This paper will appear, in a slightly shortened form, as an in-depth article Article definition Categorial grammar: a lexicalized grammar formalism based on logical typetheory. A categorial lexicon assigns one or more types to the atomic elements of a language; the assembly of form and meaning is accounted for in terms of the rules of inference for these types seen as formulas of a grammar logic. Cross-linguistic variation results from extending the invariant core of the grammar logic with facilities for structural reasoning.