We present a relational learning framework for grammar induction that is able to learn meaning as well as syntax. We introduce a type of constraint-based grammar, lexicalized well-founded grammar (lwfg), and we prove that it can always be learned from a small set of semantically annotated examples, given a set of assumptions. The semantic representation chosen allows us to learn the constraints together with the grammar rules, as well as an ontology-based semantic interpretation. We performed a set of experiments showing that several fragments of natural language can be covered by a lwfg,and that it is possible to choose the representative examples heuristically, based on linguistic knowledge.