We study privacy guarantees for the owner of an information system who wants to share some of the information in the system with clients while keeping some other information secret. The privacy guarantees ensure that publishing the new information will not compromise the secret one. We present a framework for describing privacy guarantees that generalises existing probabilistic frameworks in relational databases. We also formulate different flavors of privacy-preserving query answering as novel, purely logic-based reasoning problems and establish general connections between these reasoning problems and the probabilistic privacy guarantees.