A promising method for efficiently querying RDF data consists of translating SPARQL queries into efficient RDBMS-style operations. However, answering SPARQL queries requires handling RDF reasoning, which must be implemented outside the relational engines that do not support it. We introduce the database (DB) fragment of RDF, going beyond the expressive power of previously studied RDF fragments. We devise novel sound and complete techniques for answering Basic Graph Pattern (BGP) queries within the DB fragment of RDF, exploring the two established approaches for handling RDF semantics, namely reformulation and saturation. In particular, we focus on handling database updates within each approach and propose a method for incrementally maintaining the saturation; updates raise specific difficulties due to the rich RDF semantics. Our techniques are designed to be deployed on top of any RDBMS(-style) engine, and we experimentally study their performance trade-offs.