After two decades of experience with relational databases and almost one decade with deductive databases a substantial amount of knowledge for efficient query processing methods and query optimizer technology is broadly available. So far, however, these research and development efforts have not paid too much attention to optimizations based on semantic or heuristic information as it is often demanded in AI. This paper coins the notion of database reasoning as an approach to open deductive databases for more user-supphed semantic knowledge, both on the object level and meta-control level. We describe how applicationspecific semantic knowledge in the form of subsumption information can be combined with logic programming and fixpoint semantics, proposing the Datalog-S language extension. We experiment also with declarative recta-programming, specifying intelligent search procedures known from AI and executing them in a deductive database system. Thus database reasoning has the potential to amalgamate the power of deductive databases and of heuristic search, hence it can be apphed for solving large and complex problems in a database environment.