Rigid Lambek grammars are not learnable from strings

摘要

This paper is concerned with learning catego-rial 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). We show that in contrast to classical categorial grammars, rigid and k-valued Lambek grammars are not learnable from strings. This result holds for variants of Lambek calculus ; our proof consists in the construction of limit points in each class. Such a result aims at clarifying the possible directions for future learning algorithms.