Abstract. Semantic query optimization (SQO) has been proved to be quite useful in various applications (e.g., data integration, graphical query generators, caching, etc.) and has been extensively studied for relational, deductive, object, and XML databases. However, less attention to SQO has been devoted in the context of the Semantic Web. In this paper, we present sound and complete algorithms for the containment and minimization of RDF/S query patterns. More precisely, we consider two widely used RDF/S query fragments supporting pattern matching at the data, but also, at the schema level. To this end, we advocate a logic framework for capturing the RDF/S data model and semantics and we employ well-established techniques proposed in the relational context, in particular, the Chase and Backchase algorithms.