Every database model needs an underlying logical framework in order to support the handling of integrity constraints, database querying, etc. In this paper, it has been discussed how a many-valued logic based on possibility theory, can serve for these purposes and moreover can be advantageously in those cases where one explicitly wants to deal with missing information and/or with imperfect information. The potentials of the logic for both database modelling and database querying have been discussed. Finally, the presented approach has been compared with other existing approaches from both the traditional and the fuzzy database communities.