Urn models were developed by Veikko Rantala to provide a non-standard semantics for first-order logic in which the domains, over which the quantifiers range, are allowed to vary. Rantala uses game-theoretical semantics in his presentation, and the present paper is a study of urn models from a more classical, truth-conditional point of view. An axiomatic system for urn logic is set out and completeness is proved by the method of maximal consistent sets.