Abstract. We present an extension of Buszkowski’s learning algorithm for categorial grammars to rigid Lambek grammars and then for minimalist categorial grammars. The Kanazawa proof of the convergence in the Gold sense is simplified and extended to these new algorithms. We thus show that this technique based on principal type algorithm and type unification is quite general and applies to learning issues for different type logical grammars, which are larger, linguistically more accurate and closer to semantics. 1

This ESSLLI workshop is devoted to connecting the linguistic use of resource logics and categorial grammar to minimalist grammars and related generative grammars. Minimalist grammars are relatively recent, and although they stem from a long tradition of work in transformational grammar, they are largely informal apart from a few research papers. The study of resource logics, on the other hand, is formal and stems naturally from a long logical tradition. So although there appear to be promising connections between these traditions, there is at this point a rather thin intersection between them. The papers in this workshop are consequently rather diverse, some addressing general similarities between the two traditions, and others concentrating on a thorough study of a particular point. Nevertheless they succeed in convincing us of the continuing interest of studying and developing the relationship between the minimalist program and resource logics. This introduction reviews some of the basic issues and prior literature. 1 The interest of a convergence What would be the interest of a convergence between resource logical investigations of

This paper is concerned with learning categorial grammars in the model of Gold. We show that rigid and k-valued non-associative Lambek grammars are learnable from function-argument structured sentences. In fact, function-argument structures are natural syntactical decompositions of sentences in sub-components with the indication of the head of each sub-component. This result is

This paper is concerned with learning categorial grammars in Gold's model. In contrast to k-valued classical categorial grammars, k-valued Lambek grammars are not learnable from strings. This result was shown for several variants but the question was left open for the weakest one, the non-associative variant NL.

Recently, learning algorithms in Gold's model have been proposed for some particular classes of classical categorial grammars [Kan98]. We are interested here in learning Lambek categorial grammars.

Abstract. In addition to their limpid interface with semantics, the original categorial grammars introduced by Lambek 55 years ago enjoys another important property: learnability. After a short reminder on grammatical inference à la Gold, we provide an algorithm that learns rigid Lambek grammars with product from proof frames that are name free proof nets a generalisation of functor argument structures to those grammars — that are already known to be unlearnable from strings, as shown by Foret and Le Nir. This result strictly encompasses our previous positive results on learning Lambek grammars without product The result can be extended to k-valued versions of these grammars using k-unification although, as expected, algorithmic complexity becomes qui high. Our algorithm combines a proof net version of the principal type scheme algorithm of lambda calculus together with the unification algorithm for syntactic categories, as first explored by Buszkowski and Penn. We thereafter we provide a simple proof of the convergence of this algorithm inspired from the one by Kanazawa. Proof frames may seem complex structures to learn from, but they look like dependency structure that can be found in annotated corpora, and, as we show at the end of the paper, when the product is not used, proof frames exactly correspond to natural deduction frames that extend the functor argument structures that are commonly used for learning basic categorial grammars. We are sad to dedicate the present paper to Philippe Darondeau, with whom we started to study such questions in Rennes at the beginning of the millennium, and who passed away prematurely. We are glad to dedicate the present paper to Jim Lambek for his 90 birthday: he shows that research is an endless learning. 1

This paper is concerned with learning categorial grammars in Gold's model (Gold, 1967). Recently, learning algorithms in this model have been proposed for some particular classes of classical categorial grammars (Kanazawa, 1998).

This paper is concerned with learning categorial grammars in the model of Gold. We show that rigid and k-valued non-associative Lambek (NL) grammars are not learnable from well-bracketed sentences. In contrast to