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