Learning Lambek grammars from proof frames

Abstract

In addition to their limpid interface with semantics, catego-rial grammars enjoy another important property: learnability. This was first noticed by Buszkowski and Penn and further studied by Kanazawa, for Bar-Hillel categorial grammars. What about Lambek categorial grammars? In a previous paper we showed that product free Lambek grammars are learnable from structured sentences, the structures being incomplete natural deductions. Although these grammars were shown to be unlearnable from strings by Foret ad Le Nir, in the present paper, we show that Lambek grammars, possibly with product, are learnable from proof frames i.e. incomplete proof nets. After a short reminder on grammatical inference à la Gold, we provide an algorithm that learns Lambek grammars with product from proof frames and we prove its convergence. We do so for 1-valued "(also known as rigid) Lambek grammars with product, since standard techniques can extend our result to k-valued grammars. Because of the correspondence between cut-free proof nets and normal natural deductions, our initial result on product free Lambek grammars can be recovered. © Springer-Verlag Berlin Heidelberg 2014.