The basic categorial structure of classical predicate logic is given by the distinction of predicates (of a fixed arity or type) and individuals. The author first discusses much more general systems of categorial structures which analogously can be basic for logical systems with a metatheory quite similar to the ``usual'' one. Among them he gives special attention to categorial structures involving predicates of variable arity. This generalization is not aimed as l'art pour l'art: the paper presents a relatively simple and quite interesting approach toward a logical theory of physical quantities which, unquestionably, deserves a deeper investigation.