Publish-subscribe (pub-sub) systems are useful for many applications, including pervasive environments. In the latter context, however, great care must be taken to preserve the privacy of sensitive information, such as users' location and activities. Traditional access control schemes provide at best a partial solution, since they do not capture potential inference regarding sensitive data that a subscriber may make. We propose a logic-based pub-sub system, where inference rules are used to both derive high-level events for use in applications as well as specify potentially harmful inferences that could be made regarding data. We provide a formal definition of safety in such a system that captures the possibility of indirect information flows. We show that the safety problem is co-NP-complete; however, problems of realistic size can be reduced to a satisfiability problem that can be efficiently decided by a SAT solver.