Mapping relational databases to RDF is a fundamental problem for the development of the Semantic Web. We present a solution, inspired by draft methods defined by the W3C where relational databases are directly mapped to RDF and OWL. Given a relational database schema and its integrity constraints, this direct mapping produces an OWL ontology, which, provides the basis for generating RDF instances. The semantics of this mapping is defined using Datalog. Two fundamental properties are information preservation and query preservation. We prove that our mapping satisfies both conditions, even for relational databases that contain null values. We also consider two desirable properties: monotonicity and semantics preservation. We prove that our mapping is monotone and also prove that no monotone mapping, including ours, is semantic preserving. We realize that monotonicity is an obstacle for semantic preservation and thus present a non-monotone direct mapping that is semantics preserving.