Data translation consists of the task of moving data from a source database to a target database. This task is usually performed by developing mappings, i.e. executable transformations from the source to the target schema. However, a richer description of the target database semantics may be available in the form of an ontology. This is typically defined as a set of views over the base tables that provides a unified conceptual view of the underlying data. We investigate how the mapping process changes when such a rich conceptualization of the target database is available. We develop a translation algorithm that automatically rewrites a mapping from the source schema to the target ontology into an equivalent mapping from the source to the target databases. Then, we show how to handle this problem when an ontology is available also for the source. Differently from previous approaches, the language we use in view definitions has the full power of non-recursive Datalog with negation. In the paper, we study the implications of adopting such an expressive language. Experiments are conducted to illustrate the trade-off between expressibility of the view language and efficiency of the chase engine used to perform the data exchange.