On Categorial Grammatical Inference and Logical Information Systems

We consider several classes of categorial grammars and discuss their learnability. We review results where learning is viewed as a symbolic issue in an unsupervised setting, from raw or from structured data, for some variants of Lambek grammars and of categorial dependency grammars. In that perspective, we discuss for these frameworks different type connectives and structures, some limitations (negative results) but also some algorithms (positive results) under some hypothesis. On the experimental side, we also consider the Logical Information Systems approach, that allows for navigation, querying, updating, and analysis of heterogeneous data collections where data are given (logical) descriptors. Categorial grammars can be seen as a particular case of Logical Information System.