Learning discrete categorial grammars from structures

We define the class of discrete classical categorial grammars, similar in the spirit to the notion of reversible class of languages introduced by Angluin and Sakakibara. We show that the class of discrete classical categorial grammars is identifiable from positive structured examples. For this, we provide an original algorithm, which runs in quadratic time in the size of the examples. This work extends the previous results of Kanazawa. Indeed, in our work, several types can be associated to a word and the class is still identifiable in polynomial time. We illustrate the relevance of the class of discrete classical categorial grammars with linguistic examples. 1991 Mathematics Subject Classification. 68Q32,68T50,03B47. In 1988, I was a student in ”Mâıtrise de Mathématques Discrêtes” at Lyon University, and Serge Grigorieff was one of my professors. I was fascinating by the course on computability that he gave. I followed him when he moved to the university Paris 7 and I made a master thesis on Kolmogorov complexity. Then I made a PhD thesis under his supervision. I got a lot out of our discussions and our works in his small office in Jussieu, and in particular the ability to ask questions and to study relationships between information, complexity and computability. We wrote together a paper on Kolmogorov complexity several years later, and I studied computational linguistic and grammatical inference, with the same spirit. This paper with Jérôme, which is my first PhD student, follows this line and is dedicated to him. I owe a lot to him and not only from a scientific point of view . . .