled with derivational information) as input and yield a set of hypotheses in the form of grammars. In (Kanazawa, 1998) learning functions based on these discovery procedures were studied, and it was shown that some of the classes associated with these procedures can be eectively identi- ed in the limit from positive data. The time complexity of these functions however was still left an open question. In this paper I will show that learning functions for these classes that are responsive and consistent on their class and learn their class prudently are all NP-hard. 1 Identi cation in the Limit In the seminal paper (Gold, 1967) the concept of identi cation in the limit was introduced. In this model of learning a learning function receives an endless stream of sentences from the target langua...

In categorial systems with a fixed structural component, the learning problem comes down to finding the solution for a set of typeassignment equations. A hard-wired structural component is problematic if one want to address issues of structural variation. Our starting point is a type-logical architecture with separate modules for the logical and the structural components of the computational system. The logical component expresses invariants of grammatical composition; the structural component captures variation in the realization of the correspondence between form and meaning. Learning in this setting involves finding the solution to both the type-assignment equations and the structural equations of the language at hand. We develop a view on these two subtasks which pictures learning as a process moving through a two-stage cycle.

Abstract. This paper investigates the learnability of Pregroup Grammars, a context-free grammar formalism recently defined in the field of computational linguistics. In a first theoretical approach, we provide learnability and non-learnability results in the sense of Gold for subclasses of Pregroup Grammars. In a second more practical approach, we propose an acquisition algorithm from a special kind of input called Feature-tagged Examples, that is based on sets of constraints. Key-words. Learning from positive examples, Pregroup grammars, Computational linguistics, Categorial Grammars, Context-Free grammars.

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