In this chapter we describe an approach to grammar induction based on categorial grammars: the EMILE algorithm. Categorial grammars are equivalent to context-free grammars. They were introduced by Ajduciewicz and formalised by Lambek. Technically they can be seen as a variant of the propositional calculus without structural rules. Various learnability results for categorial grammars are known. There exists a whole landscape of these so called substructural logics. This suggests an extension of the ILP research program in the direction of what one might call substructural ILP. We discuss the application of substructural logic to database design and present some complexity results from the literature that suggest the feasibility of this approach.