The Resource Description Framework (RDF) represents information as subject - predicate - object triples. These triples are commonly interpreted as a directed labelled graph. The authors propose an alternative approach, interpreting the data as a 3-way Boolean tensor. They show how SPARQL queries - the standard queries for RDF - can be expressed as elementary operations in Boolean algebra, giving them a complete reinterpretation of RDF and SPARQL. They show how the Boolean tensor interpretation allows for new optimizations and analyses of the complexity of SPARQL queries.